SMITHSONIAN  MATHEMATICAL  TABLES 

• 


HYPERBOLIC  FUNCTIONS 


PREPARED  BY 


GEORGE  F.  BECKER  AND  C.  E.  VAN  ORSTRAND 


CITY  OF  WASHINGTON 
PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION 

1909 


ASTRONOMY/ 
LIBRARY 


ADVERTISEMENT. 


Among  the  early  publications  of  the  Smithsonian  Institution  was  a  very 
important  volume  of  meteorological  tables  by  Dr.  Arnold  Guyot.  They  were 
so  widely  used  by  geographers  and  physicists  as  well  as  by  meteorologists 
that  when  the  fourth  edition  was  exhausted  it  was  decided  to  recast  the 
entire  work  and  publish  three  separate  volumes,  Meteorological  Tables, 
Geographical  Tables,  and  Physical  Tables,  each  of  which  has  now  passed 
through  several  editions. 

In  the  application  of  the  data  of  these  volumes  to  the  study  of  natural 
phenomena  certain  mathematical  tables  beside  those  included  in  ordinary 
tables  of  logarithms  are  urgently  needed  in  order  to  save  recurrent  computa- 
tion on  the  part  of  observers  and  investigators.  It  was  therefore  decided 
to  publish  the  present  volume  of  Mathematical  Tables,  on  Hyperbolic  Func- 
tions. 

Hyperbolic  Functions  are  extremely  useful  in  every  branch  of  pure  physics 
and  in  the  applications  of  physics  whether  to  observational  and  experimental 
sciences  or  to  technology.  Thus  whenever  an  entity  (such  as  light,  velocity, 
electricity,  or  radioactivity)  is  subject  to  gradual  extinction  or  absorption, 
the  decay  is  represented  by  some  form  of  Hyperbolic  Functions.  Mercator's 
projection  is  likewise  computed  by  Hyperbolic  Functions.  Whenever  me- 
chanical strains  are  regarded  as  great  enough  to  be  measured  they  are  most 
simply  expressed  in  terms  of  Hyperbolic  Functions.  Hence  geological  de- 
formations invariably  lead  to  such  expression,  and  it  is  for  that  reason  that 
Messrs.  Becker  and  Van  Orstrand,  who  are  in  charge  of  the  physical  work 
of  the  United  States  Geological  Survey,  have  been  led  to  prepare  this  volume. 

CHARLES  D/WALCOTT,  Secretary. 
WASHINGTON,  D.  C.,  April,  1909. 


In  this  first  reprint  of  the  Hyperbolic  Functions  a  few  misprints  of  trifling  import- 
ance have  been  corrected  and  four  values  of  the  exponential  have  been  changed  by  a 
unit  in  the  eighth  significant  place. 

April,  1911.  C.  D.  W. 


iii 

340201 


CONTENTS. 


INTRODUCTION  :  PAoB 

Definitions  and  formulas vii 

Geometrical  illustrations xxviii 

Methods  of  interpolation xxxiv 

Description  of  tables , xliii 

Historical  note xlviii 

TABLE  I : 

Five  place  values  of  log  sinh  u,  log  cosh  u,  log  tanh  u,  and  log 

coth  u i 

TABLE  II : 

Five  place  values  of  sinh  u,  cosh  u,  tanh  u,  and  coth  u     .     .     .         87 

TABLE  III : 

Five  place  values  of  sin  u,  cos  u,  log  sin  u,  and  log  cos  u,  u  being 

expressed  in  radians  and  their  angular  equivalents     .     .'    .     .       173 

TABLE  IV : 

The  ascending  and  descending  exponential  to  seven  significant 

figures  with  Iog10  eu  to  seven  places 225 

Nine  place  values  of  the  same  with  ten  place  logarithms  from 

u=  i  to  u  —  100 259 

Auxiliary  table  of  multiples  of  log]0  e  for  interpolation  of  Iog10  eu.       261 

TABLE  V : 

Five  place  values  of  natural  logarithms 263 

Interpolation  coefficients  for  derivative  formula 273 

TABLE  VI : 

The  gudermannian  of  u  to  seven  places  in  radians  and  to  the  same 

order  of  accuracy  in  degrees,  minutes,  and  seconds  ....       275 

TABLE  VII : 

The  anti-gudermannian  to  hundredths  of  a  minute  in  terms  of 
the  gudermannian  expressed  in  degrees  and  minutes  from  o°  o' 
to  89°  59'.  (This  table  is  otherwise  known  as  a  table  of  me- 
ridional parts  for  a  spherical  globe) 309 

TABLE  VIII : 

Table  for  conversion  of  radians  into  angular  measure  and  vice 

versa 320 

Numerical  constants 321 


DEFINITIONS  AND  FORMULAS. 


The  hyperbolic  functions  are  named  the  hyperbolic  sine,  cosine,  tangent, 
cotangent,  secant,  and  cosecant  from  their  close  analogy  to  the  circular  func- 
tions, the  tangent  being  the  ratio  of  the  hyperbolic  sine  to  the  cosine  and 
the  other  three  functions  being  reciprocals  of  these,  as  in  circular  trigonom- 
etry. They  are  usually  denoted  by  adding  h  to  the  symbols  of  the  circular 
functions,  as  cosh  u  for  the  hyperbolic  cosine  of  u,  sinh  u  for  the  hyperbolic 
sine  of  u,  etc.1 

Historically  speaking,  the  hyperbolic  functions  were  evolved  from  studies 
of  the  hyperbola.  They  might  have  been  developed  from  the  geometry  of 
the  ellipse  or  the  catenary  or  that  of  other  curves.  These  functions,  how- 
ever, may  be  considered  independently  of  any  geometrical  interpretation  and 
can  be  derived  from  very  fundamental  functional  theorems. 

At  least  two  methods  have  been  devised  of  defining  circular  and  hyper- 
bolic functions  analytically.  One  of  these  is  due  to  Mr.  Yvon  Villarceau,2 
and  is  so  extremely  brief  that  it  can  be  given  here  in  a  somewhat  modified 
form. 

It  has  long  been  known  that 

\-         ;    "> 
g'zmiir  -  —  j  .  gu  -f  zmitr  __  gu  .  p(u  +  2tnir)t  .  _  .  aiu 

The  second  of  these  equations  has  a  single  imaginary  period,  2  zV,  and  the 
third  a  single  real  period,  2  TT.  Hence  every  exponential  eu  in  which  u  is  real 
has  a  single  imaginary  period,  2  zV,  and  every  exponential  with  the  same  base, 
but  with  an  imaginary  exponent,  has  a  real  period,  2  v.  Now,  all  real  purely 
circular  functions  may  be  expressed  in  terms  of  constants  and  exponentials 
with  purely  imaginary  exponents,  and  all  real  hyperbolic  functions  may 
be  expressed  in  terms  of  constants  and  exponentials  with  exclusively  real 
exponents. 

Hence  hyperbolic  functions  may  be  defined  as  the  singly  periodic  expo- 
nential functions  with  real  exponents.  The  circular  functions  are  then  the 
singly  periodic  exponential  functions  with  imaginary  exponents. 

It  remains  to  be  considered  how,  from  this  point  of  view,  the  hyperbolic 
functions  of  complex  variables  are  to  be  regarded.  The  question  almost 
answers  itself  ;  for 


1  More  compendious  and  convenient,  but  less  usual,  is  the  notation  employed  by  B.  de 
Saint-Venant,  sib.  u,  cob  «,  tab  u. 
"Coinptes  Rendus,  Paris,  vol.  83,  1876,  p.  594. 

vii 


Vlll  DEFINITIONS   AND    FORMULAS. 

which  is  evidently  the  product  of  two  functions  —  one  circular,  the  other 
hyperbolic.  Such  functions  have  a  real  period  and  an  imaginary  one,  but 
since  they  are  single-valued  they  are  not  elliptic  functions. 

The  circular  and  hyperbolic  functions  being  defined  as  above,  it  is  merely 
as  a  matter  of  convenience  that  a  few  of  the  simpler  combinations  of  expo- 
nentials receive  special  names,  as  sine,  cosine,  etc. 

The  other  analytical  method  of  generalizing  the  two  classes  of  functions 
is  due  to  Edward  Lucas,1  and  is  too  long  to  be  given  here  in  full,  but  the 
method  may  be  indicated.  If  a  and  b  are  the  two  roots  of  the  equation 


where  P  and  Q  are  positive  or  negative  whole  numbers,  then  two  functions 
may  be  defined  as  follows: 


Un  =  —      -";  Vn  =  a 
a  —  o 


and  these  functions  are  related  by  the  equation 


Lucas  develops  and  studies  these  functions,  limiting  n  at  first  to  whole  posi- 
tive numbers.  He  finds  that  all  the  theorems  resulting  from  this  study  are 
converted  into  those  of  ordinary  trigonometry  when  U  is  replaced  by  2  sin  n 
and  Fby  2  cos  n.  He  infers  that  between  the  limits  i  and  minus  i,  n  may 
be  replaced  by  any  real  value,  and  shows  that  the  theorems  dealing  with  U 
and  V  when  translated  into  trigonometric  formulas  on  this  assumption  can 
be  verified.  By  substituting  for  n  an  imaginary  argument,  the  hyperbolic 
functions  also  are  found  to  be  comprehended  in  the  general  functions  U 
and  V. 

Both  the  circular  and  hyperbolic  functions  may  further  be  regarded  as 
integrals  of  the  equation 

d    ,       dly         a 


If  c  =  a\  this  gives 

4J 

-  Be—, 


where  A  and  B  are  arbitrary  constants ;  so  that  the  integral  expression  in 
cludes  sinh  x,  cosh  a:,  and  the  sum  or  difference  of  these  functions. 
If  c^-b\ 

y 

~b  —  Al  cos  x  -f  /?,  sin  x. 
1  Am.  Jour,  of  Math.,  vol.  i,  1878,  p.  184. 


DEFINITIONS   AND    FORMULAS.  XI 

and  PC,  may  be  drawn  from  a  point  P  to  a  line  AB ;  the  sum  of  the  angles 
of  a  triangle  is  less  than  two  right  angles,  and  the  angle  of  parallelism  //  (/) 
is  dependent  upon  the  perpendicular  distance  p  of  the  point  P  from  the  line 
AB.  If  now  any  line  passing  through  A,  such  as  AE,  is  extended  until  the 
perpendicular  erected  at  its  middle  point  is  parallel  to  AB,  the  locus  of  the 
points  E  is  a  boundary  curve,  and  the  revolution  of  this  curve  about  AB  or 
one  of  its  parallels  develops  a  boundary  surface.  It  is  upon  this  surface  of 
constant  negative  curvature  that  L,obachevsky  imagines  a  triangle  of  sides 
a,b,c  and  angles  A,  B,  C  to  be  drawn.  He  establishes  as  fundamental  rela- 
tions between  the  sides  and  angles  of  this  triangle l 

sin  A  tan  77  (a)  =  sin  B  tan  77  (£)  =  sin  C  tan  77  (c) , 

sin  77  (£)  sin  77  (c)  =  sin  77  (a)  —  cos  77  (£)  cos  77  («r)  sin  77  (a}  cos  A, 

sin  77  («)  cos  A  —  —  cos  B  cos  C  sin  77  («  )  -f-  sin  B  sin  C, 

and  also  proves  that 

sin  77  (#)  =  (cos  in)  ~l  =  (cosh  u}  ~\ 
tan  77  (w)  =  i  (sin  z&)  -1  =  (sinh  #)  -1, 
cos  77  («)  =  —  /  tan  iu  =  tanh  #. 

Hence  the  preceding  equations  may  be  written 

sin  A         sin  B         sin  C 

sinh  «        sinh  b     ~  sinh  £ ' 

cosh  a  =  cosh  £  cosh  ^  —  sinh  £  sinh  c  cos  ^4 , 

cos  A  =  —  cos  B  cos  C  +  sin  B  sin  C  cosh  a. 

These  formulas  are,  in  fact,  precisely  those  of  spherical  trigonometry,  in 
which  the  real  sides  a,  b,  c  have  been  replaced  by  the  imaginaries  ia,  ib,  ic. 
If  the  triangle  on  the  boundary  surface  is  infinitesimal,  the  above  equations 
reduce  to  the  well-known  relations  between  the  sides  and  angles  of  a  triangle 
on  the  Euclidean  plane.  The  theorems  of  non- Euclidean  geometry  may  not 
therefore  be  inconsistent  with  experience,  for  .the  largest  triangle  which  we 
can  measure  is  infinitesimal  in  comparison  with  a  triangle  on  the  boundary 
surface.  L,obachevsky  pointed  out  that  a  triangle  on  a  boundary  surface 
would  correspond  to  a  triangle  connecting  three  stars  in  distant  parts  of  the 
universe,  and  that  the  postulates  of  his  geometry,  involving  as  they  do  the 
question  of  the  curvature  of  space,  would  be  capable  of  experimental  proof 
if  the  parallaxes  of  distant  stars  could  be  measured  with  sufficient  accuracy. 
Lastly,  there  is  an  important  relation  between  the  numerical  values  of  the 
circular  and  hyperbolic  functions.  If  the  argument  u  assumes  successive 
values  between  o  and  +  co  ,  sinh  u  assumes  successive  values  between  o  and 
+  co  just  as  tan  a  does  when  a  varies  from  o  to  90°;  cosh  u  assumes  values 
between  i  and  +  co  like  sec  /?,  and  tanh  u  assumes  values  between  o  and  i 

XH.  P.  Manning's  Non-Euclidean  Geometry,  p.  60. 


Xll 


DEFINITIONS   AND    FORMULAS. 


in  the  same  way  as  sin  y.     The  variation  of  the  hyperbolic  functions  through- 
out the  entire  plane  and  their  similarity  to  the  circular  functions  between  the 

limits  o°  and  180°  is  shown 
in  the  diagram.  Since  each 
of  the  functions  is  singly 
periodic,  there  must  be  a 
single  value  of  a,  (3,  y  cor- 
responding to  a  particular 
value  of  u,  such  that 

sinh  u  =  tan  a, 
cosh  u  =  sec  /?, 
tanh  u  =  sin  y. 

It  will  be  found  by  sub- 
stituting in  the  trigonomet- 
ric formulae  that  a  =  ft  =  y 
=  <£,  and  the  required  rela- 
tions are  therefore 

cosh  u  =  sec  <£, 
sinh  u  =  tan  <£, 
tanh  u  =  sin  <. 


The  angle  <£  which  renders 
it  possible  to  evaluate  the 
hyperbolic  functions  by 
means  of  the  circular  func- 
tions is  of  great  importance 
in  pure  and  applied  mathe- 
matics. Some  of  its  prop- 
rties  and  applications  will 
e  considered  in  the  section 
on  geometrical  illustra- 
tions. It  is  called  guder- 
mannian  u  and  is  written 

<f>  =  gd  u. 


The  following  list  of  form- 
ulae involving  the  hyper- 
bolic functions  might  be 
greatly  extended,  but  it 
includes  the  most  useful 
relations.1 


D 
FIG.  3. 


'Taken  with  additions  from  Prof.   B.  O.  Peirce  s  Short  Table  of  Integrals,  and   : 
McMahon's  Hyperbolic  Functions. 


DEFINITIONS   AND    FORMULAS.  xiii 


A.—  RELATIONS  BETWEEN  HYPERBOLIC  AND  CIRCULAR  FUNCTIONS. 

i  .  sinh  u  =  —  i  sin  iu  =  tan  gd  u. 

2.  cosh  u  —  cos  iu  =  sec  gd  u. 

3.  tanh  u  =  —  i  tan  iu  =  sin  gd  u. 

4.  tanh  \  u  —  tan  \  gd  u. 

5.  <?w  =  (  i  +  sin  %d  u)  -r-  cos  gd  u, 

=  [  i  —  cos  (  J  TT  H-  £tf  u)  ]  -*-  sin  (i  TT  -f  ^  «), 
=  tan(*ir  +  \gdu). 

6.  sinh  z«  =  z  sin  &. 

7.  cosh  iu  =  cos  &. 

8.  tanh  iu  =  i  tan  u. 

9.  sinh  («  ±  iv)  =  ±  /  sin  (z>  =H  «0, 

=  sinh  #  cos  v  ±i  cosh  w  sin  z>. 

10.  cosh  (?^  ±  zV)  =  cos  (z;  =F  /«), 

=  cosh  «  cos  v  ±  /  sinh  &  sin  z>. 

11.  cosh  (miir)  =  cos  ?^  TT.     (w  is  an  integer.) 

12.  sinh  (2  w  +  i)  J  zV  =  z  sin  (2  ra  -{-  i)  J  TT.     (w  is  an  integer.) 

B.  —  RELATIONS  AMONG  THE  HYPERBOLIC  FUNCTIONS. 

13.  sinh  u=  \(eu  —  <?~M)  =  —sinh  (—a)  =(csch  w),-1 

=  2  tanh  J  w  -^  (  i  —  tanh2  \  u}  =  tanh  u  -r-  (i  —  tanh2  w) 

14.  coshw=  J  (eu-\-e  -")  =  cosh  (—  w)  ==  (sech  a)-1, 

(i  —  tanh*iw)=  i  H-(I 

15.  tanhu=(eu  —  e-u)~-(eu-^-e-u)  =  —  tanh  (—  w), 

=  (coth  «)~x  =  sinh  ^  -=-cosh  u  —  (i  —  sech2  « 
1  6.  sech  w  =  sech  (—  u)  =  (i  —  tanh2  &)%. 
17.  csch  u  —  —  csch  (—  w)  =  (coth2  w  —  i)^. 
1  8.  coth  «  =  —  coth  (—  w)  =  (csch2  u  -f  i)^. 

19.  cosh2  «  —  sinh2  a  :=  i. 

20.  sinh  \  u  =  \/\  (cosh  u  —  i). 


21.  cosh  i  w  =  ]/  |(cosh  u  +  i). 

22.  tanh  ^  u—  (cosh  w  —  i)  -f-  sinh  w, 

=  sinh  w  -T-  (i  +  cosh  wj  =  i/(cosh  «  —  i)  -^-  (cosh  «  -f  i) 
23    sinh  271  =  2  sinh  w  cosh  w  =  2  tanh  u  -=-  (i  —  tanh2  u}. 

24.  cosh  2«  =  cosh2  u  +  sinh2  u—  2  cosh2  w  —  i, 

=  1+2  sinh2  «  =  (i  +  tanh2  w)  -r-  (i  —  tanh2  w). 

25.  tanh  2w  =  2  tanh  «  -r-  (i  +  tanh2  #). 

26.  sinh  3«  =  3  sinh  u  -f  4  sinh3  w. 

27.  cosh  3«  =  4  cosh3  «  —  3  cosh  w. 

28.  tanh  3&  =  (3  tanh  u  -f  tanh3  K)  ~  (i  -f  3  tanh2  u). 


XIV  DEFINITIONS   AND    FORMULAS. 

29.  sinh  nu  = 

n  cosh"—1  u  sinh  u  -\ -~ coshn~*  u  sinlr 

o 

30.  cosh  nu  =  cosh"  u  4  -  — -  cosh  n  ~2  u  sinh2  u  +  .  .  .  . 


3 1 .  sinh  u  4  sinh  z>  =  2  sinh  £  (w  +  v)  cosh  *  (w  —  v) . 

32.  sinh  u  —  sinh  v  =  2  cosh  J  (w  +  v)  sinh  J  («  —  v). 

33.  cosh  2*  4-  cosh  v  =  2  cosh  i  (2*  4  z>)  cosh  J  (w  —  v). 

34.  cosh  u  —  cosh  v  =  2  sinh  J  (w  +  v)  sinh  J  (2*  —  v) . 

35.  sinh  u  -j-  cosh?*  =  (i  +  tanh  \  u)  ~-  (i  — tanh  J  #)• 

36.  (sinh  u  4-  cosh  u)n  =  cosh  «w  4  sinh  w«. 

37.  tanh  w  4-  tanh  v  =  sinh  (u-\-v)-r-  cosh  2^  cosh  z>. 

38.  tanh  u  —  tanh  v  =  sinh  («  —  v)  -f-  cosh  ?^  cosh  v. 

39.  coth  z/  -f-  coth  v  —  sinh  (w  +  v)  -r-  sinh  w  sinh  v. 

40.  coth  ?^  —  coth  v  =  —  sinh  (u  —  v)  ~-  sinh  u  sinh  v. 

41.  sinh  (2*  it  z>)  =  sinh  «  cosh  v  ±  cosh  «  sinh  v. 

42.  cosh  (7^  ±:  z»)  =  cosh  «  cosh  v  ±  sinh  2^  sinh  z;. 

43.  tanh  O  ±  v)  =  (tanh  u  ±  tanh  z>)  -r-  (i  it  tanh  u  tanh  z;). 

44.  coth  (u  ±  v}  =  (coth  u  coth  z;  ±  i)  -5-  (coth  z;  ±  coth  w). 

45.  sinh  (7^  +  f)  -h  sinh  (u  —  v)  =  2  sinh  u  cosh  z>. 

46.  sinh  (u  +  v)  —  sinh  (7^  —  v)  =  2  cosh  w  sinh  v. 

47.  cosh  (a  +  z;)  +  cosh  (a  —  z;)  =  2  cosh  u  cosh  z>. 

48.  cosh  (u  -\-  v)  —  cosh  (it  —  v)  =  2  sinh  w  sinh  z;. 

49.  tanh  \  (u  +  v)  =  (sinh  7/  +  sinh  v)  -r-  (cosh  w  +  cosh  v). 

50.  tanh  i  (u  —  v)  =  (sinh  u  —  sinh  z;)  -f-  (cosh  u  +cosh  v). 

51.  coth  i  (#  -f-  z;)  =  (sinh  7^  —  sinh  v)  -f-  (cosh  u  —  cosh  v). 

52.  coth  \  (u  —  v)  =  (sinh  u  -f-  sinh  f)  -5-  (cosh  w  —  cosh  v). 
tanh  w  +  tanh  v      sinh  (2*5  -f  v) 

^      tanh  w  —  tanh  v  ~~  sinh  (u  —  v}' 

coth  w  +  coth  z>  _       sinh  (u  +  ») 
^      coth  w  —  coth  v  ~       sinh  (2^  —  z;)* 

55.  sinh  (w  +  v)  +  cosh  (w  +  v)  =  (cosh  w-f  sinh  u}  (cosh  z/  -f  sinh  v), 

56.  sinh  (w  4-  ^)  sinh  (2^  —  z;)  =  sinh2  u  —  sinh2  v, 

=  cosh2  7*  —  cosh2  v. 

57.  cosh  (w  -f  «0  cosh  (w  —  v)  =  cosh2  ?^  +  sinh2  z;, 

=  sinh2  ?/  +  cosh2  z/. 

58.  sinh  (mi ii)  =  o.     (w  is  an  integer). 

59.  cosh  (mi IT)  —  ( —  i)m. 

60.  tanh  (mi  IT)  =  o. 

61 .  sinh  (u  -f  mite)  =  ( —  i)m  sinh  u. 

62.  cosh  (u  4  mitt)  —  ( —  i)m  cosh  u. 

63.  sinh  (2  m  +  i)  i  iv=  ±  i. 


DEFINITIONS   AND    FORMULAS.  XV 

64.  COsh  (2  7#  +  I  )  |-  Z  TT  =  O. 

65.  sinh  (~  ±  uj  =  i  cosh  u. 

66.  cosh  f  —  ±u\  —  ±i  sinh  u. 

67.  tanh  (u  -f-  zV)  =  tanh  u. 

C.  —  INVERSE  HYPERBOLIC  FUNCTIONS. 

68.  sinh-1  «  =  log(«+  j/«*+  x    ^cosh'1  1/V  4-  T  =' 


t  -. 
69.  cosh-1  *  =  log  (w  +  i/V  —  i)  =  sinh  -1  ^^ZTY 


(«•— i)x 

.      du 
u)  —  Hog(i  — 


i  —  u 


71.  coth"1  u  =  Hog  (i  -\-u)  —  Hog  (u — j)==j-     — F  =  tanh    l 

»/  i  —  u 


72.  sech-^^logf  —  •f\/^T  —  :  )  = — 1~^ —   — 2^v==  cosh"1  — • 

*\u         *  u*         J  J  u(i  —  u*)*  u 

73.  csch"1  w  —  log  (—  +\/— r+  J )  — —  I     /   2  _!    NV  ^sinh"1  — • 

'Vw        ^  z^2         /  J  ?/(?^2+  ij/4  w 

74.  sin"1  ^  =  —  i  sinh"1  iu  =  — i  log  (&"#  +  V  i  —  w'2) . 

75.  cos" x  w  =  —  i  cosh"1  u  =  —  i  log  (u  +  i  V  i  —  u2). 

76.  tan"1  «  =  —i  tanh"1^  =  — .log (i  +  iu) :  log  (i  — iu). 

77.  cot"1  u=.i coth"1  iu  =  — .  log  (iu  —  i) . log  (iu  +  i). 


78.  sin"1  iu  =  i  sinh  -1  «  =  i  log  (z<*  +  V  i  -f-  &2) . 

79.  cos"1  z"&  =  —  i  cosh"1  iu  —  -   —  z*  log  (u  -f-  l/  i  -f-  z/2). 

80.  tan"1  /«  =  z tanh— x  w  =  —  log  ( i  +  u) log  ( i  —  u). 

i  i 

81.  cot"1  iu  =  —  z*  coth" 1  u  = log  (u  -f  i)  H log  («  —  i). 

82.  cosh"1  |  («  +  —)  =  sinh"1  i  [u j^tanh"1  ^9       *> 

V  K  /  \  W/  «2-f-I 

=  2  tanh"1 =  log  #. 

z^  +  i 

83.  tann"1  tan  z*  =  \gd  2.  u.     =  : 

84.  tan"1  tanh  w  =  ±gd~l2u. 

85.  cosh-1  esc  2  u  =  —  sinh-1  cot  2  u  =  —  tanh-1  cos  2  u  =  log  tan  u. 


XVI  DEFINITIONS    AND    FORMULAS. 

86.  tanh-1  tan2  (Jir  -f  -J-w)  =  T  log  esc  it. 

87.  tanh"1  tan2  \  u  =  %  log  sec  u. 

88.  cosh"1  u  ±  cosh"1  v  =  cosh"1  [uv  db  i/  (u*  —  i)  (v* i)] 


u  —  i     .     i    /  u  —  i  \     ,     i    (  u—  i  \     i 
.  log  u  =  -  +  _(_         _)4-_f_        __[.,_ 

u  2    V      u      J         3    V      z;      / 

Fw  —  i          i    /  u  —  i\3,     i    /  u  —  i  \  5  •  ~1 

.    log  U=  2      -  ---f—   (  --  -       +_       --  .  -      +.'... 

Lw-fi  V  «  -f  I  /  V  w  -h  I  /  J 


3 

w2  +  —  ?/  --  if  -\- 
234 


89.  sinh"1  u  ±  sinh"1  v  =  sinh"1  [u  V  i+i/l±vV'i+tt 

D. — SERIES. 

91.  log«  =  O—  i)  —  ~(u—  02  +  y  («  —  i)3—  •  •  • 

U  I        .        T      /  U  T    \  2    . 

92 

93 

94.  log 

95-  log 


97 


98. 


99.  tanh«  =  «-—  « 

O 

100.  «coth«=i  + 


101. 


,02. 


--  'h'"  -  ...     ("large.) 

245 


DEFINITIONS   AND    FORMULAS.  XV11 


104.   u=gd-l<j>  =  <i>  +  -— <p3  -f <p5  -f  -      —  <p7 -|-   .    .    .  (<?<—•) 

6  24  5040  V          2     / 


24 

i    u*         i     3    ub         135    d 

105.  sinh     u  =  u -  +  .  .  .       (u 2<  i.) 

23          245          2467 

_L_3_J_  +  J  _3_JLJ (^2>i) 

2    4  4  &4       24    66  w6 

106.  cosh"1  u  =  log  2  u -^-j —  ---^—4 —  -~|T— e —  •   •   •     (^'2>O 

22  U  2  4  4  «4         2  4  6  6  # 

107.  tanh"1  u  =  u  -j z^3  H 2^5  +  — w7  +  .   .   .  (#8<i.) 

O  3  l 

III  I  I 

108.  coth -1  u  =  tanh"    — = 1 r  -\-  • — ^H r+  •   •  •   (X>i-) 

u         11        $u         5 »        7 u 

,   i  2        i  w2       i  3  w4       i  3  5  ^6 

IOQ.    seen"1  &  =  cosh"  —  =  log ... 

u  u       22        244        2466        (&2<i) 

.,,1         i         ii  131  J351 

1 10.    each"1  u  =  sinh"1 


u        2   $u*        2  4  5&5        2  4  6  yw7 

-f  .  .  .  («*>!.) 


22  244  2 

H. — DERIVATIVES. 


-  -fa=uU^  -Hog**)- 

«?  sinh  « 


d  cosh  w 

i  io.   -  =  —  —  =  sinh  u. 
du 

d  tanh  2^ 

117.  -  -  =sech2  u. 

du 

d  coth  u 

118.  -  -  =  —  csch2  a. 

o'w 

^<f  sech  u 
119.   -    —  —   -=  —  sech  u.  tanh  u. 
du 

d  csch  u 
120.  -    —  —  -  =  —  csch  u.  coth  «. 


121.   - 

du  Vu*  -f 


XV111  DEFINITIONS   AND    FORMULAS. 

d  cosh  —  lu  i 


122. 

123. 
124- 
125- 
126. 
127. 


du  I'V— i 
d  tanh  ~ l  u  i 

du  i  —  zt2  ' 
d  coth  —  1  u  i 


du  i  — 

d  sech  — T  u 


du  u  |/  ! w2 

d  csch  — l  u  —  i 

du  ~  u  i/V  -f  i 
d^u 


I28    »_s^  =  secw.     ** 
du 

F. — INTEGRATE.     (INTEGRATION  CONSTANTS  ARE  OMITTED.) 

129.  J  sinh  u  du  =  cosh  u. 

130.  J  cosh  u  du  =  sinh  «. 

131.  j  tanh  udu  =  log  cosh  w. 

132.  j  coth  u  du  =  log  sinh  u. 

133.  j  sech   u  du  —  2  tan  ~~ 1  £M  =  gd  u. 

r  ft 

134.  I  csch  u  du=  log  tanh  — 

135.  J  sinhn udu  =  —  sinh"  —  1  u.  cosh  ft  —  -J  pinh"— 2  «  dfoN 

= sinh  n  + 1  u  cosh  w I  sinh  "  +  *  u  du. 

n  +  i  w  -f-  i  */ 

1-16.  (  cosh"z^  ^  =  —  sinh  w.  cosh"-1  ?^  H I  cosh" ~2 7^  du,  x 

»/  w  w   *^ 

= sinh  u  cosh"  + l  u  -\ —  I  cosh"  +  -  u  du. 

n  +  i  n  +  \J 

137.  \  u  sinh  21  du  =  u  cosh  ?/  —  sinh  ft. 

138.  J  u  cosh  w  afo  =  u  sinh  ^  —  cosh  u. 

139.  J  //'  sinh  u  du  =  (uz  +2}  cosh  u  —  2  u  sinh  u. 

140.  J  //"  sinh  u  du  =  un  cosh  u  —  ?t?fn-i  .sinh  u 

-f  w  (rc  —  i)J  un~2  sinh  7^«. 


DEFINITIONS   AND    FORMULAS.  XIX 


149. 


141.  J  sinh2  u  du  =%  (sinh  u  cosh  u  —  u). 

142.  j  sinh  u.  cosh  u  du  =  \  cosh  (2  u). 

143.  J  cosh2  udu=\  (sinh  w  cosh  w  +  w). 

144.  J  tanh2  udu  =  u  —  tanh  &. 

145.  j  coth2  u  du  =  u  —  coth  w. 

146.  j  sech2  u  du=  tanh  &. 

147.  j  sech3  u  du  =  \  sech  u  tanh  w  4-  |-  gd  u. 

148.  J  csch2  u  du  =  —  coth  u. 

.  jsinh"1  u  du  =  u  sinh-1  u  —  (i  -f  u2)^. 

150.  j  cosh"1  u  du  =  u  cosh"1  u  —  (uz  —  i)%. 

151.  j  tanh"1  u  du  =  «  tanh-1  w  +  i  log  (i  —  w2). 

152.  J  7*  sinh-1aflfo  =  J  |  (2  w2  -f-  i)  sinh-1  w  —  w  (i  4-  * 
J53-  J  a  cosh~ l udu  =-J     (2  w2  —  i)  cosh—1  u  —  u  (2**  —  i)%    . 

154.  J  (cosh  a  -f  cosh  w)  — l  du  =  2  csch  «.  tanh  ~l  (tanh  -j-  w.  tanh  J  «), 

=  csch  «      log  cosh  \  (u  +  a)  —  log  cosh  £  («  —  a)    • 

J55-  J  (cos  a  +  cos^  u}~1  du  =  2  esc  <z.  tan-1  (tanh -J-  w.  tan  |- «). 

156.  J  (i  -f  cos  a.  cosh  «)  — x  du  =  2  esc  <z.  tanh~ l  (tanh  ^  ?/.  tan  %a}. 

157.  J  sinh  u  cos  &  afo  =  \  (cosh  w.  cos  w  -f-  sinh  z^.  sin  w). 

158.  J  cosh  w.  cos  udu  =  ^  (sinh  z*.  cos  «  +  cosh  u.  sin  «). 

159.  J  sinh  w.  sin  udu  —  -|-  (cosh  ;/.  sin  u  —  sinh  74.  cos  u). 

»i6o.  J  cosh  u.  sin  u  du  =  \  (sinh  w.  sin  7^  —  cosh  7/.  cos  u). 
f 
161.  J  sinh  (mu)  sinh  (»w)  ^  v  vn 

=  ^2 ^2  I  l«  sinh  (ww)  cosh  (mu)  —  n  cosh  (ww)  sinh  (mu)\  • 


XX  DEFINITIONS   AND    FORMULAS. 

162.  J  cosh  (mu)  sinh  (nu)  dn 

=     2  _    2    m  sinh  (nu)  sinh  (mu}  —  n  cosh  (nu)  cosh  (mu)  I  • 

163.  1  cosh  (mu}  cosh  (#«)  afo 

=     z  _   2     w  sinh  (mu}  cosh  (#&)  —  n  sinh  (;»*)  cosh  (ww)    • 
1  64.    J  sinh  u  tanh  &  </«  =  sinh  u  —  gd  u. 

/u 
cosh  u  coth  udu  =  cosh  «  4~  log  tanh  — 

166.  J  sec  &  du  =  gd~  x  w. 

167.  J  sec3  <£</<£  =  J   (i  +  tan2<£)^aftan  <£  =  |  sec  <£  tan  <j>  +  \  gd  -1  <^>, 

=  \  tan  <£  (i  -J-  tan2  <#>)^  +  ^  sinh"1  (tan  <#>  ).    Here  <j>=gdu. 

C         du  .  u  C         du  u 

168      I        ,         ,        =smh~    —  .  I  ——J  --  2Tlz=sin- 

•/     («2  +  a2)^  «  J     (a2  —  u*y*  a' 

C         du  .  u  C       —  du  u 

I^>9-       ~~7~2  --  in/"  =cosh~    —  .  —  ^-J7=cos~ 

•/     (u2  —  a2)^  a  ^     (a2  —  u2)  X  a' 

/du  i  .  u  C         du  i  .    u 

-  =  —  tanh"1  —  .  -tan"1- 

O2  —  «0»<«        «  ^          J       a2  -\-  u*  a  a' 

—  du  i  ^  u  C       —  du  i  ,11 
7-2——^  -  =-  —  coth"1  —  .                        —  =  —  =  —  cot~ 

(u2  —  a2)u>a       a  a          J       a2  +  u*  a  a' 

—  du  i  u  C         du  i  u 

—  ^r/  =  —  sech"1  —  .  —  ^/  =  —  sec"    —  . 

u(a2  —  «2)^        a  a          J   u  (u-  —  a2)%         a  a 

—  du  l         v,  -  1  u  C       —  du  _L        -i  u 
u  (a2  +  u2)1/*  -  ~^  C             ~^'       J    n(u'  —  a*)   ~~~'~^C          ~^' 

/du  i  au  +  b 

7  —  rr  —  T~  r~^?  =    /=  sinh-  —  ^          a  positive,  ac  >b'\ 

(au2  +2bu+c)*       |/  a  (ac  —  &y* 

i  au-\-  b 

=  v=         (.»-•&> 

i  au  4-  b 

=  —=  cos-1  -^—         '  a  negative. 

!/_#  {tr—acy* 

/du  i  aw  -f  b 

u*  u  ==        -         *          ^^^' 

aw  4-  b  ac<b\ 

(f-acj*          au  +  b  <(&  —  acY*. 


i  aw  4-  b  ac<b\ 


coth 


_t    au  4-  b  ac<b\ 


/du 
(a—  u)(u 


DEFINITIONS   AND    FORMULAS. 
2 


XXI 


or  — -    tan 


llT 

\ 

\   h  _ 


tanh-1 


^=T' 


b  —  a 


or 


coth-1  \\u         -     (The  real  form  is  to  be  taken.) 
a  —  b 


/ 
(a  - 


du 


or  — — — -  coth 

(b—af/*  *  b  —  a 


-W-r^- 

^     h   —    n 


\  &  —  u 


or 


tan 


"1 


(a  — 
w»  __  ««^^w  =     w  «2  —  a*)*-  i  «2  cosh-1  -- 


real  form  is  to  be  taken-) 


179. 
180. 
181 
182. 


•  JV-*2-*^  =  *«(«•- 

^2    _J_   ^2^   ^    __  ^   u    ^U2  _j_ 

/_     €<1U 
~a" 

c        - e<lu 


sn- 


«2  sinh-1      . 


; 
w 


w    /* 

I  nm~l 
a    J 


du. 


du 


eau 


r  *  ^ 

i8s.     I  a    a u  =  -— : • 

J  Moga 

/«"  wn         TZ«"  wn  - ]          n  (n  —  i)  «M  u*  —*  . 
un  au  du  =  -—      • T —  H-  -  y 

log  a  (log  «)2  (log  «)8 


n  (n  —  i)  (w  —  2)  .   .   21  «u 
(log^)^1 

Caudu  au      F  i  log  a  (log  a)2 

lo^.      I   — — r —   ^^:  I  n  _  i  T  7  o  7  r~r  r        ,; 

Qogg)  n~T f  ^U  ^  "1 

"     (»-   2)(^-    3)     .     .     .      2.1     J          //       J' 

Caudu  (7^1oga)2   ,    (« 

jgg.       I-         -=\QVU-\-U^ ' 

J       n 


XXli  DEFINITIONS   AND    FORMULAS. 


/du  i    r  ~\ 

-^+6^  ==  isa  lmu  ~  log  (a  +  ^"}  J 

/ 


du 


I9i 

/du  i  

(a  4-  femu)^  =  m    '~\_ *0g  ^  V      ~*~  ^"'M  ~~  '       ^ 

-  log  (l/a  +  ^wu  +  I/a)!  - 

I93'  J  ( i  +  «/  ==  i  f  u 

/eau  loer  u          i    r  eau  du 
euu  log  u  du  =  -  —  — . 

a  a  J      u 

195.  J  log  u  du  =  u  log  u  —  ?<. 

196.  ftf" 


197.  J  (log  w)n  du  =  u  (log  ?0n  —  n  J  (log  ")n~l  <#*• 

Jwm  +1  Clog;  ?0n  n          r 

tc  (log  «)-  du  =  -   j-+i       •  m  +  l  j 

r  (log  «)•</»<      (logM)"^1 

J99-  J  -     "IT  '    nI 


J^  «  ,       i  r      du 

(log  w)n  =  "  (»  —  i)(log/^)n-1  w  —  i  J  (log?^)""1 

/?^m  du  um+l  m-\-  i  f*     nm  du 

(logw)w  "  (w  —  i)  (logw)"-1  "  w—  i  J  (Iog70n~l 

<"* 
log 


/?<"*  rfw  r  e~y 

-  dy,  where  JF  =  —  (m  4-  0  log  «. 
lo    ?^  ^ 


C_du_  __  i 

2°5'  J  u  (log  w  "  (n  —  i  )  (log  «)n  -  l 

206.  J  («  4-  ^?0m  l°g  w  ^M  = 


l 


f  («  +  ^/)BI  »•  !  ////  -i 
—  J         -S- 


DEFINITIONS   AND    FORMULAS.  XX111 

207.  j  um  log  (a  4-  bu)  du  — 

1         \~  m+i  i       f         A  Cum  +ldu~\ 

0*  4-  i    L  J    a  +  £w   J* 

C  loer  (#  4  ^^)  du 

208.  I  — s-i 

J  w 


bu          i    (  bu\*        i    /  bu 
loga.log»  +  —  ---?(—  )   +-(  —     - 


/log  ^^  ^      _  i  F_  log  u  C  _  du  _  -i 

(a  +  bu)m  ~:    b(m—i)    L      (a  +  tu)m-l+  J   n  (a  +  t>u)m~l  J. 

/log  u  du          i  i     /*  log  O  +  ^w) 

^__  =_iog«.log(a  +  te)___j_   i__  irfw. 

21  1.    f(«  +  M)  log  »  <fo  =  ^±^  log  «  - 

\s  20 

/log  u  du 


212 


—  2)  V  (a  +  bu)  4-  l/alog  (\/  a  +  bu 


-  J#  log  (l/«4-^~  l/),  if  «>o, 


=  y  [(log  «—  2)  I/  (a  +  bu)  4-  2  iX-^tan-1  ^^±^^f  a<o. 


213-    f  ^~a2"2  rf«  =    *   *  =  —  r  a). 

*/0  2«  2  a        V2' 


214. 


.  f  « 

Jo 


216. 


.      f   «?-""   l/HIdu   =^—  J  * 

Jo  2  «  A  ~~  ' 

X»-JQ    ^   ^nw  ) 

.     I  -=-du  =  JJL- 

Jo          |/  K  \     w 


2l8'  '       '-  m'V  r  o. 

az9.  JV  * 

«/0       Sll 


sinh  (nu)         2,  w 


220.  r  u 

Jo     sin 


sinh  («?^)    "  "  4  «2 ' 


DEFINITIONS    AND    FORMULAS. 

/*»  ""  /»»  7T 

221.  JQ    sinh  (mu)  .  sinh  (««)  du  =  Jo     cosh  (wz*)  .  cosh  (nu)  du 

•=•  o,  if  m  is  different  from  n. 

222.  I    ''cosh2  (mu)  du  =  —  P*  sinh2  (ww)  afo  =  1^1. 

•/O  o/O  2 

X+ilT 
sinh  (mu)  du  =  o. 
•i* 

/»i  JT 

224.  cosh  (raw)  afo  =  o. 

i/O 

XtTT 
sinh  (ftttt)  cosh  (MM)  ^  =o. 
-i» 

£J7T 
sinh  (OTK)  cosh  (mu)  du  =  o. 
_  . 

rl  logu  7T2 

227.      I  -  du  =  --  —  . 

•/o     i  —  w  6 


r1  log  u  7T2 

228.     I  -  du  =  --  . 

JQ     i  +  u  12 

r1  iog«  7T2 

220.  —-du  =  --  . 

Jo     i  —  u1  8 

C  l   ,  (    I     +    U\        du  7T2 

230.    I     log  I  -         -  )  •  -  = 
a      jo        '\i  —  u  )      u          4 

X1   log  M  du  7t 

(l-u>)%=    -Tlog2' 

«*  —  «'    rfa  A  + 


233-  r  oog  *)"  ^  =  c—  !)" 

»/0 


235 

.36 
237- 


DEFINITIONS   AND    FORMULAS.  XXV 

G. — FORMULAS  FOR  THE  SOLUTION  OF  PSEUDO- SPHERICAL  TRIANGLES. 

a. — Right  Triangles. 
cot  U  (a)          sinh  a 


sin  A  = 
cos  A  = 


cot  11  (£)          sinh  c 

cos  77  (b)  _     tanh  b 
cos  //  (£•)         tanh  c 


sin  Z?  •     »       t. 

cos  ^4  =  — ; — ..  ,  N  =  sm  B  cosh 
sin  11  (a) 

cot77(£)          sinh  £ 

cot  ^4  = 


cos       = 


cos  77  (a)         tanh  « 
cosll(a  tanh  a 


cos  77  (V)          tanh 


_,          sin  A  ,        . 

cos  B  =  —. —    ...    =  sin  A  cosh 
sin  u  (o) 

cot  77  (b)         sinh  £ 
sin  B=  — 


cot  >5  = 


cot^  (V)          sinh 
cot/7  («)          sinh 


cos  /y    ^  tanh  b 


tan  J.  tan  B  =  sin  77  (V)  =  sin  77  (a)  sin  77  (£). 
=  sech  <:  =  sech  a  sech  3. 

b. — Oblique  Triangles. 
The  general  relations  are  : 

cosh  a  =  cosh  b  cosh  £  —  sinh  £  sinh  c  cos  ^4. 
sin  ^4  sinh  b  =  sin  .Z?  sinh  a. 
coth  a  sinh  b  —  cosh  £  cos  C  +  sin  C  cot  A . 

cos  ^4  =  —  cos  B  cos  C  -4-  sin  Z?  sin  C  cosh  a. 

Forti  solves  the  six  typical  cases  in  the  following  manner: 
CASE  i. — Given  a,  b,  c.     Put  zp  =  a  -f  b  +  c.     Then, 


tan  I  A  =  J  sinh  (I  —  £).sinh(/>  —  g)  . 
'          sinh  />  sinh  (/  —  a) 

The  conditions  are  a  <  b  +  c;  b  <ia  +  c;  and  £<  <z  +  b. 

CASE  2.  —  Given  a,  b,  A.     Draw  the  geodetic  line  CD  perpendicular  to  AB. 


Then  a>CD;  A  <  i  ;  cot  i  C>  o  ;  and  tanh  ^  ^  >  o- 


XXVI  DEFINITIONS   AND    FORMULAS. 

sinh  b  sin  A 


sin  B  = 


l  ^_ 


sinh  a 
an  ^  (A  —  B)  sinh  ^  (a  4-  b} 


sinh 

!  _  _ 


CASK  3.—  Given  a,  b,  C.     2  &  =  *  —  (A  +  #-f  C). 

i  /  xf       r>\  i 

tan      A  +  B  =  cot 


sinh     (0-Hh 


sin  A  sin  (A  -f-  C) 
sin  (A  -f  A)  sin  (A  -f  B) 

CASE  4.— Given  ^,  B,c.     A  +  B  <*  and  DBC  <DBG.     The  angle 
is  the  angle  between  the  geodetic  DB  drawn  perpendicular  to  AC  and  the 
geodetic  BG  drawn  parallel  to  AC. 


„  i  r—  ^/sinh  (/>  —  a)  sinh  (p  —  b} 

tan   0  *-  —   \    -          ;     —    7      ;     ,      ,  r 

sinh/  sinh  (p  —  c) 

CASE  5. — Given  A,  B,  a.     a  >  CZ?  and  ^4  +  B  <  TT. 
Solve  the  two  right  triangles  formed  by  the  geodetic  line  CD  drawn  per- 
pendicular to  A  B. 

CASE  6.— Given  A,  B,  C.     A+  B+  C<~. 


sin  A  sin  (A  -)-  A) 
sin  (A  +  B)  sin  (A  +  C)  ' 

H. — FORMULAS  FOR  THE  SOLUTION  OF  THE  Cusic1. 

If  a  cubic  equation  is  given  in  the  form 

£  -f-  0,2*  -f-  bz  -\-  c  =  o, 

it  can  be  reduced  by  the  substitution  z  =  x  -       -  to  the  simpler  form 

v5 
**+/*+  f  =  O, 

'Taken  from  1%  Ingenieurs  Taschenbuch  der  Htitte,  Berlin,  i8th  edition. 


DEFINITIONS   AND    FORMULAS.  XXV11 

CASE  i . — When  xz  -\-  px  ±  q  =  o;  p  and  q  positive.    Compute  the  auxiliary 
variable  u  from  sinh  u  =   ^     ^f      ^;  then  the  roots  are 

Xl  =  =t=  2  v"~\p  sinh  \  u. 

x^  =  ±  V  \p  sinh  \u-\-i  V~p  cosh  |  u. 


x3=  ±  I/  \p  sinh  -I  u  —  i  V  p  cosh  \  u. 
CASE  2.  —  When  x*  —  px  ±  $  =  o;  p  and  q  positive,     (i/)3  <  (\  qf.     Com- 

pute «  from  cosh  u  =        2  '  T  ^M/>  tnen  tlie  roots  are 

'/2 


=  =F  2  l^  -|-/>  cosh 


x^  =  ±  I/  \p  cosh  \u  -\r  i  V  p  sinh  \  u. 
xz  =  ±  V  \P  cosh  J  «  —  *  t/  ^  sinh  ^  w. 

CASE  3. — When  #3  — /j;  ±q  =o-,  p  and  ^  positive.     (^-/)3 >(-J- ^)2.     Com- 
pute the  angle  u  from  cos  u  =  ^-^7\~^\y'>  then  tlie  roots  are 


x^  =  =F  2  I/7  |/>  cos  ^  w. 

^T2  =  =h  2  I/  |/>    COS  (i  «  +   120°). 

x9  =  =i=  2  I/  -^/>  cos  (^  w  +  240°). 
CASE  4. — When  x* — px±q  =  o;  /  and  ^  positive.   (-J-  ff  = 


For  applications  of  hyperbolic  and  circular  functions  to  the  solution  of  the 
cubic  whose  coefficients  are  general  (i.  e.,  real  or  complex),  see  a  brief  paper 
by  Mr.  W.  D.  Lambert  in  American  Mathematical  Monthly  for  April,  1906. 


GEOMETRICAL  ILLUSTRATIONS  OF  HYPERBOLIC 

FUNCTIONS.. 

The  algebraic  relationship  of  the  hyperbolic  functions  to  the  circular  func- 
tions has  been  discussed  in  the  section  on  definitions  and  formulas.  A  close 
relationship  also  exists  between  the  elliptic  functions  and  the  hyperbolic 
functions.  Thus  it  may  be  shown  that  the  elliptic  integral  of  the  first  kind, 


V  i  — 


sn 


in  which  k  is  the  modulus  and  <£  the  amplitude,  reduces  to  «  =  gd~l  <£  when 
k  =  i  .  The  elliptic  functions  thus  degenerate  into  the  hyperbolic  functions 
when  the  modulus  is  equal  to  unity.  A  case  in  point  is  the  elastica,  the 
equation  of  which  takes  the  form  of  an  elliptic  integral,  excepting  when  the 
modulus  is  unity.  It  then  reduces  to  the  two  equations 

X  1/2 

—  =  K  —  2  tanh  u;  -  —  =  —         —  , 
a  a          cosh  u 

which  is  a  syntractrix  described  by  the  free  end  of  a  rod  whose  middle  point 
traces  out  the  tractory.1 

Ligowski  gives  the  following  easy  geometrical  method  of  demonstrating 
the  relations  between  the  hyperbolic  and  circular  functions.  Let  the  equation 
of  the  circle  of  unit  radius  be 


and  call 

y 


uc  the  arc  of  this  circle  from  the  positive  x  axis  to  the  point  xc  yc 
Then,  of  course,  the  circle  may  be  repre- 
sented by  the  two  equations 

xc  =  cos  uc ;  yc  =  sin  uc . 
Now,  the  area  of  the  circular  sector,  whose 

O     77         T 

chord  is  2yc,  is  -        -  —  uc,  so  that  xc  and 

yc  may  be  regarded  as  the  cosine  and  sine  of 
a  sector  uc.  The  ellipse  may  be  derived 
from  the  unit  circle  by  multiplying  the  or- 
dinates  yc  by  b.  Hence,  in  the  ellipse,  the 
area  of  the  sector  subtended  by  the  chord 
2  ye  is,  say,  ne  and  ue  =  bnc. 

1  If  in  these  equations  m  is  substituted  for  2  they  represent  any  syntractrix.    The  two 
equations,  with  this  substitution,  can  be  combined  to  the  following  : 


(au  — 


' 


showing  that  the  curve  is  traced  by  a  point  on  a  circle  of  radius  am  whose  center  is  in 
motion.  It  is  noteworthy  that  if  in  this  equation  the  hyperbolic  sector  u  is  replaced  by 
a  circular  sector  </>,  the  new  equation  represents  a  prolate  or  a  curtate  cycloid,  or  In  tier 
the  syncycloid.  Thus  the  syntractrix  may  be  considered  as  a  syncycloid  with  an  infinite 

period. 

acxviii 


GEOMETRICAL   ILLUSTRATIONS.  xxix 

Thus 

Uf, 

xc  —  cos  uc  =  cos  -r-» 


so  that  for  the  ellipse, 


. 

yc  =  sin  wc  =  y  =  sin  — 


^2     ,       ^  _  . 

*  e  ~     72        ~  -1 » 


,     • 

xe=xe  =  cos  —  ;  ye  =  b  sin  -7-- 

0  0 

The  equation 

jt2—  y  =  i 

represents  an  equilateral  hyperbola,  and  if  u  is  the  area  of  the  hyperbolic 
sector  whose  chord  is  2_y,  then  there  can  be  no  objection  to  writing 

x  =  cosh  u  ;  y  =  sinh  u, 

where  cosh  and  sinh  are  functions  whose  nature  is  still  to  be  determined. 
The  most  evident  relation  is 

cosh2  u  —  sinh2  u  =  i . 


Now  if  i  =  V  —  i,  the  hyperbola  may  be  written 


which  is  an  ellipse  whose  major  axis  is  unity  and  whose  minor  axis  is  i. 
Comparing  this  with  the  ellipse  discussed  above,  it  appears  at  once  that 

x  =  cosh  u  =  cos  — -> 
i 

-..  .  .    .     u 

y  =  sinh  u  =  i  sin  — r> 

or,  in  an  equivalent  form, 

cosh  u  =  cos  iu  ;  sinh  u  =  —  i  sin  iu, 
cosh  iu  =  cos  u  ;  sinh  iu  =  i  sin  u. 

The  investigation  of  cosh  u  and  sinh  u  can  be  completed  in  various  ways  ; 
for  example,  by  writing  out  the  series  for  cos  iu  and  —  i  sin  iu  and  showing 
that  their  sum  or  difference  is  e  ±  M. 

The  geometrical  properties  of  the  hyperbolic  functions  themselves  are  com- 
monly discussed  in  reference  to  the  equilateral  hyperbola.  They  could  also 
be  derived  from  the  geometry  of  the  ellipse  without  reference  to  the  hyper- 
bola ;  but  a  more  perspicuous  method  seems  to  be  to  study  the  relations  of 
these  functions  to  both  curves  at  the  same  time.1 

In  any  ellipse, 


JSee  Bull.  Geol.  Soc.  Am.,  vol.  2,  1891,  p.  49,  and  Am.  Jour.  Sci.,  vol.  46,  1893,  p.  337. 


XXX 


GEOMETRICAL    ILLUSTRATIONS. 


the  area  a  (3  may  be  chosen  as  the  unit  area,  so  that  the  equation  of  the 


curve  becomes 


By  varying  the  value  of  a  in  this  equation  a  family  of  ellipses  is  obtained 
each  of  area  TT,  all  with  the  same  center  and  all  with  axes  lying  in  the  axes 
of  coordinates.  The  envelope  of  this  system  of  curves  is  the  hyperbola 
xy  =  ^-,  and  this  may  be  conceived  as  generated  by  the  motion  of  a  single 
point.  The  coordinates  of  the  point  Plt  at  which  the  hyperbola  is  tangent 
to  the  ellipse,  are 


Via  \       2 

and  the  coordinates  of  the  point  c  at  which  the  hyperbola  is  tangent  to  the 
unit  circle,  are 

i 


=  7T 


<~*d 

4: 


J  X-t    *    ' 

*        i 


n 


f;*tt*s 


0        ~tv(jL         ^•'"-    ' 


FIG.  5. 


If  the  hyperbola  is  conceived  as  generated  by  the  point  c  in  moving  from 
its  original  position  to  Pl  (or  as  a  "  line  of  flow  "),  its  radius  vector  sweeps 
over  an  hyperbolic  sector  ocPr  If  this  area  is  called  — ,  then  by  a  well- 
known  formula,  dtl  =  x  dy  -  y  dx, 


GEOMETRICAL   ILLUSTRATIONS.  XXXI 

and  because  xy  =  %, 


dy        dx\ 

du  =  i  I  -  -  ) . 

J   \  y         x  ) 

Since  no  integration  constant  is  required, 

u  •=.  \  log  —  =  \  log  a2  or  a  =  ew. 
xl 

The  area  u  is  the  sector  oPl  cP^  where  the  coordinates  of  Pt  are  x2  =yiy 
and  y2  =  xr  It  is  noteworthy  that  two  other  areas,  APl  cPz  B  and  CD  Pl 
cP2,  have  this  same  value,  for  evidently 


X%  /*.Va 

y  dx  =    I      X  dy  =  log  a  =  U. 
J2/i 


The  length  of  the  chord  />  />8  is 


and  half  of  this,  or  />  a,  is  the  hyperbolic  sine  which  may  evidently  be  put 
in  the  form 

eu_e-u 

smh  u  =  —     . 

2 

Since  the  curve  Pl  cP2  is  an  hyperbola, 


and  therefore 


«  +  *-« 


oa=  |/  1  —  sinh2  u  =  -        -  =  cosh  u. 


The  diameters  connecting  the  points  of  intersection  of  the  unit  circle  and 
the  ellipse  whose  axes  are  a  and  a—1,  may  be  called  the  isocyclic  diameters 
of  the  ellipse,  because  the  circle  and  the  ellipse  have  the  same  area.  These 
diameters  are  not  conjugate.  If  the  ellipse  is  conceived  as  the  section  on 
the  greatest  and  least  axes  ot  an  ellipsoid  of  unit  volume,  the  isocyclic 
diameters  are  the  traces  of  the  circular  sections  of  the  ellipsoid.  The  coordi- 
nates of  one  of  the  points  of  intersection,  say  E,  are 


x  = 


l/a2-hl 


and  therefore  the  angle  v,  which  the  vector  oE  makes  with  the  major  axis  of 
the  ellipse,  is  given  by  the  relation 


tan  v  —  a—1  =e 
and  it  follows  that 


I                      tan  f 2v\  =  -J-  (cot  v  —  tan  v)  =  sinh  u. 
is  angle  ( 2v\  is  gd  u,  or  the  gudermannian  of  u,  so  that  in  any 


XXX11  GEOMETRICAL   ILLUSTRATIONS- 

ellipse  whatever  the  angle  made  by  any  line  parallel  to  one  isocyclic  diameter 
with  a  perpendicular  on  the  other  isocyclic  diameter  is  the  gudermannian  of  the 
natural  logarithm  of  the  semi-major  axis,  this  being  expressed  in  terms  of  the 
isocyclic  radius,  which  in  the  general  case  is  the  square  root  of  the  prod- 
uct of  the  semiaxes.1  In  the  diagram  the  gudermannian  bob^  is  shown  as 
bisected  by  the  axis  of  the  hyperbola,  and  it  is  worth  remarking  that  if  the 
ellipse  were  to  be  distorted  into  a  circle  by  compressing  the  major  axis  and 
elongating  the  minor  axis,  the  line  ob  would  be  brought  into  coincidence 
with  ob^  so  that  gd  u  can  be  defined  as  the  angle  through  which  an  isocyclic 
diameter  has  swept  when  the  ellipse  has  been  derived  from  a  circle  by  irro- 
tational  plane  strain. 

The  angle  45°  -f  —f  —which  occurs  in  the  formula  for  meridional  parts 

is  the  angle  made  by  either  isocyclic  diameter  of  the  ellipse  with  the  minor 
axis,  and  the  tangent  of  this  angle  is  the  semi-major  axis  a. 

The  twofold  relations  of  the  hyperbolic  functions  to  the  hyperbola  and 
the  ellipse  are  illustrated  in  a  somewhat  different  manner  in  figure  6. 

Here  the  curve  pl  c  pz  is  an  arc  of  an  hyperbola  jy2  —  x1  =  i.  If  the  area 
of  the  sector  o pl  c  p^  is  called  u,  a  />1  =  sinh  u  and  oa  =  cosh  u.  Make 
bc=pl  a  and  draw  the  associated  ellipse  shown  in  the  diagram.  Then  the 
angle  boc=gdu  /  bo  =  cosh  u  and 

tan  gd  u  =  sinh  u 
sec  gd  u  =  cosh  u 
sin  gdu  =  tanh  u. 

The  ellipse  has  corresponding  properties.  Since  the  gudermannian  is  the 
angle  between  either  isocyclic  diameter  and  a  line  perpendicular  to  the  other, 
the  line  ob  may  be  regarded  as  coinciding  with  one  isocyclic  diameter  and  the 
axis  of  abscissas  with  the  other.  The  major  axis  of  the  ellipse  then  bisects 

LThe  isocyclic  diameter  used  in  this  illustration  of  hyperbolic  functions  lies  in  the 
circular  section  of  a  shear  ellipsoid,  or  an  ellipsoid  in  which  the  mean  axis  is  a  mean 
proportional  between  the  greatest  and  least  axes.  The  position  of  the  circular  section 
of  the  general  ellipsoid  is  also  readily  expressed  in  terms  of  hyperbolic  functions.  Let 
the  equation  of  the  ellipsoid  be 

*-2          v?  9.2 

£  + IT +  •£—«•!*>»>« 

If  —  =  cosh  ult  and  -j-  =  cosh  w2, 
the  angle  v  which  the  circular  section  makes  with  the  greatest  axis  is  given  by 

i  b  — »  —  a  - *          tanh  w, 

tan  „=  T  tanh  „  =  c-._b-*  =      ..nhl^' 

If  Ul  =  w,  and  -?-  =  a  this  expression  reduces  to  tan  v  =  a  -\  or  to  the  case  of  the 
shear  ellipsoid. 


GEOMETRICAL   ILLUSTRATIONS.  XXX111 

the  angle  90°  —  gdu,  its  magnitude  is  2  eu,  and  the  equation  of  the  ellipse  is 


4  xy  tan  gd  u 


tan2 


-+-  i)  =  i. 


'  By  varying  the  value  of  tan  gd  u  (or  sinh  u)  a  system  of  ellipses  is  obtained 
whose  envelopes  are  y  —  ±  i  ,  so  that  if  any  one  of  the  ellipses  is  supposed 
to  be  derived  from  the  circle  by  distortion,  the  process  is  that  generally 
known  as  "shearing  motion  or  scission." 

If  the  points  in  the  circle  are  sought  which  correspond  to  the  points  on  the 


FIG.  6. 

major  axis  of  the  ellipsoid,  it  will  be  found  that  the  angle  between  the  two 
positions  (the  angle  of  rotation)  is  equal  to  the  gudermannian.1 

If  instead  of  the  horizontal,  the  vertical  line  in  figure  6  had  been  taken  as 
coinciding  with  the  isocyclic  diameter  of  the  ellipse,  the  result  would  have 
been  the  discovery  of  a  system  of  ellipses  whose  envelopes  are  x  —  d=  i, 
similar  in  all  respects  excepting  orientation  to  that  discussed. 

1  Love's  Treatise  on  the  Theory  of  Elasticity,  vol.  i,  p.  43. 


METHODS  OF  INTERPOLATION. 


It  is  not  easy  to  describe  the  use  of  the  tables  which  follow  without  some 
notes  on  the  methods  of  interpolation  with  reference  to  which  they  are 
arranged.  In  all  of  them  the  argument  advances  by  equal  increments,  each 
equal,  say,  to  o>.  It  is  required  to  find  a  value  of  the  function  F interme- 
diate between  two  tabulated  values,  FQ  and  Flt  corresponding  to  a  fractional 
value  of  the  argument  or  to  wo>,  where  n  is  always  less  than  unity,  and 
preferably  less  than  one-half. 

Let  Fn  be  the  value  of  the  function  to  be  determined  ;  let  F—i  and  /*!.  2  be 
tabulated  values  of  F  immediately  preceding  Fot  and  let  Flt  F^  be  values 
immediately  following  F0.  Denote  Fl  —  F0  by  aly  other  first  differences  (A') 
being  similarly  represented.  If  also  aa  —  al  =  b^  bl  —  bQ  =  clt  etc. ,  the  whole 
system  of  functions  and  differences  is  shown  in  the  following  schedule  :l 


F 

A' 

A" 

A'" 

A™ 

J« 

* 

>-, 

b" 

d" 

r 

a" 

c" 

^' 

^-i 

b' 

d' 

f 

a 

c 

e 

^0 

t>o 

d* 

/. 

F, 

a\ 

* 

ci 

4 

*\ 

/, 

*, 

< 

/ 

The  most  familiar  formula  of  interpolation  is  due  to  Newton,  and  in  the 
above  notation  it  may  be  written  thus: 


Fn  —  F0  =  na^ 


n  ftt—  i)  Q—  -2) 


2\ 


, 


n  (n—  i)  (n  —  2)  (»  — 3)     , 
—-  a, 


JThe  notation  and  general  outline  of  treatment  here  presented  closely  follow  Mr. 
Herbert  L.  Rice's  treatise,  Theory  and  Practice  of  Interpolation,  1899.  The  Nichols 
Press,  Lynn,  Massachusetts. 

xxxiv 


METHODS   OF   INTERPOLATION.  XXXV 

The  coefficients  are  those  of  the  binomial  theorem.  This  formula  is  appli- 
cable to  the  first  intervals  of  a  series,  which  is  not  the  case  with  any  other 
mode  of  interpolation.  It  may  also  be  adapted  to  the  last  intervals  by  sub- 
stituting —  n  for  n  and  a,  b'  ',  c",  d"  ',  .  .  .  for^,  biy  c^  d^  .  .  .  .  In  systematic 
interpolation,  such  as  is  involved  in  the  construction  of  tables,  it  is  usual  to 
employ  the  more  rapidly  converging  formulas  of  Stirling  or  Bessel;  but  when 
a  computing  machine  and  a  table  of  products  are  available  it  is  sometimes 
less  laborious  to  compute  an  extra  term  of  Newton's  formula  than  to  calcu- 
late and  apply  the  mean  differences  called  for  by  the  other  methods.  Both 
Stirling's  and  Bessel'  s  formulas  can  be  derived  from  Newton's  by  known 
relations  between  the  several  differences. 

In  Stirling's  formula  the  mean  of  the  first  differences  next  preceding  and 
following  FQ  is  made  use  of  instead  of  only  the  latter,  as  in  Newton's  formula. 
The  third  differences  are  similarly  treated,  so  that  #0,  c0,  etc.,  being  new 
quantities,  are  defined  by 


These  mean  values  are  used  in  conjunction  with  the  even  differences  on  the 
same  horizontal  line  with  FQ  in  the  schedule,  and  Stirling's  formula  is 

n*  n  (n2  —  i)  ril  (n2  —  i) 

Fn  —  Ft  =  nat+-^b,  +  -     ^i-       r°  +  -     ^T"          ° 

»(«'  —  i)Q2  —  4)   . 

5!  *"" 

To  interpolate  backward  it  is  only  needful  to  substitute  —  n  for  n. 

In  Bessel's  formula  use  is  made  of  mean  differences  of  the  even  orders,  and 
if  b\  d,  etc.  ,  are  these  means  they  are  defined  in  terms  of  the  scheduled  differ- 
ences, thus  : 


They  are  used  in  conjunction  with  the  simple  odd  differences  ar  cly  etc.,  and 

the  formula  is 

p p_n      i     n(n — T)  fl-L.  n(n — *)(** — i)      t(n-\-i)n(n  — i    (n  — 2)   . 

2  !  3  !  4  ! 

;«  +  !)«(»  — i)  (n  —2)  (»  — 

5 

When  n  =  ^,  or  for  interpolation  to  the  middle  of  an  interval,  the  co- 
efficient of  ^  vanishes  and  Fn  —  F0is  independent  of  third  differences,  which 
is  clearly  a  great  advantage.  In  general  this  method  is  very  advantageous 
.when  n  approaches  one-half,  while  Stirling's  formula  is  preferred  for  small 
values  of  n. 


V7*_    -  i.)  n\n-  -i;    ^ ^;  ^n -%) 

f  \  €l   ~T    •     •     •     . 


XXXVI  METHODS   OF   INTERPOLATION. 

When  Bessel's  formula  is  used  for  backward  interpolation,  it  may  be 
written 

*__/?=  -na>  +  i^H  (A±*L)  -."'"--H"-*)^  .....  > 

«  being  taken  as  positive. 

A  distinct  method  of  interpolation  is  founded  directly  upon  Taylor's 
theorem.  If  F0'  F0",  etc.,  are  the  successive  derivatives  of  F0,  and  w  is  the 
constant  increment  of  the  argument,  this  fundamental  theorem  may  be 
written 

zr          Z7  V     ,       »*  w2  V       .      "S  «'  ^o'"  «*  «*  ^o" 

/^—  ^0  =  «o,^0  +  -—J-0        ___^       T^     ...... 

and  this  becomes  an  interpolation  formula  when  the  derivatives  are  ex- 
pressed in  terms  of  the  differences.  This  is  readily  accomplished  to  any 
degree  of  exactness  whenever  the  differences  become  rigorously  or  sensibly 
constant  at  some  particular  order  and  the  tabular  interval  is  small  relatively 
to  the  period  of  the  function.  To  find  the  numerical  values  of  the  deriva- 
tives it  is  not  necessary  that  the  analytical  expression  of  the  function  should 
be  known  ;  for,  rearranging  the  terms  of  the  formula  of  Bessel  and  Stirling 
according  to  ascending  powers  of  n  and  comparing  coefficients, 

(Bessel.)  (Stirling.) 

-..  .^-Ifo.-K  + 

f."  =       (*-*',-T<r  <*  +  *«.+  •  •  •)         =       (*.-**,+ 


Hence,  to  compute  the  first  derivative,  say  from  Stirling's  formula,  when 
the  6th  differences  and  -fa  of  the  mean  of  the  corresponding  third  differences 
are  negligible,  it  is  only  needful  to  take  the  mean  of  the  first  differences  pre- 
ceding and  following  the  tabular  value  of  the  function,  subtract  from  it  one- 
sixth  (£)  of  the  mean  of  the  corresponding  third  differences,  and  divide  the 
result  by  o>. 

Newton's  formula  gives  for  arguments  near  the  beginning  of  the  series  of 
tabular  values  : 


METHODS   OF   INTERPOLATION.  XXXV11 


and  for  arguments  near  the  end  of  the  series  of  tabular  values, 
F;  =  ±  («'  +  *  *'  +  i  c"  +  i  d"  +  \  e'"  +  .  .  . 
F>'  =  4  (<*'  +  c"  +  H  d"  +  f  *'"  +  .  .  .) 


The  differences  of  the  derivatives  may  of  course  be  found  and  discussed 
in  the  same  manner  as  those  of  any  other  function,  and  the  higher  deriva- 
tives, Fn"  ',  Fn"  t  .....  can  be  expressed  in  terms  of  the  differences  of  Fn  . 
To  distinguish  the  differences  of  F'  from  those  of  Ft  they  may  be  denoted 
by  Greek  letters,  and  the  notation  is  exhibited  in  the  following  scheme  : 


a  y  a^  -\-  a    =  2  aQ 

F;  ft        s» 

ai  7i  7i  +  y  =  2  7o 

FS  A 

s 

^ 

Using  Stirling's  formulae,  page  xxxvi,  the  successive  derivatives  inclusive 
of  fifth  differences  are  now 


and  the  interpolation  formula  may  be  written 


or,  neglecting  fifth  differences, 


and  for  backward  interpolation 

/         n         \    n*  a          n    (  n2  \     ~| 

;'  --ao  +-  ^o-  _  (-  --  :)  yoj. 


XXXV111  METHODS   OF   INTERPOLATION. 

In  the  tables  which  follow,  the  first  derivatives  multiplied  by  <o  are  tabu- 
lated in  units  of  the  last  decimal  place  of  the  tabulated  function  (except 
Table  VII),  and  the  remaining  quantities  required  in  the  computation  can 
be  found  by  mere  inspection.  The  higher  order  of  differences  will  be  needed 
only  for  a  very  few  arguments  at  the  beginning  or  end  of  those  tabular 
values  whose  numerical  magnitudes  approach  o  or  oo.  For  the  remaining 
arguments  it  will  be  found  that  the  -£$  part  of  the  second  difference  of  to  Fnf 
is  not  great  enough  to  influence  the  result,  and  it  is  therefore  sufficient  to  use 


2 

wao  being  the  mean  first  difference  of  w  F'  corresponding  to  F0.  This  formula 
is  rigorous  when  third  differences  are  zero.  In  most  cases °  can  be  found 

mentally,  and  since  o>  f  Fj  -\-  —  oj  is  here  to  be  regarded  as  an  interpolated 

value  of  w  F0',  no  confusion  can  arise  as  to  the  sign  of  the  correction.  It  thus 
becomes  almost  as  easy  to  include  ^  ao  in  the  computation  as  to  omit  it.  A 
convenient  rule  is  :  Find  by  linear  interpolation  the  value  ^  F'  for  one-half 

the  interval  f  —  J  ;  multiply  this  interpolated  value  by  the  entire  interval  (?i) 

and  apply  the  product  to  the  tabular  value  of  the  function,  either  positively 
or  negatively,  according  as  the  function  is  increasing  or  decreasing.  To 
illustrate  the  application  of  this  rule,  find  Iog10  sinh  0.00304.  In  this  case 
n  =  0.4  and  the  table  gives 

^0  =  7-4771 2;  «>F0'  =  1447.7;  «*«»>  =  -48,3, 

the  last  two  quantities  being  expressed  in  units  of  the  fifth  decimal  place. 
Interpolating  a>  F'  linearly  for  one-half  the  interval, 

H 

u)  Fn  =  to  (F0f  -\ s)—  J447»7  —  0.2  x  48,3  =  1438,0  ; 

~ 

multiplying  this  value  by  n  and  adding  the  result  to  the  tabular  value  of  the 
function,  there  results 

/;=  1438,0  X  0.4  + 7. 47712 -=7.48287. 
The  corresponding  difference  formula  (Bessel's)  is 


The  derivative  formula  (£)  with  two  terms  has  the  advantage  of  being  much 
more  convenient  than  the  difference  formula,  while  the  accuracy  of  the  two 
is  the  same  (five-eighths  of  a  unit)  when  the  derivatives  are  tabulated  to  the 


METHODS   OF   INTERPOLATION.  XXXIX 

same  order  of  decimal  as  the  function.  In  the  case  of  linear  interpolation, 
however,  it  is  in  general  more  accurate  to  use  the  differences,  the  maximum 
error  of  the  difference  formula  being  one -half  of  a  unit  and  that  of  the  de- 
rivative formula  three-fourths  of  a  unit  in  the  next  succeeding  decimal  place. 
The  accuracy  of  the  two  formulas  is  the  same  when  the  next  succeeding 
decimal  of  the  derivative  is  tabulated.  The  error  of  the  derivative  formula 
is  then  simply  the  error  of  the  tabular  value,  while  the  error  of  the  difference 
formula  may  be  =,  >  or  <  than  that  of  the  tabular  value,  but  is  never  greater 
than  one-half  of  a  unit. 

Interpolation  formulas  which  are  applicable  only  to  a  single  function  are 
rarely  advantageous,  because  as  much  time  is  often  consumed  in  looking  them 
up  as  is  saved  by  employing  them  ;  but  some  formulas  applicable  to  hyper- 
bolic functions  are  so  simple  that  when  once  suggested  they  can  hardly  be 
forgotten.  Thus,  Taylor's  theorem  gives  at  once 

n2  o>2                     n3  co3 
cosh  (u  -j-  n  o>)  —  cosh  u  =  n  o>  sinh  u  -| —  cosh  u  -j j—  sinh  u  -f  .   .   . , 

and  the  form  for  the  sine  is  of  course  similar.  Again,  when,  as  here,  the 
cosine  is  tabulated  with  an  argument  in  terms  of  radians, 

cos  (u  +  n  co)  —  cos  u  =  —  no)  sin  u —  cos  u  -j j—  sin  u  -f-  .  .  .  . , 

the  series  for  the  sine  being  similar. 
So,  too, 

logc  (u  +  n w)  —  log,,  u  =  loge  (J  +  -^ 
n  ot         .    n*  u?         .    n*  «>3 


Simplest  of  all  is  the  exponential, 

eu  +  n»_eu  ^euen<*_l=e 


=  eu(-\-  o.  01  n  +  o.ooo,  05  rc2  -f  0.000,000,167  n3  +  .   .   .),  («>  —  o.oi) 
=  £"(+  o.  ooi  n  -f-  o.ooo,  000,5  n2  -f-  .   .   .).  (</>=o.ooi) 


The  series  in  ni»  may  be  replaced  by  7z,  and  this  may  have  any  finite  value. 
Especially  when  a  computing  machine  is  available,  this  formula  is  easily  ap- 
plied and  is,  of  course,  rigorous. 

From  time  to  time  inverse  interpolation  by  a  method  more  accurate  than 
first  differences  is  called  for  ;  indeed,  whenever  interpolation  of  a  function 
by  higher  differences  is  needful,  it  is  equally  needful  that  the  argument  cor- 
responding to  a  given  function  should  be  ascertained  by  a  like  process.  The 
method  ordinarily  pursued  in  such  cases  is  to  estimate  two  values  of  the  argu- 
ment, one  a  little  greater  and  the  other  a  little  less  than  that  of  the  required 
argument,  interpolate  corresponding  values  of  the  function,  and  finally  inter- 
polate linearly  over  the  reduced  interval  for  a  final  value  of  the  argument. 


xl  METHODS   OF   INTERPOLATION. 

Another  method  consists  in  interpolating  values  of  the  function  and  its  deriv- 
atives for  an  approximate  value  of  the  required  interval  and  then  computing 
a  correction  to  this  approximate  value  by  means  of  a  reversed  Taylor's  series.1 
If  second  differences  only  are  to  be  taken  into  account,  the  usual  method 
of  procedure  is  to  estimate  an  approximate  value  of  w,  say  ri  ',  and  with  this 
estimated  value  we  interpolate  linearly  as  before  and  find  the  value  of  &  /v 

~T 

corresponding  to  one-half  of  the  estimated  interval  (  —  —  J  .    Then  the  required 

interval  («)  is  equal  to  the  difference  between  the  given  value  and  the  nearest 
tabular  of  the  function  divided  by  w  Fn>  .  This  method  is  in  fact  simply  the 

reverse  of  the  one  for  direct  interpolation.  A  recomputation  is  of  course 
necessary  if  the  values  of  n  and  n'  are  not  practically  the  same.  As  an  illus- 
tration, find  u  when  Iog10  sinh  11  —  7.48287.  We  first  compute 

,        7.48287  —  7.47712 
1448,0 

then  the  value  of  w  /v   in  terms  of  the  last  tabular  unit  is  found  as  before 

2 

by  linear  interpolation  to  be  1438,0.     Hence 

7.48287  —  7.47712 
n  =  —  -  -  —^       -  =  0.40  and  u  =  0.00304. 

Since  the  estimated  and  computed  values  of  the  interval  agree,  there  is  no 
need  of  a  recomputation. 

The  methods  which  are  based  upon  an  estimated  value  of  the  argument 
are  unsystematic  and  clumsy.  It  is  much  better  to  use  a  formula  which 
gives  the  required  result  by  a  direct  and  rigorous  method.  To  find  such  a 
formula,  divide  Taylor's  series  (eq.  a)  by  w  /?',  and  put 

Fn  —  F0  «S  F'f  atFJ"  ^  F»  "5  /o'     . 


then  the  interpolation  formula  may  be  written 


Reversing  this  series  in  accordance  with  the  relation,2 

x  =  2-  +  ^  (  -  «,)  +  4  (  —  «0  «,  +  2  a?) 


0  «i  ^  —  5  «i 

2  «   «^  —  2  1 


1  Rice's  Theory  and  Practice  of  Interpolation,  section  83. 

2  Prof.  James  McMahon  :  "  On  the  General  Term  in  the  Reversion  of  Series."     Hull. 
Am.  Math.  Soc.,  April,  1894. 


METHODS   OF   INTERPOLATION.  xli 

which  is  the  reversed  series  of 

and  rearranging  the  terms,1 

n  =  nl-}-nl    [ —  ^/2  +  2  (^/2)2 —  5  (nif^  +  14  (ni/2Y  +  •   •   •] 
+  "?  [«,/,  (-1+5  («!/,)  -  21  (^/2)2  +  .   .  )] 
+  v*  \_nJi  (—1+6  «!/,)  +  3  (»i/8  )2  +•...] 
+  «/ [-«i/.+  •   •   •]      •  ,     W- 

In  the  actual  computation  it  is  convenient  to  put 

r=     n'     ; 

2  u>  /*" ' 

then,  when  successive  values  of  «»  Fn  are  tabulated  in  units  of  the  last  decimal 
place,  and  Stirling's  coefficients  are  used, 

nif*  =  rt»(ao  —  :k  7o)  ^1/3  =  i  r  w  (A  —  T2  So) 

«i /4  =  T2  r  <o  y0  Wi/5  —  <rV  ^  »  80- 

The  formula  is  rigorous  inclusive  of  fifth  differences,  and  does  not  require 
the  computation  of  an  approximate  value  of  n.  It  is  applicable  to  any  func- 
tion or  series  of  tabulated  values  whose  successive  derivatives  become  evanes- 
cent. It  is  particularly  convenient  when  differences  higher  than  the  second 
are  neglected.  The  formula  then  becomes 

n  =  nl  +  «!  [ —  r  w  a0  -\-  2  (ra>  a0)2  —  5  (r  a>  a0)3  +  14  (ro)  a0)4] . 

Since  r  a  a0  is  a  very  small  quantity,  the  higher  powers  are  seldom  needed,  and, 
should  they  be  required,  are  easily  taken  into  account.  As  an  example,  let 
it  be  required  to  find  u  when  Iog10  sinh  u  =  7.48287.  We  compute 

».=  7.48287 -7.477i2   =04Q 


»!  0.40 

r=-  -1—  7-  =  -  -  -  =  0.0001; 

20*  F9         2  x  i447>7 
and 

nlrioaQ  =  0.40  x  o.oooi  X  (  —  48,3)  =  o.oo. 

Hence  n  =  n^  =  0.40  and  w  =  0.00304,  the  same  as  obtained  by  the  other 
method. 

When  Fn  =  eu,  it  is  easily  shown,  either  by  means  of  series  (d)  or  by  inde- 
pendent methods,  that 


n=  +  nl  —  0.005  n\  +  0.000,033  ?/j3  +  .  .  .  ,     (a»  =  o.oi  ) 

n=-\-nl  —  0.0005  V  +  .....  O  =  o.ooi) 

These  formulae  afford  an  easy  means  of  finding  the  natural  logarithm  of  a 


1  See,  also,  "  Inverse  Interpolation  by  Means  of  a  Reversed  Series,"  Phil.  Mag.,  May,  1908. 


xlii 


METHODS    OP   INTERPOLATION. 


number  from  the  tabular  values  of  e±u.     Thus,  to  find  the  natural  logarithm 
of  0.9642102,  we  compute 

0.9646403  —  0.9642102 

ni  —  —  — 7- — 7 —  ~==r°'44587' 

0.0009646403 

Substituting  in  the  last  of  the  above  equations 

n  =  0.44587  —  0.0005  x  (o.45)2  =  0.44577, 
hence  nat  log  of  0.9642102  =  —  0.0364458. 

One  of  the  most  important  applications  of  differences  is  the  detection  of 
errors  in  values  tabulated  at  equal  intervals  of  the  argument.  It  may  be 
shown  by  substitution  in  the  schedule  of  differences  (page  xxxiv)  that  an 
error,  +  e,  in  FQ  produces  errors  in  the  successive  differences  of  any  order 
which  are  multiples  of  e,  the  law  of  distribution  of  the  multiples  being  that 
of  the  corresponding  coefficients  of  the  binomial  theorem,  and  the  signs  of 
the  errors  being  alternately  positive  and  negative.  Since  some  order  of  dif- 
ferences of  every  continuous  function  must  vanish,  the  presence  of  an  error 
in  a  tabular  value  must  ultimately  result  in  producing  successive  differences 
of  a  certain  order  which  alternate  in  sign.  A  comparison  of  these  differences 
with  the  corresponding  binomial  coefficients  enables  one  to  estimate  the  mag- 
nitude of  the  error.  Thus  in  the  series  which  follows  : 


X 

X3 

A' 

A" 

A"' 

Aiv 

13 

2197 

547 

14 

2744 

84 

631 

6 

15 

3375 

90 

+  2 

721 

8 

16 

4096 

98 

-  8 

819 

0 

17 

4915 

98 

+  12 

917 

12 

18 

5832 

110 

-  8 

1027 

4 

19 

6859 

114 

+  2 

1141 

6 

20 

8000 

120 

1261 

21 

9261 

the  alternation  in  sign  occurs  in  the  fourth-order  differences,  and  the  numer- 
ical values  are  twice  the  coefficients  of  (a  +  £)4.  Hence  there  is  an  error  of 
4- 2  units  in  the  value  4915.  The  corrections  —  2,  +8,  — 12, -f  8, — 2  ap- 
plied to  the  fourth  differences  causes  them  to  vanish,  and  the  corrections  —  2, 
4-6,  — 6,  4-2  applied  to  the  third  differences  reduces  them  to  a  constant 

This  method  is  particularly  useful  in  detecting  large  accidental  errors  in  a 
series  of  .observed  values  and  in  estimating  their  magnitudes. 


DESCRIPTION  OF  TABLES. 


Table  I  is  devoted  to  5-place  values  of  the  logarithmic  hyperbolic  sine, 
cosine,  tangent,  and  cotangent  of  u  expressed  in  radians.  The  argument 
u  advances  by  ten-thousandths  from  o  to  o.i,  by  thousandths  from  o.i  to 
3.0,  and  by  hundredths  from  3.0  to  6.0  In  this  as  in  all  the  tables  (except 
Table  VII),  instead  of  the  first  differences,  the  first  derivatives  of  the  func- 
tions multiplied  by  the  tabular  interval  (w)  are  tabulated  in  units  of  the  last 
decimal  place,  under  the  heading  w/^'.  As  noted  above,  this  agrees  with 
much  of  the  most  authoritative  modern  practice  and  facilitates  interpolation. 
It  did  not  appear  worth  while  to  extend  the  tabulation  of  the  table  beyond 
six  radians,  because  higher  values  are  seldom  needed  ;  but  in  Table  IV  a  few 
very  high  values  of  e  -u  are  given,  from  which  in  case  of  need  the  hyper- 
bolic functions  can  be  found. 

In  Table  II  the  natural  values  of  the  hyperbolic  functions  are  tabulated 
for  the  same  arguments  as  in  Table  I.  In  some  instances  the  values  are 
given  to  one  or  to  two  places  of  decimals  more  than  would  be  obtained  by 
taking  the  inverse  logarithms  of  the  preceding  table. 

Table  III  gives  sin  u  =  —  i  sinh  iu  and  cos  u  =  cosh  in  with  their  loga- 
rithms to  5  decimal  places,  the  argument  u  being  expressed  in  radians. 
The  tabulation  extends  from  u  =  o.oooo  to  o.  1000,  and  from  u  =  o.  100  to 

i. 600,  because  90°  =  1.570  7963  radians;  so  that,  this  value  of  --  being 

borne  in  mind,  the  table  affords  the  means  of  finding  the  sine  or  cosine  of  any 
arc  expressed  in  radians. 

Independently  of  hyperbolic  functions,  this  table  is  often  convenient.  It 
also  facilitates  the  computation  of  the  principal  hyperbolic  functions  of 
complex  variables.  Thus 

sinh  (ft  ±  iv)  =  sinh  u  cos  v±i  cosh  u  sin  v, 
cosh  (u  ±  iv)  =  cosh  u  cos  v  =±=  /  sinh  u  sin  v, 

and  to  compute  either  of  these  functions  it  is  only  needful  to  take  out  two 
tabulated  logarithms  from  Table  III,  two  from  Table  I,  make  two  additions, 
and  look  out  two  antilogarithms.  It  is  of  course  conceivable  that  all  the 
four  quantities  involved  should  be  tabulated  once  for  all ;  but  even  if  u  and 
v  advanced  only  by  hundredths,  such  a  table  would  occupy  200  pages.  To 
find  from  it  functions  corresponding  to  u  and  v  expressed  in  thousandths 
would  require  three  interpolations — a  process  quite  as  laborious  as  the  use 
of  the  tables  here  given. 

Space  which  would  otherwise  be  vacant  is  utilized  to  give  the  angular 
values  of  the  radian  arguments,  or  a  table  of  conversion  of  radians  from 

xliii 


xliv  DESCRIPTION    OF   TABLES, 

o.oooo  to  o.  1000  and  from  o.  100  to  1.600  into  degrees,  minutes,  seconds, 
and  hundredths  of  a  second. 

Table  IV  gives  the  values  of  Iog10  eu  ,  eu  and  e  ~u  to  7  decimal  places  from 
u  =  o.ooo  to  3.000  and  from  3.00  to  6.00.  The  values  of  eu  and  e~ "  enter 
into  a  vast  number  of  equations  representing  natural  phenomena,  especially 
those  (as  Cournot  remarked)  which  can  be  classed  under  the  generic  denom- 
ination of  phenomena  of  absorption  or  gradual  extinction.  The  ascending 
and  descending  exponentials  may  be  regarded  at  will  either  as  hyperbolic 
functions  or  as  independent  components  of  hyperbolic  functions,  since 

e  ±  "  =  cosh  u  ±  sinh  u 
while,  on  the  other  hand, 

eu  —  e~u                        eu  -f  e~u 
sinh  21  = ;  cosh  u  = ; 


e  u  —  e~u  TT 

tanh  u  =  ——-      —  -  ;  gd  u  ==  2  tan  ~leu  --  . 

6       ~T~   6  2 

It  is  further  evident  that  a  table  of  e  ±  "  is  a  table  of  natural  antilogarithms. 
Formula  e  on  page  xli  affords  an  easy  means  of  obtaining  the  natural  loga- 
rithm of  a  number  from  the  tabular  values  of  c±u.  It  is  of  course  unneces- 
sary to  give  the  derivative  of  eu,  since  this  is  eu,  while  the  derivative  e~u  is 
—  e  ~M.  In  general  the  interpolation  or  extrapolation  of  the  function  is 
very  easy.  (See  formula  c,  page  xxxix).  The  logarithm  of  e  ~  "  is  not  given 
because,  being  merely  the  arithmetical  complement  of  the  Iog10  eu,  it  can 
be  read  off  as  fast  as'it  can  be  written  down. 

In  any  table  of  Iog10  eu  where  the  interval  of  u  is  %  the  difference  of 
successive  logarithms  is  constant  and  equal  to  ^  Iog10<?  or  0.4342  9448*0. 
If  the  logarithm  of  eu  +  n<a  is  required,  this  will  be 

(u  +  not}  Iog10  e  =  Iog10  eu  +  nu  Iog10  e. 

Hence  it  is  practicable  to  prepare  an  extended  table  of  proportional  parts  or 
a  table  of  n  Iog10  e  which  is  applicable  to  any  table  of  Iog10  eu  when  the  tab- 
ulated values  are  multiplied  by  </>.  Such  an  auxiliary  table  is  given  at  the 

close  of  Table  IV,  in  which  the  argument  —  varies  from  o.ooo  to  0.500.     If 

ID  is  unity,  this  is  merely  a  5-place  table  of  Iogi0  eu  .  If,  on  the  other  hand, 
ia  is  o.ooi,  as  in  the  earlier  part  of  Table  IV,  the  auxiliary  table  gives  the 
increments  corresponding  to  n  to  8  places  of  decimals.  Thus,  if  log,0  &  -088245 
is  required,  Table  IV  gives  log,0  <?°-088  =  0.0382179,  the  auxiliary  table  gives 

for—  =  0.245,  n  log,,,  e  =  0.10640;  and  since  &  =  o.ooi,  <u  n  Iog10  c  = 
at 

0.00010640,  which  added  to  log,0  £°-088,  gives  log,0  <?°-088245  ==  0.0383243.     In 


the  latter  portion  of  Table  IV  &  is  only  o.oi;  so  that,  if  the  Iog10  e*-™- 
wanted,  the  main  table  gives  log  ^•°°=  1.3028834,  and  ^  times  n  log  c  is 
o  0010640;  so  that  the  required  number  is  i  3039474. 


DESCRIPTION     OF   TABLES. 

When  Iog10  eu  is  required  for  u  >  6.00  the  auxiliary  table  is  insufficient  to 
give  7-place  values.  Then  the  main  table,  IV,  may  be  used  as  an  auxiliary 
table.  Thus 

I0g  ^11.088245  =  I0g  e\\  _f_  I0g  ^0.088245 

=  4.7772393  +0.0383243  =  4.8155636. 

In  the  second  part  of  Table  IV  values  of  e  -  u  and  the  logarithms  of  eu  are 
given,  u  varying  from  i  to  100.  The  logarithms  are  given  to  10  decimals  ; 
the  other  functions  to  9  significant  figures.  Such  high  values  are  seldom 
needed,  but  are  included  here  lest  these  tables  might  some  times  fail  the 
computer. 

Table  V  gives  the  natural  logarithms  of  numbers  from  i  to  1000,  with 
their  derivatives  to  5  places  of  decimals.  These  derivatives  are  merely  the 

reciprocals  of  the  arguments,  and  since  loge  (—-)  =  —  loge>',  the  logarithms 

of  the  derivatives  are  the  tabulated  logarithms  taken  negatively.  The 
table  thus  gives,  in  addition  to  the  logarithms  of  1000  whole  numbers,  the 
logarithms  of  1000  proper  fractions  lying  between  o.ooi  and  unity. 

THe  interpolation  of  natural  logarithms  is  much  less  simple  than  is  that 
of  common  logarithms,  and  this  is  the  main  reason  why  the  latter  are  pre- 
ferred for  computation.  A  few  simple  rules,  however,  facilitate  the  needful 
calculations.  When  the  natural  logarithm  of  a  vulgar  fraction  is  required 
it  is  best  to  look  out  the  logarithm  of  both  numerator  and  denominator  and 
subtract.  If  the  natural  logarithm  is  required  of  a  fractional  number  stated 
decimally  and  less  than  21.000,  no  attempt  should  be  made  to  interpolate  it 
directly,  because  the  third  differences  of  the  table  cannot  be  neglected  for 
numbers  so  near  the  beginning  of  the  table.  If  the  number  lies  between 
10.000  and  21.000,  as,  for  example,  12.345,  it  should  be  written  123.45  / 10> 
and  the  required  logarithm  will  be  nat  log  123.45  —  nat  log  10.  It  is  safe  to 
interpolate  the  first  of  these  between  nat  log  123  and  nat  log  124,  using  the 
formula  for  second  differences.  If  the  number  whose  logarithm  is  to  be 
found  lies  between  i  and  10,  as,  for  example,  8.2468,  it  should  be  written 
824.68  / 100,  so  that  the  required  quantity  is  nat  log  824.68  —  nat  log  100. 
The  first  of  these  logarithms  can  be  found  by  using  only  the  mean  first 
differences  or  the  tabulated  derivatives  between  the  logarithms  of  824  and 
825.  For  values  of  the  argument  between  21  and  158  interpolation  requires 
the  use  of  second  differences,  while  above  158  average  first  differences  or 
the  first  derivative  is  sufficiently  accurate,  inasmuch  as  the  error  involved  is 
less  than  half  a  unit  in  the  fifth  decimal  place. 

It  would  be  possible  to  interpolate  the  negative  logarithms  of  the  smaller 
fractions  given  by  the  derivatives — that  is,  from  the  reciprocal  of  159  on  to 
the  end  of  the  table,  or  for  numbers  between  0.00628  and  o.ooioo — but  this 
would  not  be  expedient,  because  these  reciprocals  are  themselves  rounded 
values.  If  the  natural  logarithm  of  0.0068352  is  wanted  as  accurately  as 


DESCRIPTION    OF  TABLES. 

the  tables  will  give  it,  it  is  best  to  find  the  logarithm  of  683.52  and  to  sub- 
tract from  it  the  logarithm  of  100,000.  (See  also  formula  e,  page  xli.) 

The  use  of  second  differences  may  be  avoided  altogether  if  the  computer 
chooses,  for  any  number  not  lying  between  158  and  1,000  may  be  multiplied 
and  divided  by  another  number  which  will  bring  the  numerator  within 
these  limits.  Thus,  if,  as  before,  nat  log  12.345  is  required,  this  number 
may  be  written  246.90  /  20,  and  the  natural  logarithm  of  the  numerator  found 
by  help  of  the  derivative,  less  nat  log  20,  is  the  required  value. 

The  awkwardness  of  a  table  of  natural  logarithms  is  inherent  and  cannot 
be  overcome  by  any  device.  It  depends  on  the  fact  that  e  and  the  base  of 
numeration,  the  number  10,  are  incommensurable  quantities.  If  our  numer- 
ation were  duodecimal,  as  it  might  have  been  had  six  fingers  to  a  hand  been 
the  rule  instead  of  the  exception,  12  would  also  have  been  the  most  convenient 
base  for  a  table  of  logarithms.  A  great  table  of  natural  logarithms,  such  as 
Barlow's  8-place  table  of  all  numbers  from  i  to  10,000,  is  only  a  little  more 
convenient  than  that  here  offered,  and  with  it,  too,  it  is  expedient  to  multiply 
any  small  number  by  a  factor  such  that  the  product  approaches  10,000. 

Table  VI  gives  the  values  of  the  gudermannian  of  u  to  7  places  from 
u  =  o.ooo  to  u  =  3.000  and  from  u  =  3.00  to  u  =  6.00.  In  this  table  u  is 
expressed  in  radians,  and  %d  u  both  in  radians  and  in  angular  measure.  For 
theoretical  work  the  gudermannian  in  radians  is  usually  the  more  convenient, 
but  for  use  in  finding  hyperbolic  functions  it  must  be  reduced  to  an  angle. 

The  gudermannian,  gd  #,  is  connected  with  the  hyperbolic  functions  by 
the  following  well-known  relations  : 

sinh  u  =  tan  gd  u  /  cosh  u  =  sec  gd  u  ;  tanh  u  =  sin  gd  u 
tanh  --  =  tan  \  gd  u  ;  u  =  loge  tan  ( -  -  4- 

Thus  Table  VI,  with  the  help  of  a  y-place  table  of  logarithms  of  the  cir- 
cular functions,  gives  y-place  values  of  the  hyperbolic  functions. 

The  derivative  of  gd  u  is  sech  u,  and  can  be  used  independently  of  the 
gudermannian. 

Table  VII  is  substantially  a  reversion  of  Table  VI,  and  gives  the  anti- 
gudermannian  in  terms  of  the  gudermannian,  both,  however,  being  expressed 
in  minutes  and  decimals  of  a  minute.  If  m  is  the  antigudermannian  ex- 
pressed in  minutes  and  u  the  same  function  expressed  in  radians, 


™  =  3437-7468  u  =  3437.7468  loge  tan  (—  - 

Table  VII  is  a  table  of  m,  and  if  m  is  multiplied  by  o.ooo  2908  8821  the 
product  is  u  in  radians.  This  table  is  known  to  navigators  as  a  table  of 
Meridional  Parts  for  a  Spherical  Globe.  It  is  frequently  of  use  in  the  dis- 
cussion of  physical  questions  and  is  the  very  foundation  of  navigation  with 
Mercator  charts.  In  the  more  modern  works  on  navigation,  however,  the 


DESCRIPTION    OF   TABLES.  xlvii 

ellipticity  of  the  meridian  is  allowed  for  in  computing  tables  of  meridional 
parts,  and  consequently  this  table  will  probably  never  be  reproduced  in  a 
navigator.  For  this  reason  it  is  here  preserved  for  computers  who  are  not 
engaged  in  navigation. 

To  test  this  table,  which  is  borrowed  from  Inman,  200  of  the  values,  or 
one  in  every  27  entries,  were  compared  with  Gudermann's  y-decimal  place 
table  of  the  antigudermannian  in  radian  measure.  In  nearly  all  cases  Inman's 
last  figure  was  confirmed,  but  in  a  few  instances  the  last  figure  is  incorrect 
by  a  unit.  Inquiry  into  these  cases  showed  that  the  maximum  error  detected 
was  less  than  o  006  of  a  minute.  Thus  the  last  figure  is  not  absolutely  trust- 
worthy, but  is  near  enough  to  enable  the  computer  to  interpolate  accurately 
to  5  places.  If  7  places  of  the  antigudermannian  are  required,  they  can  be 
found  by  inverse  interpolation  in  Table  VI. 

The  earlier  part  of  Table  VII  may  be  interpolated  by  first  differences  with- 
out considerable  error.  At  about  84°3O/  one-eighth  of  the  second  difference 
becomes  approximately  half  a  unit  in  the  last  tabulated  place,  and  beyond 
this  point  second  differences  should  be  taken  into  account. 

Table  VIII  is  a  table  for  converting  radians  into  angular  measure  and 
vice  versa.  A  few  numerical  constants  are  appended. 


HISTORICAL  NOTE. 


The  first  and  most  important  application  of  the  functions  now  known  33 
hyperbolic  was  made  by  Gerhard  Mercator  (Kremer)  when  he  issued  his 
map  on  "  Mercator 's  projection,"  in  1569,  or,  as  some  say,  in  1550,  while 
Bowditch  gives  the  date  as  1566.  To  this  day  substantially  all  of  the  deep- 
sea  navigation  of  the  world  is  carried  on  by  the  help  of  this  projection, 
which  has  been  modified  only  to  the  extent  of  correcting  the  "meridional 
parts"  for  the  ellipticity  of  the  meridian.  Mercator' s  problem  was  to  find 
a  projection  on  which  the  loxodrome  should  be  a  straight  line.  The  solu- 
tion is  unique,  and  for  a  spherical  globe  is  \—gd —  where  A  is  the  latitude, 

m  the  "meridional  part,"  or  the  ordinate  on  the  projection  of  a  point  in 
latitude  A.,  and  a  is  the  radius  of  the  sphere.  Of  course,  this  relation  gives 

m 

—  =  loge  tai 

a 

and  this  Mercator  must  have  tabulated.  He  published  his  map  without 
explanation,  however,  and  it  was  left  to  Edward  Wright  in  1599  to  state 
the  formula  for  m. 

"The  actual  inventor  of  the  hyperbolic  trigonometry,"  says  Professor 
McMahon,  "was  Vincenzo  Riccati,  S.  J.  (Opuscula  ad  res  Phys.  et  Math, 
pertinens,  Bonpniae,  1757).  He  adopted  the  notation  Sh.  <j>,  C/i.  <#>,  for  the 
hyperbolic  functions  and  Sc.  <£,  Cc.  <f>  for  the  circular  ones.  He  proved  the 
addition  theorem  geometically,  and  derived  a  construction  for  the  solution 
of  a  cubic  equation.  Soon  after  Daviet  de  Foncenex  showed  how  to  inter- 
change circular  and  hyperbolic  functions  by  the  use  of  |/  -  —  i ,  and  gave 
the  analogue  of  de  Moivre's  theorem,  the  work  resting  more  on  analogy, 
however,  than  on  clear  definition  (Reflex,  sur  les  quant,  imag.,  Miscel. 
Turin  Soc.,  Tom.  i).  Johann  Heinrich  Lambert  systematized  fhe  subject 
and  gave  the  serial  developments  and  the  exponential  expressions.  He 
adopted  the  notation  sinh  «,  etc.,  and  introduced  the  transcendent  angle, 
now  called  the  gudermannian,  using  it  in  computation  and  in  the  construc- 
tion of  tables1." 

C.  Gudermann  published  an  important  memoir  on  Potential  or  Cyclic- 
hyperbolic  functions  in  1830*,  followed  by  extended  tables.  In  recogni- 

1  James  McMahon,  Hyperbolic  Functions,  p.  71. 

7  Crelle's  Journal,  vols.  6,  7,  8,  and  9.  These  memoirs  were  afterwards  reprinted  in  a 
separate  volume.  xlviii 


HISTORICAL     NOTE.  xlix 

tion  of  his  contributions  to  the  subject,  Cay  ley,  in  I862,1  proposed  the 
name  gudermannian2  for  the  angle  which  Lambert  called  transcendent, 
and  which  had  been  variously  designated  by  others.  Among  other  more 
recent  works  on  hyperbolic  functions  are  Siegmund  Giinther's  Lehre 
von  den  Hyperbelfunctionen,  1881,  and  Mr.  James  McMahon's  Hyper- 
bolic Functions,  4th  edition,  1906. 

The  first  large  table  of  hyperbolic  functions  we  have  met  with  is  Legen- 

dre's  table  of  log  tan  (  —  +  —  )  to  12  decimals.     The  argument  advances 
\  4         2  / 

by  increments  of  30  minutes,  but  five  differences  are  tabulated  to  facilitate 
interpolation.3  Gudermann  in  1831  published  a  table  of  the  same  func- 
tion, using  centesimal  degrees  and  advancing  by  hundredths  of  a  degree 
(o°o'32".4)  from  o  to  an  entire  quadrant,  the  function  being  given  to  seven 
decimal  places.  This  was  later  supplemented  by  a  table  advancing  by  hun- 
dredths of  a  degree  from  88°  to  100°,  the  function  being  given  to  eleven 
decimal  places.  Gudermann  also  gave  a  9-place  table  of  log  cosh  u,  log 
sinh  u,  and  log  tanh  u,  from  u  =  2.000  to  u  =  5.000,  and  a  lo-place 
table  of  the  same  functions  from  u  =  5.00  to  u  =  12.00. 

In  1862  Z.  F.  W.  Gronau4  published  a  5-place  table  of  hyperbolic  func- 
tions, the  argument  being  the  gudermannian  gd  u  in  sexagesimal  degrees 
and  minutes.  He  tabulated  to  this  argument  log  cosh  &,  log  sinh  uy  and  the 

Briggs  logarithm  of  f  —  -f  — J  instead  of  the  natural  logarithms  of  this 

function,  following  therein  a  suggestion  of  Lambert. 

A  In  1890  W.  Ligowski  issued  his  Tafeln  der  Hyperbelfunctionen  und  der 
Kreisfunctionen,  which  is  admirably  accurate  and  much  the  most  useful 
collection  of  tables  of  the  hyperbolic  functions  hitherto  printed.  He  filled 
the  gap  left  by  Gudermann  by  computing  log  sinh  «,  log  cosh  u,  and  log 
tanh  u  from  u  =0.000  to  2.000.  These  he  gives  to  only  5  places,  but  in 
addition  he  tabulates  gd  u  in  degrees,  minutes,  seconds,  and  decimals  of  a 
second.  These  values  are  in  all  cases  sufficiently  accurate  to  enable  the  com- 
puter to  take  out  from  an  ordinary  table  of  logarithms  7 -place  values  of  the 
logarithms  of  cosh  &,  sinh  «,  and  tanh  u.  The  argument  ranges  from  o.ooo 
to  2.000  and  from  2.00  to  6.00  for  gd  u,  while  log  cosh  u  and  log  sinh  u  are 
carried  up  to  u  =  9.00.  Ligowski  also  gives  the  natural  functions  cosh  u, 
sinh  u,  cos  u,  and  sin  u  to  6  decimals  for  values  of  u  in  radians  from  o.oo  to 
2  oo,  the  cosh  u  and  sinh  u  being  continued  to  u  =  8.00.  The  only  fault 
we  can  find  with  Ligowski 's  tables  is  that  the  increments  of  the  argument 
are  sometimes  inconveniently  large. 

1  Phil.  Mag.,  vol.  24,  p.  19. 

2  Thus  spelled  in  Cayley's  paper. 

3  Exercises  de  Cal.  Int.,  vol.  2,  1816. 

*Neueste  Schriften  der  Naturforscher-Gesellschaft  in  Danzig,  vol.  6,  1862. 


1  HISTORICAL     NOTE. 

In  1883  F.  W.  Newman  published  a  12  place  table1  of  the  descending  ex- 
ponential from  it  =  o.ooo  to  u  =  15.349,  and  a  i4-place  table  of  the  same  func- 
tion advancing  by  two- thousandths  from  15.350  to  17.298  and  by  five-thou- 
sandths from  17.298  to  27.635.  In  the  same  volume  appeared  Mr.  J.  W.  L. 
Glaisher's  tables  of  the  ascending  and  descending  exponential  to  nine  sig- 
nificant figures,  with  lo-place  logarithms.  The  argument  advances  by  one- 
thousandth  to  o.i ;  by  one-hundredth  to  2.00;  by  one-tenth  to  10,  and  by  a 
single  unit  to  500. 

Mr.  A.  Forti's  Nuove  Tavole  delle  Funzioni  Iperboliche  were  pub- 
lished in  1892.  The  hyperbolic  sines,  cosines,  and  tangents,  together 
with  their  logarithms,  are  given  to  six  decimals  from  o.oooo  to  0.2000, 
from  0.200  to  2.000,  and  from  2.00  to  8.00.  Frequent  errors,  however,  of 
one,  two,  and  three  units  in  the  last  decimal  place  practically  limit  these 
tables  to  five  places.  The  gudermannian  is  tabulated  in  degrees,  minutes, 
seconds,  and  tenths  of  a  second,  and  the  logarithms  of  the  arguments  are 
given  to  seven  places. 

In  the  volume  here  presented  the  first  thousand  values  of  log  sinh  u,  log 
cosh  u,  and  log  tanh  u  have  been  computed;  the  remaining  values  have  been 
taken  from  the  tables  of  Gudermann  or  Ligowski.  The  values  of  the  nat- 
ural hyperbolic  sines  and  cosines  for  values  of  the  argument  <  o.  i  and  of 
the  tangents  for  arguments  >  2.0  have  been  computed;  the  remaining  values 
have  been  taken  from  the  tables  of  Forti  and  Ligowski.  A  recomputation 
of  a  great  number  of  the  borrowed  values  was  made  in  order  to  obtain  the 
required  accuracy.  The  values  of  coth  u  and  log  coth  u  have  been  computed. 
In  Table  III  the  sines  and  cosines  were  obtained  by  interpolation  from 
the  7-place  values  of  natural  sines  and  cosines  given  in  Hiilsse's  Vega, 
where  the  argument  is  expressed  in  angle.  The  logarithms  of  the  sines  and 
cosines  and  the  angular  equivalents  of  the  arguments  have  been  computed. 
In  Table  IV  the  values  of  c  ~u  are  all  taken  from  Newman's  great 
table.  Those  of  c  +  u  from  o.ooo  to  o.  100  and  from  i  to  100  are  from 
Glaisher's  table.  The  remainder  we  computed,  checking  the  results  by 
Glaisher's  table  or  by  reciprocating.  It  should  be  noted  that  the  7  place 
table  of  en  given  in  Hiilsse's  edition  of  Vega  is  inaccurate  and  really 
amounts  to  no  more  than  a  5  place  table.  The  logarithms  of  en  were  com- 
puted independently  of  the  values  of  eu. 
Tables  V  and  VIII  are  borrowed. 

The  values  of  gd  u  in  Table  VI  in  terms  of  angle  are  taken  from  Ligow- 
ski, excepting  the  thousand  values  between  u  =  2.000  and  3.000.  These 
were  interpolated  from  Ligowski's  values  (2.00  to  3.00)  with  due  checks  on 
his  accuracy.  In  preparing  the  table  of  gdu  in  radians  it  was  necessary  for 
us  to  make  an  independent  computation  of  this  function  from  u  =  0.300  to 
u  =  3.000  in  order  to  secure  accuracy  in  the  seventh  significant  figure. 
The  remaining  values  were  derived  from  Ligowski  by  converting  angles 

1  Cambridge  Phil.  Soc.,  Trans.,  vol.  13,  1883. 


HISTORICAL     NOTE.  li 

into  radians.     A  considerable  number  of  his  values,  however,  were  tested 
by  independent  computation. 

Table  VII  is  borrowed  from  the  Nautical  tables  of  James  Inman,  revised 
by  James  W.  Inman,  London,  1867,  with  a  few  small  corrections. 

Finally,  it  may  be  remarked  that  the  derivatives  as  given  in  these  tables 
have  been  computed  for  them.  They  are  not  derived  from  the  diSerences 
of  the  values  as  printed,  but  from  more  extended  values,  or  are  computed 
independently,  and  the  error  of  the  derivatives  as  well  as  of  the  functions  is 
less  than  one-half  of  a  unit  in  the  next  succeeding  decimal  place. 

These  tables  were  prepared  in  connection  with  the  geophysical  work  of 
the  United  States  Geological  Survey,  and  are  published  with  the  permission 
of  the  Director. 

GEORGE  F.  BECKER. 
C.  E.  VAN  ORSTRAND. 

WASHINGTON,  D.  C.,  January,  1908. 


TABLE  I 


LOGARITHMS  OF  HYPERBOLIC  FUNCTIONS 


Logarithms  of  Hyperbolic  Functions. 


u 

loq  shh  M 

*  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

-  Fo' 

log  coth  u 

o.oooo 

CO 

—  CO 

o.ooooo 

0,0 

—  oo 

=F  co 

oo 

.0001 

6.0OOOO 

43429,4 

.00000 

6.00000 

43429,4 

4.OOOOO 

.0002 

.30103 

21714,7 

.00000 

.30103 

21714,7 

3.69897 

.0003 

.47712 

14476,5 

.00000 

.47712 

14476,5 

.52288 

.0004 

.60206 

10857,4 

.00000 

.60206 

10857,4 

•39794 

0.0005 

6.69897 

8685,9 

o.ooooo 

0,0 

6.69897 

8685,9 

3-30103 

.0006 

.77815 

7238,2 

.00000 

.77815 

7238,2 

.22185 

.0007 

.84510 

6204,2 

.00000 

.84510 

6204,2 

•15490 

.0008 

.90309 

5428,7 

.00000 

.90309 

5428,7 

.09691 

.0009 

.95424 

4825,5 

.00000 

.95424 

4825,5 

.04576 

O.OOIO 

7.00000 

4342,9 

o.ooooo 

0,0 

7.00000 

4342,9 

3.OOOOO 

.OOII 

•04139 

3948,1 

.00000 

.04139 

3948,1 

2.95861 

.0012 

.07918 

3619,1 

.00000 

.07918 

3619,1 

.92082 

.0013 

•II394 

3340,7 

.00000 

.11394 

3340,7 

.88606 

.0014 

.  14613 

3102,1 

.00000 

.  14613 

3102,1 

.85387 

0.0015 

7.17609 

2895,3 

o.ooooo 

0,0 

7.17609 

2895,3 

2.82391 

.0016 

.20412 

2714,3 

.00000 

.20412 

2714,3 

.79588 

.0017 

.23045 

2554,7 

.00000 

.23045 

2554,7 

•76955 

.0018 

•25527 

2412,7 

.00000 

.25527 

2412,7 

•74473 

.0019 

.27875 

2285,8 

.00000 

.27875 

2285,8 

.72125 

O.OO2O 

7-30103 

2171,5 

o.ooooo 

0,0 

7.30103 

2171,5 

2.69897 

.0021 

.32222 

2068,1 

.00000 

.  32222 

2068,  1 

.67778 

.OO22 

.34242 

1974,1 

.00000 

.34242 

1974,1 

.65758 

.OO23 

.36173 

1888,2 

.00000 

.36173 

1888,2 

.63827 

.OO24 

.38021 

1809,6 

.00000 

.38021 

1809,6 

.61979 

0.0025 

7-39794 

1737,2 

o.ooooo 

0,0 

7.39794 

1737,2 

2.60206 

.0026 

.41497 

1670,4 

.00000 

.41497 

1670,4 

.58503 

.OO27 

.43136 

1608,5 

.00000 

.43136 

1608,5 

.56864 

.0028 

.44716 

I55IJ 

.00000 

.44716 

1551,0 

.55284 

.0029 

.46240 

1497,6 

.00000 

.46240 

1497,6 

.53760 

O.OO30 

7.47712 

1447,7 

o.ooooo 

0,0 

7.47712 

1447,6 

2.52288 

.0031 

.49136 

1401,0 

.00000 

.49136 

1400,9 

.50864 

.0032 

.50515 

1357,2 

.00000 

.50515 

1357,2 

.49485 

.0033 

.51851 

1316,0 

.00000 

.51851 

1316,0 

.48149 

.0034 

.53148 

1277,3 

.00000 

.53148 

1277,3 

.46852 

0.0035 

7.54407 

1240,8 

o.ooooo 

0,0 

7.54407 

1240,8 

2.45593 

.0036 

.55630 

1206,4 

.00000 

.55630 

1  206,4 

•44370 

.0037 

.56820 

ii73,8 

.00000 

.56820 

1173,8 

.43180 

.0038 

.57978 

1142,9 

.00000 

.57978 

1142,9 

.42022 

.0039 

•59107 

1113,6 

.00000 

.59106 

1113.6 

.40894 

0.0040 

7.60206 

1085,7 

o.ooooo 

0,0 

7.60206 

1085,7 

2.39794 

.0041 

.61279 

1059,3 

.00000 

.61278 

1059,2 

.38722 

.0042 

.62325 

1034,0 

.00000 

.62325 

1034,0 

.37675 

.0043 

.63347 

IOIO,O 

.00000 

.63347 

IOIO,O 

.36653 

.0044 

.64345 

987,0 

.00000 

.64345 

987,0 

.35655 

0.0045 

7.65321 

065,1 

o.ooooo 

0,0 

7.65321 

965,1 

2.34679 

.0046 

.66276 

944.1 

.00000 

.66275 

944,1 

.33725 

.0047 

.67210 

924,0 

.00000 

.67209 

924,0 

.32791 

.0048 

.68124 

904,8 

.00001 

.68124 

004,8 

.31876 

.0049 

.69020 

886,3 

.00001 

.69019 

886,3 

.30981 

0.0050 

7.69807 

868,6 

0.00001 

0,0 

7.69807 

868,6 

2.30103 

u 

log  tan  ad  u 

«F0' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

o>  Fo' 

log  cosh  u 

-FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0050 

7.69897 

868,6 

O.OOOOI 

0,0 

7.69897 

868,6 

2.30103 

.0051 

.70757 

851,6 

.00001 

.70757 

851,5 

.29243 

.0052 

.71601 

835,2 

.00001 

.71600 

835,2 

.28400 

.0053 

.72428 

819,4 

.00001 

.72427 

819,4 

.27573 

.0054 

.73240 

804,3 

.00001 

.73239 

804,2 

.26761 

0.0055 

7.74036 

789,6 

O.OOOOI 

0,0 

7.74036 

789,6 

2.25964 

.0056 

.74819 

775,5 

.00001 

.74818 

775,5 

.25182 

.0057 

.75588 

761,9 

.00001 

.75587 

761,9 

.24413 

.0058 

.76343 

748,8 

.00001 

.76342 

748,8 

.23658 

.0059 

.77085 

736,i 

.00001 

.77085 

736,1 

.22915 

0.0060 

7.77815 

723,8 

O.OOOOI 

0,0 

7.77815 

723,8 

2.22185 

.0061 

.78533 

712,0 

.00001 

.78532 

711,9 

.21468 

.0062 

.79239 

700,5 

.00001 

•79239 

700,5 

.20761 

.0063 

•79934 

689,4 

.00001 

.79933 

689,3 

.20067 

.0064 

.80618 

678,6 

.00001 

.80617 

678,6 

.  19383 

0.0065 

7.81292 

668,1 

O.OOOOI 

0,0 

7.81291 

668,1 

2.18709 

.0066 

.81955 

658,0 

.00001 

.81954 

658,0 

.18046 

.0067 

.82608 

648,2 

.00001 

.82607 

648,2 

.  17393 

.0068 

.83251 

638,7 

.00001 

.83250 

638,6 

.  16750 

.0069 

.83885 

629,4 

.00001 

.83884 

629,4 

.16116 

0.0070 

7.84510 

620,4 

O.OOOOI 

0,0 

7.84509 

620,4 

2.15491 

.0071 

.85126 

6n,7 

.00001 

.85125 

611,7 

.14875 

.0072 

.85734 

603,2 

.00001 

.85732 

603,2 

.14268 

.0073 

.86333 

594,9 

.00001 

.86332 

594,9 

.13668 

.0074 

.86924 

586,9 

.00001 

.86922 

586,9 

.  13078 

0.0075 

7.87507 

579,1 

O.OOOOI 

0,0 

7.87505 

579,0 

2.12495 

.0076 

.88082 

57i,4 

.00001 

.88081 

57i,4 

.11919 

.0077 

.88649 

564,0 

.00001 

.88648 

564,0 

.11352 

.0078 

.89210 

556,8 

.00001 

.80209 

556,8 

.  10791 

.0079 

.89763 

549,7 

.00001 

.89762 

549,7 

.  10238 

0.0080 

7.90309 

542,9 

O.OOOOI 

0,0 

7.90308 

542,8 

2.09692 

.0081 

.90849 

536,2 

.00001 

.90848 

536,i 

.09152 

.0082 

.91382 

529,6 

.00001 

.91380 

529,6 

.08620 

.0083 

.91908 

523,2 

.00001 

.91907 

523,2 

.08093 

.0084 

.92428 

517,0 

.00002 

.92427 

5i7,o 

.07573 

0.0085 

7.92942 

510,9 

0.00002 

0,0 

7.92941 

5io,9 

2.07059 

.0086 

•93450 

505,0 

.00002 

•93449 

505,o 

.06551 

.0087 

.93952 

499,2 

.00002 

.93951 

499,2 

.06049 

.0088 

.94449 

493,5 

.00002 

.04447 

493,5 

•05553 

.0089 

.94940 

488,0 

.00002 

.94938 

487,9 

.05062 

0.0090 

7.95425 

482,6 

O.OOO02 

0,0 

7.95423 

482,5 

2.04577 

.0091 

.95905 

477,3 

.00002 

.95903 

477,2 

.04097 

.0092 

.96379 

472,1 

.00002 

.96378 

472,0 

.03622 

.0093 

.96849 

467,0 

.00002 

.96847 

467,0 

.03153 

.0094 

.97313 

462,0 

.00002 

.97312 

462,0 

.02688 

0.0095 

7.97773 

457,2 

O.OOOO2 

0,0 

7.97771 

457,i 

2.02229 

.0096 

.98228 

452,4 

.00002 

.98226 

452,4 

.01774 

.0097 

.98678 

447,7 

.00002 

.98676 

447,7 

.01324 

.0098 

.99123 

443,2 

.00002 

.99121 

443,1 

.00879 

.0099 

.99564 

438,7 

.00002 

.99562 

438,7 

.00438 

O.OIOO 

8.00001 

434,3 

O.OOOO2 

0,0 

7.09999 

434,3 

2.OOOOI 

u 

log  tan  gd  u 

<•>  FQ' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

W  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

»Fo' 

log  cosh  u 

™ 

log  tanh  u 

«  Fo' 

log  coth  u 

O.OIOO 

8.OOOOI 

434,3 

O.OOOO2 

O,O 

7.99999 

434,3 

2.OOOOI 

.OIOI 

•00433 

430,0 

.00002 

8.00431 

430,0 

1.99569 

.0102 

.00861 

425,8 

.OOO02 

.00859 

425,7 

.99141 

.0103 

.01284 

421,7 

.OOOO2 

.OI282 

421,6 

.98718 

.0104 

.01704 

417,6 

.OOOO2 

.OI7O2 

417,6 

.98298 

0.0105 

8.O2I20 

413,6 

O.OOOO2 

0,0 

8.02II7 

413,6 

1.97883 

.0106 

.02531 

409,7 

.00002 

.02529 

409,7 

•97471 

.0107 

.02939 

405,9 

.OOOO2 

.02937 

405,9 

.97063 

.0108 

•03343 

402,1 

.00003 

.03341 

402,1 

.96659 

.0109 

.03744 

398,5 

.00003 

.03741 

398,4 

.96259 

O.OIIO 

8.04140 

394,8 

O.OOOO3 

0,0 

8.04138 

394,8 

1.95862 

.OIII 

.04533 

39i,3 

.00003 

.04531 

391,2 

.95409 

.OII2 

.04923 

387,8 

.00003 

.O492O 

387,7 

.0113 

.05309 

384,4 

.00003 

.05306 

384,3 

.04694 

.0114 

.05691 

381,0 

.00003 

.05689 

380,9 

•943II 

0.0115 

8.06071 

377,7 

0.00003 

0,0 

8.06068 

377,6 

1.93932 

.0116 

•06447 

374,4 

.00003 

0,1 

.06444 

374,4 

.93556 

.0117 

.06820 

371,2 

.00003 

.06817 

37i,2 

.93183 

.0118 

.07189 

368,1 

.00003 

.07186 

368,0 

.92814 

.0119 

.07556 

365,0 

.00003 

.07553 

364,9 

.92447 

O.OI2O 

8.07919 

36i,9 

0.00003 

0,1 

8.07916 

36i,9 

1.92084 

.OI2I 

.08280 

358,9 

.00003 

.08276 

.91724 

.OI22 

.08637 

356,0 

.00003 

.08634 

355,9 

.91366 

.OI23 

.08992 

353,i 

.00003 

.08988 

353,0 

.91012 

.OI24 

•09343 

350,3 

.00003 

.09340 

350,2 

.90660 

0.0125 

8.00692 

347,5 

0.00003 

0,1 

8.09689 

347,4 

I.903II 

.OI26 

.10038 

344,7 

.00003 

.10035 

344,6 

.89965 

.0127 

.  10382 

342,0 

.00004 

.  10378 

341,9 

.89622 

.0128 

.  10722 

339,3 

.00004 

.10719 

339,3 

.89281 

.OI29 

.11060 

336,7 

.00004 

.11057 

336,6 

.88943 

0.0130 

8.11396 

334,1 

0.00004 

0,1 

8.11392 

334,0 

I.8860S 

.0131 

.11728 

331,5 

.00004 

.11725 

331,5 

.88275 

.0132 

.  12059 

329,0 

.00004 

.  12055 

329,0 

.87945 

.0133 

.12386 

326,6 

.00004 

.12383 

326,5 

.87617 

.0134 

.12712 

324,1 

.00004 

.12708 

324,1 

.87292 

0.0135 

8.13035 

321,7 

0.00004 

0,1 

8.13031 

33L7 

1.86969 

.0136 

.  13355 

319,4 

.00004 

.13351 

319,3 

.86649 

•0137 

.  13673 

317,0 

.00004 

.13669 

3i7,o 

.86331 

.0138 

.13989 

.00004 

.13985 

.86015 

.0139 

.14303 

312,5 

.00004 

.14299 

312,4 

.85701 

0.0140 

8.  14614 

310,2 

0.00004 

0,1 

8.14610 

310,2 

1.85390 

.OI4I 

.  14923 

308,0 

.00004 

.  14919 

308,0 

.8508l 

.0142 

.15230 

305,9 

.00004 

.15226 

305,8 

.84774 

.0143 
.0144 

.15535 
.15838 

303,7 
301,6 

.00004 
.00005 

.15531 
.15833 

303,7 
301,6 

.84469 
.84167 

0.0145 

8.16138 

299,5 

0.00005 

0,1 

8.16134 

299,5 

1.83866 

.0146 

.  16437 

297,5 

.00005 

.  16432 

297,4 

.83568 

.0147 

.  16733 

295,5 

.00005 

.16729 

295,4 

.83271 

.0148 

.17028 

293,5 

.00005 

.17023 

293,4 

.82977 

.0149 

.17320 

291,5 

.00005 

.17315 

291,4 

.82685 

0.0150 

8.17611 

289,6 

0.00005 

0,1 

8.17606 

289,5 

1.82394 

U 

log  tan  gd  u 

*F0' 

log  sec  gd  u 

«Fo' 

log  sin  gd  u 

«F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

»  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

w  Fo' 

log  coth  u 

0.0150 

8.17611 

289,6 

0.00005 

0,1 

8.17606 

289,5 

1.82394 

.0151 

.17899 

287,6 

.O0005 

.17894 

287,6 

.82106 

.0152 

.18186 

285,7 

.00005 

.18181 

285,7 

.81819 

.0153 

.18471 

283,9 

.00005 

.18466 

283,8 

.81534 

.0154 

.18754 

282,0 

.00005 

•  18749 

282,0 

.81251 

0.0155 

8.19035 

280,2 

0.00005 

0,1 

8.19030 

280,1 

1.80970 

.0156 

.19314 

278,4 

.00005 

.19309 

278,3 

.80691 

.0157 

.19592 

276,6 

.00005 

.19586 

276,6 

.80414 

.0158 

.19868 

274,9 

.00005 

.19862 

274,8 

.80138 

.0159 

.20142 

273,2 

.00005 

.20136 

273,1 

.79864 

0.0160 

8.20414 

271,5 

0.00006 

0,1 

8.20408 

271,4 

1.79592 

.0161 

.20684 

269,8 

.00006 

.20679 

269,7 

.79321 

.0162 

.20953 

268,1 

.00006 

.20948 

268,0 

.79052 

.0163 

.21221 

266,5 

.00006 

.21215 

266,4 

.78785 

.0164 

.21486 

264,8 

.00006 

.21480 

264,8 

.78520 

0.0165 

8.21750 

263,2 

o.oooo5 

0,1 

8.21744 

263,2 

1.78256 

.0166 

.22OI3 

26l,6 

.00006 

.22007 

261,6 

.77993 

.0167 

.22274 

200,1 

.00006 

.22268 

260,0 

•77732 

.0168 

.22533 

258,5 

.00006 

.22527 

258,5 

.77473 

.0169 

.22791 

257,0 

.00006 

.22785 

256,9 

.77215 

0.0170 

8.23047 

255,5 

0.00006 

0,1 

8.23041 

255,4 

1.76959 

.0171 

.23302 

254,o 

.00006 

.23295 

253,9 

.76705 

.0172 

.23555 

252,5 

.00006 

.23549 

252,4 

•76451 

.0173 

.23807 

251,1 

.00006 

.23800 

251,0 

.76200 

.0174 

.24057 

249,6 

.00007 

.24051 

249,5 

•75949 

0.0175 

8.24306 

248,2 

0.00007 

0,1 

8.24299 

248,1 

i.  75701 

.0176 

•24554 

246,8 

.00007 

•24547 

246,7 

•75453 

.0177 

.24800 

245,4 

.00007 

.24793 

245,3 

.75207 

.0178 

.25044 

244,0 

.00007 

•25037 

243,9 

.74963 

.0179 

.25288 

242,6 

.60007 

.25281 

242,6 

.74719 

0.0180 

8.25530 

241,3 

0.00007 

0,1 

8.25523 

241,2 

1.74477 

.0181 

.25770 

240,0 

.00007 

.25763 

239,9 

.74237 

.0182 

.26010 

238,6 

.00007 

.26002 

238,6 

.73998 

.0183 

.26248 

237,3 

.00007 

.26240 

237,3 

.73760 

.0184 

.26484 

236,1 

.00007 

.26477 

236,0 

.73523 

0.0185 

8.26720 

234,8 

0.00007 

0,1 

8.26712 

234,7 

1.73288 

.0186 

.26954 

233,5 

.00008 

.26946 

233,4 

.73054 

.0187 

.27187 

232,3 

.00008 

.27179 

232,2 

.72821 

.0188 

.27418 

231,0 

.00008 

.27411 

231,0 

.72589 

.0189 

.27649 

229,8 

.00008 

.27641 

229,7 

.72359 

0.0190 

8.27878 

228,6 

0.00008 

0,1 

8.27870 

228,5 

1.72130 

.0191 

.28106 

227,4 

.00008 

.28098 

227,3 

.71902 

.0192 

.28333 

226,2 

.00008 

.28325 

226,1 

.71675 

.0193 

.28558 

225,1 

.00008 

.28550 

225,0 

.71450 

.0194 

.28783 

223,9 

.00008 

.28775 

223,8 

.71225 

0.0195 

8.20006 

222,7 

o.ooooS 

0,1 

8.28998 

222,7 

1.71002 

.0196 

.29228 

221,6 

.00008 

.29220 

221,5 

.70780 

.0197 

.29449 

220,5 

.00008 

.29441 

220,4 

.70559 

.0198 

.29669 

219,4 

.00009 

.29661 

219,3 

.70339 

.0199 

.29888 

218,3 

.00009 

.29880 

2l8,2 

.70120 

O.O2OO 

8.30106 

217,2 

0.00009 

0,1 

8.30097 

217,1 

1.69903 

U 

log  tan  gd  u 

»  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

o»  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

<o  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

co  Fo' 

log  coth  u 

0.02OO 

8.30106 

217,2 

O.OOO09 

0,1 

8.30097 

217,1 

1.69903 

.O2OI 

.30323 

216,1 

.OOOOQ 

.30314 

2  1  6,0 

.69686 

.C2O2 

.30538 

215,0 

.00009 

.30529 

214,9 

.69471 

.0203 

•30753 

214,0 

.00009 

.30744 

213,9 

.69256 

.O204 

.30966 

212,9 

.00009 

.30957 

212,8 

.69043 

0.0205 

8.3H78 

211,9 

0.00009 

0,1 

8.31169 

211,8 

1.68831 

.0206 

.31390 

210,9 

.00009 

.31381 

210,8 

.68619 

.0207 

.31600 

209,8 

.00009 

.31591 

209,7 

.68409 

.0208 

.31809 

208,8 

.00009 

.31800 

208,7 

.68200 

.0209 

.32018 

207,8 

.00009 

.32008 

207,7 

.67992 

O.02IO 

8.32225 

206,8 

O.OOOIO 

0,1 

8.32216 

206,7 

1.67784 

.O2II 

.32431 

205,9 

.00010 

.32422 

205,8 

.67578 

.O2I2 

.32637 

204,9 

.00010 

.32627 

204,8 

.67373 

.O2I3 

.32841 

203,9 

.00010 

.32831 

203,8 

.67169 

.0214 

.33045 

203,0 

.00010 

.33035 

202,9 

.66965 

0.0215 

8.33247 

202,0 

O.OOOIO 

0,1 

8.33237 

20  1,  9 

1.66763 

.0216 

•33449 

2OI,I 

.00010 

.33439 

201,0 

.66561 

.0217 

.33649 

2OO,2 

.00010 

.33639 

200,1 

.66361 

.0218 

.33849 

199,2 

.00010 

.33839 

199,2 

.66161 

.O2I9 

.34048 

198,3 

.00010 

.34037 

198,2 

.65963 

0.0220 

8.34246 

197,4 

O.OOOII 

0,1 

8.34235 

197,3 

1.65765 

.0221 

.34443 

196,5 

.OOOII 

.34432 

196,4 

.65568 

.O222 

.34639 

195,7 

.OOOII 

.34628 

195,6 

.65372 

.0223 

.34834 

194,8 

.OOOII 

.34823 

194,7 

.65177 

.0224 

.35028 

193,9 

.OOOII 

.35018 

193,8 

.64982 

0.0225 

8.35222 

I93,i 

O.OOOII 

0,1 

8.35211 

193,0 

1.64789 

.0226 

.35415 

192,2 

.OOOII 

.35403 

192,1 

.64597 

.0227 

.356o6 

191,4 

.OOOII 

•35595 

191,3 

.64405 

.0228 

•35797 

190,5 

.OOOII 

.35786 

190,4 

.64214 

.O229 

.35987 

189,7 

.OOOII 

.35976 

189,6 

.64024 

O.O230 

8.36177 

188,9 

O.OOOII 

0,1 

8.36165 

188,8 

1.63835 

.O23I 

.36365 

188,0 

.00012 

.36353 

187,9 

.63647 

.0232 

.36553 

187,2 

.00012 

.36541 

187,1 

.63459 

.0233 

.36740 

186,4 

.00012 

.36728 

186,3 

.63272 

.0234 

.36926 

185,6 

.00012 

.36914 

185,5 

.63086 

0.0235 

8.37IH 

184,8 

O.OOOI2 

0,1 

8.37099 

184,7 

1.62901 

.0236 

.37295 

184,1 

.00012 

.37283 

184,0 

.62717 

.0237 

.37479 

183,3 

.00012 

.37467 

183,2 

.62533 

.0238 

.37662 

182,5 

.00012 

.37649 

182,4 

.62351 

.0239 

.37844 

181,7 

.00012 

.37832 

181,6 

.62168 

0.0240 

8.38025 

181,0 

0.00013 

O,I 

8.38013 

180,9 

1.61987 

.O24I 

.38206 

180,2 

.00013 

.38193 

180,1 

.61807 

.O242 

.38386 

179,5 

.00013 

.38373 

179,4 

.61627 

.0243 

.38565 

178,8 

.00013 

.38552 

178,7 

.61448 

.0244 

.38743 

178,0 

.00013 

.38730 

177,9 

.61270 

0.0245 

8.38921 

177,3 

0.00013 

0,1 

8.38908 

177,2 

1.61092 

.0246 

.39098 

176,6 

.00013 

.30085 

176,5 

.60915 

.0247 

.39274 

175,9 

.00013 

.39261 

175,8 

.00739 

.0248 

•39450 

175,2 

.00013 

.30436 

T75,o 

.60564 

.0249 

.39624 

174,5 

.00013 

.39611 

174,3 

.60389 

0.0250 

8.39799 

173,8 

0.00014 

0,1 

8,39785 

173,6 

1.60215 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  F,/ 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

<-Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

loo  coth  u 

0.0250 

8.39799 

173,8 

0.00014 

0,1 

8.39785 

173,6 

1.60215 

.0251 

.39972 

173,1 

.00014 

.39958 

173,0 

.60042 

.0252 

.40145 

172,4 

.00014 

.40131 

172,3 

.59869 

.0253 

•40317 

171,7 

.00014 

•40303 

171,6 

.59697 

.0254 

.40488 

171,0 

.00014 

.40474 

170,9 

.59526 

0.0255 

8.40659 

170,3 

0.00014 

0,1 

8.40645 

170,2 

1.59355 

.0256 

.40829 

i69,7 

.00014 

.40815 

169,6 

.59185 

.0257 

.40998 

169,0 

.00014 

.40984 

168,9 

.59016 

.0258 

.41167 

168,4 

.00014 

.4H52 

168,3 

.58848 

.0259 

.41335 

167,7 

.00015 

.41320 

167,6 

.58680 

0.0260 

8.41502 

167,1 

0.00015 

0,1 

8.41488 

167,0 

1.58512 

.0261 

.41669 

166,4 

.00015 

.41654 

166,3 

.58346 

.0262 

.41835 

165,8 

.00015 

.41820 

l65,7 

.58180 

.0263 

.412001 

165,2 

.00015 

.41986 

165,1 

.58014 

.0264 

.42165 

164,5 

.00015 

.42150 

164,4 

.57850 

0.0265 

8.42330 

163,9 

0.00015 

0,1 

8.42314 

163,8 

1.57686 

.0266 

.42493 

163,3 

.00015 

.42478 

163,2 

.57522 

.0267 

.42656 

162,7 

.00015 

.42641 

162,6 

•57359 

.0268 

.42819 

162,1 

.00016 

.42803 

162,0 

•57197 

.0269 

.42980 

161,5 

.00016 

.42965 

161,4 

•57035 

0.0270 

8.43142 

160,9 

O.OOOi6 

0,1 

8.43126 

160,8 

1.56874 

.0271 

•43302 

160,3 

.00016 

.43286 

160,2 

.56714 

.0272 

.43462 

159,7 

.00016  • 

.43446 

159,6 

.56554 

.0273 

.43622 

I59,i 

.00016 

.43605 

i59,o 

.56395 

.0274 

.43780 

158,5 

.00016 

.43764 

158,4 

•56236 

0.0275 

8.43939 

158,0 

O.OOOI6 

0,1 

8.43922 

157,8 

1.56078 

.0276 

.44096 

157,4 

.00017 

.44080 

157,3 

•55920 

.0277 

.44254 

156,8 

.00017 

.44237 

156,7 

.55763 

.0278 

.44410 

156,3 

.00017 

•  44393 

156,1 

.55607 

.0279 

.44566 

155,7 

.00017 

.44549 

155,6 

•55451 

0.0280 

8.44721 

I55,i 

0.00017 

0,1 

8.44704 

i55,o 

1.55206 

.0281 

.44876 

154,6 

.00017 

.44859 

154,5 

.55141 

.0282 

.45031 

154,0 

.00017 

•45013 

153,9 

.54987 

.0283 

.45184 

153,5 

.00017 

•45i67 

153,4 

.54833 

.0284 

.45338 

153,0 

.00018 

•45320 

152,8 

.54680 

0.0285 

8.45490 

152,4 

O.OOOlS 

0,1 

8-45473 

152,3 

1.54527 

.0286 

•45643 

I5i,9 

.00018 

.45625 

151,8 

•54375 

.0287 

.45794 

I5i,4 

.00018 

•45776 

151,2 

.54224 

.0288 

.45945 

150,8 

.00018 

•45927 

150,7 

•54073 

.0289 

.46096 

150,3 

.00018 

.46078 

150,2 

•53922 

0.0290 

8.46246 

149,8 

0.00018 

0,1 

8.46228 

149,7 

1-53772 

.0291 

.46395 

149,3 

.00018 

.46377 

149,2 

•53623 

.0292 

.46544 

148,8 

.00019 

.46526 

148,6 

•53474 

.0293 

.46693 

148,3 

.00019 

.46674 

148,1 

•53326 

.0294 

.46841 

147,8 

.00019 

.46822 

147,6 

.53178 

0.0295 

8.46989 

147,3 

0.00019 

0,1 

8.46970 

147,1 

I  •  53030 

.0296 

.47136 

146,8 

.00019 

.47116 

146,6 

.52884 

.0297 

.47282 

146,3 

.00019 

.47263 

146,1 

.52737 

.0298 

.47428 

145,8 

.00019 

.47409 

145,7 

.52591 

.0299 

.47574 

145,3 

.00019 

•47554 

145,2 

.52446 

0.0300 

8.47719 

144,8 

O.OOO20 

0,1 

8.47699 

144,7 

1.52301 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

w  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

-FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0300 

8.47719 

144,8 

O.OO02O 

0,1 

8.47699 

144,7 

I.5230I 

.0301 

.47863 

144,3 

.00020 

.47844 

14-1,2 

.52156 

.0302 

.48007 

143,8 

.00020 

.47987 

143,7 

.52013 

.0303 

.48151 

143,4 

.00020 

.48131 

143,2 

.51869 

.0304 

.48294 

142,9 

.00020 

.48274 

142,8 

.51726 

0.0305 

8.48437 

142,4 

O.OOO20 

O,I 

8.48417 

142,3 

I.5I583 

.0306 

.48579 

142,0 

.OO020 

.48559 

141,8 

.51441 

.0307 

.48721 

I4i,5 

.0002O 

.48700 

141,4 

.51300 

.0308 

.48862 

141,0 

.00021 

.48841 

140,9 

.5H59 

.0309 

.49003 

140,6 

.OOO2I 

.48982 

140,5 

.51018 

0.0310 

8.49143 

140,1 

O.OOO2I 

0,1 

8.49122 

140,0 

1.50878 

.0311 

.49283 

139,7 

.O002I 

.49262 

139,6 

.50738 

.0312 

.49423 

139,2 

.O002I 

.49401 

139,1 

.50599 

.0313 

.49562 

138,8 

.00021 

•49540 

138,7 

.50460 

.0314 

.49700 

138,4 

.OOO2I 

.49679 

138,2 

.50321 

0.03'is 

8.40838 

137,9 

O.OOO22 

0,1 

8.49817 

137,8 

1.50183 

.0316 

.49976 

137,5 

.OOO22 

•49954 

137,3 

.50046 

.0317 

.50113 

I37,o 

.OO022 

.50091 

136,9 

.49909 

.0318 

.50250 

136,6 

.OO022 

.50228 

136,5 

.49772 

.0319 

.50386 

136,2 

.OOO22 

.50364 

136,1 

.49636 

0.0320 

8.50522 

135,8 

O.OOO22 

0,1 

8.50500 

135,6 

1.49500 

.0321 

.50658 

135,3 

.OO022 

.50636 

135,2 

.49364 

.0322 

.50793 

134,9 

.00023 

• 

.50771 

134,8 

.49229 

.0323 

.50928 

134,5 

.00023 

.50905 

134,4 

.49095 

.0324 

.51062 

134,1 

.00023 

.51039 

133,9 

.48961 

0.0325 

8.51196 

133,7 

O.OO023 

0,1 

8.5H73 

133,5 

1.48827 

.0326 

.51329 

133,3 

.00023 

.51306 

I33,i 

.48694 

.0327 

.51463 

132,9 

.00023 

.51439 

132,7 

.48561 

.0328 

.51595 

132,5 

.00023 

.51572 

132,3 

.48428 

.0329 

.51727 

132,1 

.00023 

.51704 

I3i,9 

.48296 

0.0330 

8.51859 

I3i,7 

O.O0024 

0,1 

8.51836 

I3i,5 

1.48164 

•0331 

.51991 

I3i,3 

.00024 

•51967 

131,1 

.48033 

-0332 

.52122 

130,9 

.00024 

.52098 

130,7 

.47902 

•0333 

.52252 

130,5 

.00024 

.52228 

130,3 

.47772 

•0334  . 

.52383 

130,1 

.OO024 

.52358 

129,9 

.47642 

0.0335 
.0336 

8.52513 
.52642 

129,7 
129,3 

o  00024 
.00025 

0,1 

8.52488 
.52618 

129,5 

129,2 

I.475I2 
.47382 

•  0337 

.52771 

128,9 

.00025 

.52747 

128,8 

.47253 

.0338 

.52900 

128,5 

.00025 

.52875 

128,4 

.47125 

•0339 

.53028 

128,2 

.00025 

.53003 

128,0 

.46997 

0.0340 

8.53156 

127,8 

0.00025 

0,1 

8.53I3I 

127,6 

1.46869 

.0341 

.53284 

127,4 

.00025 

.53259 

127,3 

.46741 

.0342 

•534II 

127,0 

.00025 

.53386 

126,9 

.46614 

•  0343 

.53538 

126,7 

.00026 

•53512 

126,5 

.46488  1 

•  0344 

^^ 

.53664 

126,3 

.00026 

.53639 

126,1 

.46361 

0.0345 

8.53791 

125,9 

0.00026 

0,1 

8.53765 

125,8 

1.46235 

.0346 

.53916 

125,6 

.00026 

0,2 

.53890 

125,4 

.46110 

•0347 

.54042 

125,2 

.00026 

.54016 

125,1 

•4S9&4 

.0348 

.54167 

124,8 

.00026 

.54140 

124,7 

.45860 

.0349 

.54291 

124,5 

.00026 

.54265 

124,3 

.45735 

0.0350 

8.S44I6 

124,1 

0.00027 

0,2 

8.54389 

124,0 

1.45611 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

»F0' 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

w  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

w  Fo' 

log  coth  u 

0.0350 

8.54416 

124,1 

0.00027 

0,2 

8.54389 

124,0 

I.456II 

.0351 

.54540 

123,8 

.00027 

.54513 

123,6 

.45487 

.0352 

.54663 

123,4 

.00027 

.54636 

123,3 

.45364 

.0353 

.54786 

123,1 

.00027 

•54759 

122,9 

.45241 

.0354 

.54909 

122,7 

.00027 

.54882 

122,6 

.45n8 

0.0355 

8.55032 

122,4 

0.00027 

0,2 

8.55005 

122,2 

1-44995 

•0356 

.55154 

I22,O 

.00028 

.55127 

121,9 

.44873 

.0357 

.55276 

121,7 

.00028 

.55248 

121,5 

•44752 

.0358 

.55398 

121,4 

.00028 

•55370 

121,2 

.44630 

•  0359 

.55519 

I2I,O 

.00028 

•55491 

120,9 

.44509 

0.0360 

8.55640 

120,7 

0.00028 

0,2 

8.55611 

120,5 

1.44389 

.0361 

.55700 

120,4 

.00028 

.55732 

1  2O,2 

.44268 

.0362 

.55880 

I20.O 

.00028 

.55852 

119,9 

.44148 

.0363 

.56000 

H9,7 

.00029 

.55972 

H9,5 

.44028 

.0364 

.56120 

119,4 

.00029 

.56091 

119,2 

.43909 

0.0365 

8.56239 

119,0 

0.00029 

0,2 

8.56210 

118,9 

1.43790 

.0366 

.56358 

118,7 

.00029 

.56329 

118,6 

.43671 

.0367 

.56476 

118,4 

.00029 

.56447 

1  1  8,2 

•43553 

.0368 

.56595 

118,1 

.00029 

.56565 

H7,9 

•43435 

.0369 

.56712 

117,7 

.00030 

.56683 

117,6 

.43317 

0.0370 

8.56830 

117,4 

0.00030 

0,2 

8.56800 

H7,3 

1.43200 

.0371 

.50947 

ii7,i 

.00030 

.56917 

117,0 

.43083 

.0372 

.57064 

116,8 

.00030 

.57034 

116,6 

.42966 

•0373 

.57i8i 

116,5 

.00030 

.57151 

116,3 

.42849 

•  .0374 

.57297 

116,2 

.00030 

.57267 

116,0. 

.42733 

0.0375 

8.57413 

H5,9 

0.00031 

0,2 

8.57383 

H5,7 

1.42617 

.0376 

•57529 

115,6 

.00031 

.57498 

H5,4 

.42502 

.0377 

.57644 

H5,3 

.00031 

.57614 

115,1 

.42386 

.0378 

.57760 

114,9 

.00031 

.57729 

114,8 

.42271 

.0379 

.57874 

114,6 

.00031 

.57843 

114,5. 

.42157 

0.0380 

8.57989 

114,3 

0.00031 

0,2 

&.S7957 

114,2 

1.42043 

.0381 

.58103' 

114,0 

.00032 

.58071 

113,9 

.41929 

.0382 

.58217 

113,7 

.00032 

.58185 

113,6 

.41815 

.0383 

.58330 

H3,4 

.00032 

.58299 

H3,3 

.41701 

.0384 

•58444 

113,2 

.00032 

.58412 

113,0 

.41588 

0.0385 

8.58557 

112,9 

0.00032 

0,2 

8.58525 

112,7 

I.4I475 

.0386 

.58670 

112,6 

.00032 

.58637 

112,4 

.41363 

.0387 

.58782 

112,3 

.00033 

.58749 

112,1 

.41251 

.0388 

.58894 

II2,O 

.00033 

.58861 

111,8 

.41139 

.0389 

.59006 

111,7 

.00033 

.58973 

in,5. 

.41027 

0.0390 

8.59H7 

111,4 

0.00033 

0,2 

8.59084 

111,2 

1.40916 

.0391 

.59229 

iii.i 

.00033 

.59196 

111,0 

.40804 

.0392 

.59340 

110,8 

.00033 

.59306 

110,7 

.40694 

.0393 

•59450 

110,6 

.00034 

.59417 

110,4 

.40583 

.0394 

•59561 

110,3 

.00034 

.59527 

110,1 

•40473 

0.0395 

8.59671 

110,0 

0.00034 

0,2 

8.59637 

109,8 

1.40363 

.0396 

.59781 

109,7 

.00034 

.59747 

109,6 

.40253 

•  0397 

.59890 

109,5 

.00034 

.59856 

109,3 

.40144 

.0398 

.60000 

109,2 

.00034 

.59965 

109,0 

.40035 

•0399 

.60109 

108,9 

.00035 

.60074 

108,7 

.39926 

0.0400 

8.60218 

108,6 

0.00035 

0,2 

8.60183 

io8,5 

1.39817 

u 

log  tan  gd  u 

<-  Fo' 

log  sec  gd  u 

«Fo' 

log  sin  gd  u 

«F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0400 

8.60218 

108,6 

0.00035 

0,2 

8.60183 

108,5 

I.398I7 

.0401 

.60326 

108,4 

.00035 

.60291 

108,2 

.39709 

.0402 

.60434 

108,1 

.00035 

.60399 

107,9 

.39601 

.0403 

.60542 

107,8 

.00035 

.60507 

107,6 

•39493 

.0404 

.60650 

107,6 

.00035 

.60615 

107,4 

.39385 

0.0405 

8.60757 

107,3 

0.00036 

0,2 

8.60722 

107,1 

I  .39278 

.0406 

.60865 

IO7,O 

.00036 

.60829 

106,9 

.39171 

.0407 

.60971 

106,8 

.00036 

.60935 

106,6 

.39065 

.0408 

.61078 

106,5 

.00036 

.61042 

106,3 

.38958 

.0409 

.6~n84 

100,2 

.00036 

.61148 

106,1 

.38852 

0.0410 

8.61291 

106,0 

0.00036 

0,2 

8.61254 

105,8 

1.38746 

.0411 

.61396 

105,7 

.00037 

.61360 

105,5 

.38640 

.0412 

.61502 

105,5 

.00037 

.61465 

105,3 

.38535 

.0413 

.61607 

105,2 

.00037 

.61570 

105,0 

.38430 

.0414 

.61712 

105,0 

.00037 

.61675 

104,8 

.38325 

0.0415 

8.61817 

104,7 

0.00037 

0,2 

8.61780 

104,5 

1.38220 

.0416 

.61922 

104,5 

.00038 

.61884 

104,3 

.38116 

.0417 

.62026 

104,2 

.00038 

.61988 

104,0 

.38012 

.0418 

.62130 

104,0 

.00038 

.62092 

103,8 

.37908 

.0419 

.62234 

103,7 

.00038 

.62196 

103,5 

.37804 

0.0420 

8.62338 

103,5 

0.00038 

0,2 

8.62299 

103,3 

I.3770I 

.0421 

.62441 

103,2 

.00038 

.62403 

103,0 

.37597 

.0422 

.62544 

103,0 

.00039 

.62505 

102,8 

•37495 

.0423 

.62647 

102,7 

.00039 

.62608 

102,5 

.37392 

.0424 

.62750 

102,5 

.00039 

.62711 

102,3 

.37289 

0.0425 

8.62852 

102,2 

0.00039 

0,2 

8.62813 

102,1 

1.37187 

.0426 

.62954 

IO2,O 

.00039 

.62915 

101,8 

.37085 

.0427 

.63056 

101,8 

.00040 

.63016 

101,6 

.36984 

.0428 

.63158 

101,5 

.00040 

.63118 

101,3 

.36882 

.0429 

.63259 

101,3 

.00040 

.63219 

101,1 

.36781 

0.0430 

8.63360 

101,1 

0.00040 

0,2 

'8.63320 

100,9 

1.36680 

.0431 

.63461 

100,8 

.00040 

.63421 

100,6 

.36579 

.0432 

.63562 

100,6 

.00041 

.63521 

100,4 

.36479 

•0433 

.63662 

100,4 

.00041 

.63622 

100,2 

.36378 

•  0434 

.63763 

IOO,I 

.00041 

.63722 

99,9 

.36278 

0.0435 

8.63863 

99,9 

0.00041 

0,2 

8.63822 

99,7 

1.36178 

.0436 

.63962 

99,7 

.00041 

.63921 

99,5 

.0437 

.64062 

99,4 

.00041 

.64020 

99,3 

.35980 

.0438 

.64161 

99,2 

.00042 

.64120 

99,0 

.35880 

.0439 

.64260 

99,0 

.00042 

.64219 

98,8 

.35781 

0.0440 

8.64359 

98,8 

0.00042 

0,2 

8.64317 

98,6 

1.35683 

.0441 

.64458 

98,5 

.00042 

.64416 

98,4 

.35584 

.0442 

.64556 

98,3 

.00042 

.64514 

98,1 

.35486 

•  0443 

.64655 

98,1 

.00043 

.64612 

97,9 

.35388 

.0444 

.64753 

97,9 

.00043 

.64710 

97,7 

.35290 

0.0445 

8.64850 

97,7 

0.00043 

0,2 

8.64807 

97,5 

I.35I93 

.0446 

.64948 

97,4 

.00043 

.64905 

97,2 

.35095 

.0447 

.65045 

97,2 

.00043 

.65002 

97,0 

.34998 

.0448 

.65142 

97,o 

.00044 

.65009 

96,8 

•34901 

.0449 

.65239 

96,8 

.00044 

.65195 

96,6 

.34805 

0.0450 

8.65336 

96,6 

0.00044 

0,2 

8.65292 

96,4 

1.34708 

u 

log  tan  od  u 

«  Fo' 

log  tec  gd  u 

«Fo' 

log  tin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLCS 


10 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0450 

8.65336 

96,6 

0.00044 

0,2 

8.65292 

96,4 

1.34708 

.0451 

.65432 

96,4 

.00044 

.65388 

96,2 

.34612 

.0452 

.65529 

96,1 

.00044 

.65484 

96,0 

.34516 

.0453 

.65625 

95,9 

.00045 

.65580 

95,7 

.34420 

.0454 

.65721 

95,7 

.00045 

.65676 

95,5 

.34324 

0.0455 

8.65816 

95,5 

0.00045 

0,2 

8.65771 

95,3 

1.34229 

.0456 

.65912 

95,3 

.00045 

.65866 

95,1 

.34134 

•  0457 

.66007 

95,1 

.00045 

.65961 

949 

.34039 

.0458 

.66102 

94,9 

.00046 

.66056 

94,7 

•33944 

.0459 

.66197 

94,7 

.00046 

.66151 

94,5 

.33849 

0.0460 

8.66291 

94,5 

0.00046 

0,2 

8.66245 

943 

1.33755 

.0461 

.66385 

94,3 

.00046 

.66339 

94,1 

.33661 

.0462 

.66480 

94,1 

.00046 

.66433 

93,9 

.33567 

.0463 

.66574 

93,9 

.00047 

.66527 

93,7 

•33473 

.0464 

.66667 

93,7 

.00047 

.66621 

93,5 

.33379 

0.0465 

8.66761 

93,5 

0.00047 

0,2 

8.66714 

93,3 

1.33286 

.0466 

.66854 

93,3 

.00047 

.66807 

93,1 

.33193 

.0467 

.66947 

93,1 

.00047 

.66900 

92,9 

.33100 

.0468 

.67040 

92,9 

.00048 

.66993 

92,7 

.33007 

.0469 

.67133 

92,7 

.00048 

.67085 

92,5 

.32915 

0.0470 

8.67226 

92,5 

0.00048 

0,2 

8.67178 

92,3 

1.52822 

.0471 

.67318 

92,3 

.00048 

.67270 

92,1 

.32730 

.0472 

.67410 

92,1 

.00048 

.67362 

91,9 

.32638 

•0473 

.67502 

91,9 

.00049 

.67454 

91,7 

.32546 

.0474 

.67594 

91,7 

.00049 

.67545 

91,5 

.32455 

0.0475 

8.67686 

91,5 

0.00049 

0,2 

8.67637 

91,3 

1.32363 

.0476 

.67777 

91,3 

.00049 

.67728 

91,1 

.32272 

.0477 

.67868 

9i,i 

.00049 

.67819 

90,9 

.32181 

.0478 

.67959 

90,9 

.00050 

.67910 

90,7 

.32090 

.0479 

.68050 

90,7 

.00050 

.68000 

90,5 

.32000 

0.0480 

8.68141 

90,5 

0.00050 

0,2 

8.68091 

90,3 

I.3I9Q9 

.0481 

.68231 

90,4 

.00050 

.68181 

90,2 

.31819 

.0482 

.68322 

00,2 

.00050 

.68271 

90,0 

.31729 

.0483 

.68412 

90,0 

.00051 

.68361 

89,8 

.31639 

.0484 

.68501 

89,8 

.00051 

.68451 

89,6 

.31549 

0.0485 

8.68591 

89,6 

0.00051 

0,2 

8.68540 

80,4 

1.31460 

.0486 

.68681 

89,4 

.00051 

.68629 

89,2 

.31371 

.0487 

.68770 

89,2 

.00051 

.68719 

89,0 

.31281 

.0488 

.68859 

89,1 

.00052 

.68808 

88,9 

.31192 

.0489 

.68948 

88,9 

.00052 

.68896 

88,7 

.31104 

0.0490 

8.69037 

88,7 

0.00052 

0,2 

8.68985 

88,5 

I.3IOI5 

.0491 

.69126 

88,5 

.00052 

.69073 

88,3 

.30927 

.0492 

.69214 

88,3 

.00053 

.69161 

88,1 

.30839 

•0493 

.69302 

88,2 

.00053 

.69250 

87,9 

.30750 

.0494 

.69390 

88,0 

.00053 

.69337 

87,8 

.30663 

0.0495 

8.69478 

87,8 

0.00053 

0,2 

8.69425 

87,6 

1.30575 

.0496 

.69566 

87,6 

.00053 

•69513 

87,4 

.30487 

.0497 

.69654 

87,5 

.00054 

.69600 

87,2 

.30400 

.0498 

.69741 

87,3 

.00054 

.69687 

87,1 

.30313 

.0499 

.69828 

87,1 

.00054 

.69774 

86,9 

.30226 

0.0500 

8.69915 

86,9 

0.00054 

0,2 

8.69861 

86,7 

I.30I39 

u 

log  tan  gd  u 

W  Fo' 

log  sec  gd  u 

»  Fo' 

log  sin  gd  u 

«FO' 

logcscgdu 

SMITHSONIAN  TABLES 


II 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

a,  Fo' 

log  cosh  u 

«F</ 

log  tanh  u 

»  Fo' 

log  coth  u 

0.0500 

8.69915 

86,9 

O.OOO54 

0,2 

8.69861 

86,7 

I.30I39 

.0501 

.70002 

86,8 

.00054 

.69947 

86,5 

.30053 

.0502 

.70089 

86,6 

.00055 

.70034 

86,4 

.29966 

.0503 

.70175 

86,4 

.00055 

.70120 

86,2 

.29880 

.0504 

.70261 

86,2 

.00055 

.70206 

86,0 

.29794 

0.0505 

8.70348 

86,1 

0.00055 

0,2 

8.70292 

85,9 

1.29708 

.0506 

•70434 

85,9 

.00056 

.70378 

85,7 

.29622 

.0507 

.70519 

85,7 

.00056 

.70464 

85,5 

.29536 

.0508 

.70605 

85,6 

.00056 

.70549 

85,3 

.29451 

.0509 

.70691 

85,4 

.00056 

.70634 

85,2 

.29366 

0.0510 

8.70776 

85,2 

0.00056 

0,2 

8.70719 

85,0 

1.29281 

.0511 

.70861 

85,1 

.00057 

.70804 

84,8 

.29196 

.0512 

.70946 

84,9 

.00057 

.70889 

8-U7 

.29111 

.0513 

.71031 

84,7 

.00057 

.70974 

84,5 

.20026 

.0514 

•7III5 

84,6 

.00057 

.71058 

84,3 

.28942 

0.0515 

8.7I2OO 

84,4 

0.00058 

0,2 

8.7II42 

84,2 

1.28858 

.0516 

.71284 

84,2 

.00058 

.71226 

84,0 

.28774 

.0517 

.71368 

84,1 

.00058 

.71310 

83,9 

.28690 

.0518 

.71452 

83,9 

.00058 

•71394 

83,7 

.28606 

.0519 

.71536 

83,8 

.00058 

.71478 

83,5 

.28522 

0.0520 

8.71620 

83,6 

0.00059 

0,2 

8.71561 

83,4 

1.28439 

.0521 

.71703 

83,4 

.00059 

.71644 

83,2 

.28356 

.0522 

.71787 

83,3 

.00059 

.71728 

83,0 

.28272 

.0523 

.71870 

83,1 

.00059 

.71811 

82,9 

.28189 

.0524 

.71953 

83,0 

.00000 

.71893 

82,7 

.28107 

0.0525 

8.72036 

82,8 

0.00060 

0,2 

8.71976 

82,6 

1.28024 

.0526 

.72119 

82,6 

.00060 

.72059 

82,4 

.27941 

.0527 

.722OI 

82,5 

.00060 

.72141 

82,3 

.27859 

.0528 

.72284 

82,3 

.00061 

.72223 

82,1 

.27777 

.0529 

.72366 

82,2 

.00061 

.72305 

81,9 

.27695 

0.0530 

8.72448 

82,0 

0.00061 

0,2 

8.72387 

81,8 

1.27613 

.0531 

.72530 

81,9 

.00061 

.72469 

81,6 

.27531 

.0532 

.72612 

81,7 

.00061 

.72550 

81,5 

.27450 

•  0533 

.72693 

81,6 

.00062 

.72632 

81,3 

.27368 

.0534 

.72775 

81,4 

.00062 

.72713 

81,2 

.27287 

0.0535 

8.72856 

81,3 

0.00062 

0,2 

8.72794 

81,0 

1.27206 

.0536 

.72937 

81,1 

.00062 

.72875 

80,9 

.27125 

•  0537 

.73018 

81,0 

.00063 

.72956 

80,7 

.27044 

.0538 

.73099 

80,8 

.00063 

.73036 

80,6 

.26964 

.0539 

.73180 

80,7 

.00063 

.73H7 

80,4 

.26883 

0.0540 

8.73260 

80,5 

0.00063 

0,2 

8.73197 

80,3 

1.26803 

.0541 

•73341 

80,4 

.00064 

.73277 

80,  i 

.26723 

.0542 

•73421 

80,2 

.00064 

.73357 

80,0 

.26643 

.0543 

•73501 

80,1 

.00064 

.73436 

79,8 

.26564 

.0544 

.73581 

79,9 

.00064 

.73517 

79,7 

.26483 

0.0545 

8.73661 

79,8 

0.00064 

0,2 

8.73597 

79,5 

1.26403 

.0546 

•73741 

79,6 

.00065 

.73676 

79,4 

.26324 

.0547 

.73820 

79,5 

.00065 

•73755 

79,2 

.26245 

.0548 

.73900 

79,3 

.00065 

.73835 

79,1 

.26165 

.0549 

•73979 

79,2 

.00065 

.739M 

78,9 

.26086 

0.0550 

8.74058 

79,0 

0.00066 

0,2 

8.73993 

78,8 

I.2OOO7 

u 

log  tan  gd  u 

-FO' 

log  sec  gd  u 

•  F0' 

log  sin  gd  u 

-Fo' 

logcscgdu 

SMITHSONIAN  TABLES 


12 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

•  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0550 

8.74058 

79,0 

O.OOO66 

0,2 

8-73993 

78,8 

1.26007 

.0551 

.74137 

78,9 

.00066 

.74071 

78,7 

.25929 

.0552 

.74216 

78,8 

.00066 

.74150 

78,5 

.25850 

•0553 

•  74295 

78,6 

.00066 

.74228 

78,4 

.25772 

.0554 

•74373 

78,5 

.00067 

•74307 

78,2 

.25693 

0.0555 

8.74452 

78,3 

0.00067 

0,2 

8.74385 

78,i 

1.25615 

.0556 

.74530 

78,2 

.00067 

.74463 

77,9 

•25537 

•0557 

.74608 

78,0 

.00067 

.74541 

77,8 

.25459 

.0558 

.74686 

77,9 

.00068 

.74618 

77,7 

.25382 

.0559 

.74704 

77,8 

.00068 

.74696 

77,5 

.25304 

0.0560 

8.74841 

77,6 

0.00068 

0,2 

8.74773 

77,4 

1.25227 

.0561 

.74919 

77,5 

.00068 

.74851 

77,3 

.25149 

.0562 

.74996 

77,4 

.00069 

.74928 

77,i 

.25072 

•  0563 

•75074 

77,2 

.00069 

•75005 

77,o 

.24995 

.0564 

.75151 

77,1 

.00069 

.75082 

76,8 

.24918 

0.0565 

8.75228 

76,9 

0.00069 

0,2 

8.75159 

76,7 

1.24841 

.0566 

.75305 

76,8 

.00070 

.75235 

76,6 

.24765 

.0567 

.75382 

76,7 

.00070 

.75312 

76,4 

.24688 

.0568 

•75458 

76,5 

.00070 

.75388 

76,3 

.24612 

.0569 

.75535 

76,4 

.00070 

.75464 

76,2 

.24536 

0.0570 

8.75611 

76,3 

O.OOO7I 

0,2 

8.75540 

76,0 

1.24460 

.0571 

.75687 

76,1 

.00071 

.75616 

75,9 

.24384 

.0572 

.75763 

76,0 

.OOO7I 

.75692 

75,8 

.24308 

.0573 

.75839 

75,9 

.00071 

.75768 

75,6 

.24232 

.0574 

.75915 

75,7 

.00072 

.75844 

75,5 

.24156 

0.0575 

8.75991 

75,6 

0.00072 

0,2 

8.75919 

75,4 

1.24081 

.0576 

.76066 

75,5 

.00072 

0,2 

•75994 

75,2 

.24006 

.0577 

.76142 

75,4 

.00072 

o,3 

.76069 

75,1 

.23931 

.0578 

.76217 

75,2 

.00073 

.76144 

75,o 

.23856 

.0579 

.76292 

75,i 

.00073 

.76219 

74,8 

.23781 

0.0580 

8.76367 

75,o 

0.00073 

o,3 

8.76294 

74,7 

1.23706 

.0581 

.76442 

74,8 

.00073 

.76369 

74,6 

.23631 

.0582 

.76517 

74,7 

.00074 

.76443 

74,5 

.23557 

.0583 

.76591 

74,6 

.00074 

.76518 

74,3 

.23482 

•  0584 

.76666 

74,5 

.00074 

.76592 

74,2 

.23408 

0.0585 

8.76740 

74,3 

0.00074 

0,3 

8.76666 

74,1 

1.23334 

.0586 

.76815 

74,2 

.00075 

.76740 

73,9 

.23260 

.0587 

.76889 

74,1 

.00075 

.76814 

73,8 

.23186 

.0588 

.76963 

73,9 

.00075 

.76888 

73,7 

.23112 

.0589 

.77037 

73,8 

.00075 

.76961 

73,6 

.23039 

0.0590 

8.77110 

73,7 

0.00076 

0,3 

8.77035 

73,4 

1.22965 

.0591 

.77184 

73,6 

.00076 

.77108 

73,3 

.22892 

.0592 

.77258 

73,4 

.00076 

.77181 

73,2 

.22819 

.0593 

•77331 

73,3 

.00076 

.77255 

73,1 

.22745 

.0594 

.77404 

73,2 

.00077 

.77328 

72,9 

.22672 

0.0595 

8.77477 

73,i 

0.00077 

0,3 

8.77400 

72,8 

1.22600 

.0596 

.77550 

73,o 

.00077 

.77473 

72,7 

.22527 

.0597 

.77623 

72,8 

.00077 

.77546 

72,6 

.22454 

.0598 

.776o6 

72,7 

.00078 

.77618 

72,5 

.22382 

.0599 

.77769 

72,6 

.00078 

.77691 

72,3 

.22309 

0.0600 

8.77841 

72,5 

0.00078 

o,3 

8.77763 

72,2 

1.22237 

u 

og  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«-  Fo' 

log  cosh  u 

•  F0' 

log  tanh  u 

«F0' 

log  coth  u 

0.0600 

8.77841 

72,5 

0.00078 

0,3 

8.77763 

72,2 

1.22237 

.0601 

.77914 

72,3 

.00078 

.77835 

72,1 

.22165 

.0602 

.77986 

72,2 

.00079 

.77907 

72,0 

.22093 

.0603 

.78058 

72,1 

.00079 

•77979 

7i,8 

.22021 

.0604 

.78130 

72,0 

.00079 

.78051 

71,7 

.21949 

0.0605 

8.78202 

71,9 

0.00079 

o,3 

8.78123 

71,6 

I.2I877 

.0606 

.78274 

7i,8 

.00080 

.78194 

7i,5 

.21806 

.0607 

.78346 

7i,6 

.00080 

.78266 

7i,4 

•21734 

.0608 

.78417 

7i,5 

.00080 

.78337 

7i,3 

.21663 

.0609 

.78489 

71,4 

.00086 

.78408 

7i,i 

.21592 

0.0610 

8.78560 

71,3 

0.00081 

o,3 

8.78479 

71,0 

I.2I52I 

.0611 

.78631 

71,2 

.00081 

.78550 

70,9 

.2-1450 

.0612 

.78702 

7i,i 

.00081 

.78621 

70,8 

.21379 

.0613 
.0614 

.78773 
.78844 

70,9 
70,8 

.00082 
.00082 

.78692 
.78762 

70,7 
70,6 

.21308 
.21238 

0.0615 

8.78915 

70,7 

0.00082 

o,3 

8.78833 

70,4 

I.2II67 

.0616 

.78986 

70,6 

.00082 

.78903 

70,3 

.21097 

.0617 

.79056 

70,5 

.00083 

.78973 

70,2 

.21027 

.0618 

.79127 

70,4 

.00083 

.79044 

70,i 

.20956 

.0619 

.79197 

70,3 

.00083 

.79114 

70,0 

.20886 

0.0620 

8.79267 

70,1 

0.00083 

o,3 

8.79184 

69,9 

1.20816 

.0621 

.79337 

70,0 

.00084 

•79253 

69,8 

.20747 

.0622 

.79407 

69,9 

.00084 

.79323 

69,6 

.20677 

.0623 

•79477 

69,8 

.OOO&l 

•79393 

69,5 

.20607 

.0624 

•79547 

69,7 

.00084 

.79462 

69,4 

.20538 

0.0625 

8.79616 

69,6 

0.00085 

o,3 

8-79532 

69,3 

1.20468 

.0626 

.79686 

69,5 

.00085 

.79601 

69,2 

.20399 

.0627 

.79755 

69,4 

.00085 

.79670 

69,1 

.20330 

.0628 

.79825 

69,2 

.00086 

•79739 

69,0 

.20261 

.0629 

.79894 

69,1 

.00086 

.79808 

68,9 

.20192 

0.0630 

8.79963 

69,0 

0.00086 

0,3 

8.79877 

68,8 

1.20123 

.0631 

.80032 

68,9 

.00086 

.79945 

68,6 

.20055 

.0632 

.80101 

68,8 

.00087 

.80014 

68,5 

.19986 

.0633 

.80169 

68,7 

.00087 

.80082 

68,4 

.19918 

.0634 

.80238 

68,6 

.00087 

.80151 

68,3 

.19849 

0.0635 

8.80307 

68,5 

0.00088 

o,3 

8.80219 

68,2 

1.19781 

.0636 

.80375 

68,4 

.00088 

.80287 

68,1 

.19713 

.0637 

.80443 

68,3 

.00088 

.80355 

68,0 

.19645 

.0638 

.80512 

68,2 

.00088 

.80423 

67,9 

.  19577 

.0639 

.80580 

68,1 

.00089 

.80491 

67,8 

.19509 

0.0640 

8.80648 

68,0 

0.00089 

0,3 

8.80559 

6>,7 

I.I944T 

.0641 

.80716 

67,8 

.00089 

.80626 

67,6 

.  19374 

.0642 

.80783 

67,7 

.00089 

.80694 

67,5 

.19306 

.0643 

.80851 

67,6 

.00000 

.80761 

67,4 

.  19239 

.0644 

.80919 

67,5 

.00090 

.80829 

6>,3 

.19171 

0.0645 

8.80986 

6>,4 

o.ooooo 

o,3 

8.80896 

67,1 

I  .  19104 

.0646 

.81053 

67,3 

.00091 

.80963 

67,0 

.10037 

.0647 

.81121 

67,2 

.00091 

.81030 

66,9 

.18970 

.0648 

.81188 

67,1 

.00091 

.81007 

66,8 

.18003 

.0649 

.81255 

67,0 

.00091 

.81164 

66,7 

.18836 

0.0650 

8.81322 

66,9 

0.00092 

0,3 

8.81230 

66,6 

I  .  187/0 

u 

log  tan  gd  u 

«FO' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

«F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

lOQ  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«F0' 

log  coth  u 

0.0650 

8.81322 

66,9 

0.00092 

0,3 

8.81230 

66,6 

I  .  18770 

.0651 

.81389 

66,8 

.00092 

.81297 

66,5 

.  18703 

.0652 

.81456 

66,7 

.00092 

.81363 

66,4 

.18637 

.0653 

.81522 

66,6 

.00093 

.81430 

66,3 

.  18570 

.0654 

.81589 

66,5 

.00093 

.81496 

66,2 

.18504 

0.0655 

8.8l65'5 

66,4 

0.00093 

0,3 

8.81562- 

66,1 

1.18438 

.0656 

.81722 

66,3 

.00093 

.81628 

66,0 

.18372 

.0657 

.81788 

66,2 

.00094 

.81694 

65,9 

.18306 

.0658 

.81854 

66,1 

.00094 

.81760 

65,8 

.18240 

.0659 

.81920 

66,0 

.00094 

.81826 

65,7 

.  18174 

0.0660 

8.81986 

65,9 

0.00095 

0,3 

8.81891 

65,6 

1  .  18109 

.0661 

.82052 

65,8 

.00095 

.81957 

65,5 

.18043 

.0662 

.82118 

65,7 

.00095 

.82022 

65,4 

.17978 

.0663 

.82183 

65,6 

.00095 

.82088 

65,3 

.17912 

.0664 

.82249 

65,5 

.00096 

.82153 

65,2 

.17847 

0.0665 

8.82314 

65,4 

0.00096 

0,3 

8.82218 

65,1 

I.I7782 

.0666 

.82380 

65>3 

.00096 

.82283 

65,0 

.17717 

.0667 

.82445 

65,2 

.00097 

.82348 

64,9 

.17652 

.0668 

.82510 

65,1 

.00097 

.82413 

64,8 

.17587 

.0669 

.82575 

65,0 

.00097 

.82478 

64,7 

.17522 

0.0670 

8.82640 

64,9 

0.00097 

0,3 

8.82543 

64,6 

I.  17457 

.0671 

.82705 

64,8 

.00098 

.82607 

64,5 

.17393 

.0672 

.82770 

64,7 

.00098 

.82672 

64,4 

.17328 

.0673 

.82834 

64,6 

.00098 

.82736 

64,3 

.17264 

.0674 

.82899 

64,5 

.00099 

.82800 

64,2 

.17200 

0.0675 

8.82963 

64,4 

0.00099 

.   0,3 

8.82864 

64,1 

1.17136 

.0676 

.83028 

6^3 

.00099 

.82929 

64,1 

.  17071 

.0677 

.83092 

64,2 

.00099 

.82994 

64,0 

.17006 

.0678 

.83156 

64,2 

.00100 

.83056 

63.9 

.16944 

.0679 

.83220 

64,1 

.00100 

.83120 

63,8 

.16880 

0.0680 

8.83284 

64,0 

O.OOIOO 

0,3 

8.83184 

63,7 

1.  16816 

.0681 

.83348 

63,9 

.OOIOI 

.83248 

63,6 

.16752 

.0682 

.83412 

63,8 

.OOIOI 

.833H 

63,5 

.16689 

.0683 

.83476 

63,7 

.OOIOI 

.83375 

63,4 

.16625 

.0684 

.83539 

63,6 

.00102 

.83438 

63,3 

.  16562 

0.0685 

8.83603 

63,5 

0.00102 

0,3 

8.83501 

63,2 

1.16499 

.0686 

.83666 

63,4 

.00102 

.83564 

63,1 

.16436 

.0687 

.83730 

63,3 

.00102 

.83627 

63,0 

.  16373 

.0688 

.83793 

63,2 

.00103 

.83690 

62,9 

.  16310 

.0689 

.83856 

63,1 

.00103 

.83753 

62,8 

.  16247 

0.0690 

8.83919 

63,0 

0.00103 

0,3 

8.83816 

62,7 

1.16184 

.0691 

.83982 

63,0 

.00104 

.83879 

62,7 

.16121 

.0692 

.84045 

62,9 

.00104 

.83941 

62,6 

.16059 

.0693 

.84108 

62,8 

.00104 

.84004 

62,5 

.15996 

.0694 

.84171 

62,7 

.00105 

.84066 

62,4 

.  15934 

0.0695 

8.84233 

62,6 

0.00105 

0,3 

8.84129 

62,3 

1.15871 

.0696 

.84296 

62,5 

.00105 

.84191 

62,2 

.15809 

.0697 

.84358 

62,4 

.00105 

.84253 

62,1 

.  15747 

.0698 

.84421 

62,3 

.00106 

.84315 

62,0 

.15685 

.0699 

.84483 

62,2 

.00106 

.84377 

61,9 

.  15623 

0.0700 

8.84545 

62,1 

0.00106 

0,3 

8.84439 

61,8 

1.15561 

u 

loo  tan  od  u 

«  Fo' 

log  sec  gd  u 

«F/ 

log  sin  gd  u 

«F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

u.  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0700 

8.84545 

62,1 

0.00106 

0,3 

8.84439 

6!,8 

I.ISS^I 

.0701 

.84607 

62,1 

.00107 

.84501 

61,8 

•15499 

.0702 

.84669 

62,0 

.00107 

.84562 

61,7 

.15438 

.0703 

.84731 

61,9 

.00107 

.84624 

61,6 

.15376 

.0704 

.84793 

61,8 

.00108 

.84686 

6i,5 

.15314 

0.0705 

8.84855 

6i,7 

0.00108 

0,3 

8.84747 

61,4 

I.I5253 

.0706 

.84917 

61,6 

.00108 

.84808 

61,3 

.15192 

.0707 

.84978 

61,5 

.00108 

.84870 

61,2 

•15130 

.0708 

.85040 

6M 

.00109 

.84931 

61,1 

.15069 

.0709 

.85101 

61,4 

.00109 

.84992 

61,0 

.15008 

0.0710 

8.85162 

61,3 

O.OOI09 

0,3 

8.85053 

61,0 

I  .  14947 

.0711 

.85224 

61,2 

.OOIIO 

.85114 

60,9 

.14886 

.0712 

.85285 

61,1 

.00110 

.85175 

60,8 

.  14825 

.0713 

.85346 

61,0 

.OOIIO 

.85235 

60,7 

.  14765 

.0714 

.85407 

60,9 

.00111 

.85296 

60,6 

.  14704 

0.0715 

8.85468 

60,8 

O.OOIII 

0,3 

8.85357 

6o,5 

I.I4643 

.0716 

.85528 

60,8 

.OOIII 

.85417 

60,4 

.14583 

.0717 

.85589 

60,7 

.OOII2 

.85478 

60,4 

.  14522 

.0718 

.85650 

60,6 

.OOII2 

.85538 

60,3 

.14462 

.0719 

.85710 

60,5 

.OOII2 

.85598 

60,2 

.14402 

0.0720 

8.85771 

60,4 

O.OOII2 

0,3 

8.85658 

60,1 

I  .  14342 

.0721 

.85831 

60,3 

.00113 

.85718 

60,0 

.14282 

.0722 

.85891 

60,3 

.00113 

.85778 

59,9 

.14222 

.0723 

.85952 

60,2 

.00113 

.85838 

59,9 

.14162 

.0724 

.86012 

60,1 

.OOII4 

.85898 

.14102 

0.0725 

8.86072 

60,0 

O.OOII4  . 

0,3 

8.85958 

59,7 

I  .  14042 

.0726 

.86132 

59,9 

.OOII4 

.86017 

59,6 

.13983 

.0727 

.86192 

59,8 

.00115 

.86077 

59,5 

.13923 

.0728 

.86251 

59,8 

.00115 

.86137 

59,5 

•13863 

.0729 

.86311 

59,7 

.OOII5 

.86196 

59,4 

.13804 

0.0730 

8.86371 

59,6 

O.OOII6 

0,3 

8.86255 

59,3 

I  .  13745 

.0731 

.86430 

59,5 

.00116 

.86314 

59,2 

.13686 

.0732 

.86400 

59,4 

.OOIl6 

.86374 

59,1 

.13626 

.0733 

.86549 

59,4 

.OOII7 

.86433 

59,0 

.13507 

.0734 

.86609 

59,3 

.00117 

.86492 

59,0 

.13508 

0.0735 

8.86668 

59,2 

O.OOII7 

o,3 

8.86551 

58,9 

I.  13449 

.0736 

.86727 

59,1 

.OOIlS 

.86609 

58,8 

.13391 

•0737 

.86786 

59,o 

.OOIlS 

.86668 

58,7 

.13332 

.0738 

.86845 

59,0 

.OOIlS 

.86727 

58,6 

.  13273 

.0739 

.86904 

58,9 

.OOIlS 

.86785 

58,6 

.13215 

0.0740 

8.86963 

58,8 

O.OOII9 

0,3 

8.86844 

58,5 

I.I3I56 

.0741 

.87022 

58,7 

.OOII9 

.86902 

58,4 

.13098 

.0742 

.87080 

58,6 

.OOII9 

.86961 

58,3 

.  13039 

.0743 

•87139 

58,6 

.OOI2O 

.87019 

58,2 

.12981 

.0744 

.87197 

58,5 

.OOI20 

.87077 

58,2 

.12923 

0.0745 

8.87256 

584 

O.OOI2O 

0,3 

8.87135 

58,1 

1.12865 

.0746 

.87314 

58,3 

.OOI2I 

.87193 

58,0 

.13807 

.0747 

.87372 

58,2 

.00121 

.87251 

57,9 

.  12749 

.0748 

.87431 

58,2 

.00121 

.87309 

57,8 

.12691 

.0749 

.87489 

58,1 

.00122 

.87367 

57,8 

.12633 

0.0750 

8.87547 

58,0 

O.OOI22 

0,3 

8.87425 

57,7 

I.  I  2575 

u 

log  tan  <jd  u 

«  Fo' 

log  sec  gd  u 

•  Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


16 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«-  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0750 

8.87547 

58,0 

O.OOI22 

0,3 

8.87425 

57,7 

I.I2575 

.0751 

.87605 

57,9 

.OOI22 

.87482 

57,6 

.12518 

.0752 

.87663 

57,9 

.00123 

.87540 

57,5 

.12460 

•  0753 

.87721 

57,8 

.00123 

.87508 

57,5 

.  12402 

.0754 

.87778 

57,7 

.00123 

.87655 

57,4 

•  12345 

0.0755 

8.87836 

57,6 

O.OOI24 

0,3 

8.87712 

57,3 

I.I2288 

.0756 

.87894 

57,6 

.OOI24 

.87770 

57,2 

.  12230 

.0757 

.8795*1 

57,5 

.OOI24 

.87827 

57,2 

.12173 

.0758 

.88009 

57,4 

.00125 

.87884 

57,i 

.12116 

.0759 

.88066 

57,3 

.00125 

.87941 

57,o 

.12059 

0.0760 

8.88123 

57,3 

O.OOI25 

0,3 

8.87098 

56,9 

I  .  12002 

.0761 

.88180 

57,2 

.OOI26 

.88055 

56,8 

.11945 

.0762 

.88238 

57,1 

.OOI26 

.88112 

56,8 

.11888 

.0763 

.88295 

57,o 

.OOI26 

.88168 

56,7 

.11832 

.0764 

.88352 

57,o 

.00127 

.88225 

56,6 

.H775 

0.0765 

8.88408 

56,9 

O.OOI27 

0,3 

8.88282 

56,5 

1.11718 

.0766 

.88465 

56,8 

.OOI27 

.88338 

56,5 

.11662 

.0767 

.88522 

56,7 

.OOI28 

.88394 

56,4 

.11606 

.0768 

.88579 

56,7 

.00128 

.88451 

56,3 

.H549 

.0769 

.88635 

56,6 

.OOI28 

.88507 

56,3 

.H493 

0.0770 

8.88692 

56,5 

0.00129 

0,3 

8.88563 

56,2 

i.  H437 

.0771 

.88748 

56,4 

.OOI29 

.88620 

56,i 

.11380 

.0772 

.88805 

56,4 

.OOI29 

.88676 

56,0 

.11324 

.0773- 

.88861 

56,3 

.OOI3O 

.88732 

56,0 

.11268 

.0774 

.88917 

56,2 

.00130 

.88787 

55,9 

.11213 

0.0775 

8.88974 

56,2 

O.OOI3O 

0,3 

8.88843 

55,8 

1.11157 

.0776 

.89030 

56,1 

.00131 

.88899 

55,7 

.IIIOI 

.0777 

.89086 

56,o 

.00131 

.88955 

55,7 

.11045 

.0778 

.89142 

55,9 

.00131 

.89010 

55,6 

.10990 

•0779 

.89198 

55,9 

.00132 

.89066 

55,5 

.10934 

0.0780 

8.89253 

55,8 

0.00132 

0,3 

8.89122 

55.5 

i  .  10878 

.0781 

.89309 

55,7 

.00132 

.89177 

55,4 

.10823 

.0782 

.89365 

55,6 

.00133 

.89232 

55,3 

.10768 

.0783 

.89421 

55,6 

.00133 

.89288 

55,2 

.  10712 

.0784 

.89476 

55,5 

.00133 

.89343 

55,2 

.10657 

0.0785 

8.89532 

55,4 

O.OOI34 

0,3 

8.89398 

55,1 

1.10602 

.0786 

.89587 

55,4 

.00134 

.89453' 

55,0 

.10547 

.0787 

.89642 

55,3 

.00134 

.89508 

55,o 

.10492 

.0788 

.89698 

55,2 

.00135 

.89563 

54,9 

.  10437 

.0789 

.89753 

55,2 

.00135 

.89618 

54,8 

.  10382 

0.0790 

8.89808 

55,i 

.  0.00135 

0,3 

8.89672 

54,7 

i  .  10328 

.0791 

.89863 

55,o 

.00136 

.89727 

54,7 

.  10273 

.0792 

.89918 

54,9 

.00136 

.89782 

54,6 

.10218 

.0793 

.89973 

54,9 

.00136 

.89836 

54,5 

.  10164 

.0794 

.90028 

54,8 

.00137 

.89891 

54,5 

.10109 

0.0795 

8.90082 

54,7 

0.00137  . 

0,3 

8.89945 

54,4 

I  .  10055 

.0796 

.00137 

54,7 

.00137 

.90000 

54,3 

.10000 

.0797 

.90192 

54,6 

.00138 

.90054 

54,3 

.09946 

.0798 

.90246 

54,5 

.00138 

.90108 

54,2 

.09892 

•0799 

.90301 

54,5 

.00138 

.90162 

54,1 

.09838 

0.0800 

8.90355 

54,4 

0.00139 

0,3 

8.90216 

54,1 

1.09784 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

»Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

»F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0800 

8.00355 

54,4 

0.00139 

0,3 

8.90216 

54,1 

1.09784 

.0801 

.90410 

54,3 

.00139 

.90271 

54,0 

.09729 

.0802 

.90464 

54,3 

.00140 

.00324 

53,9 

.09676 

.0803 

.90518 

54,2 

.00140 

.90380 

53,9 

.09620 

.0804 

.90572 

54,1 

.00140 

.90432 

53,8 

.09568 

0.0805 

8.90626 

54,1 

0.00141 

o,3 

8.90486 

53,7 

I.095I4 

.0806 

.90681 

54,0 

.00141 

o,3 

.90540 

53,6 

.09460 

.0807 

•90734 

53,9 

.00141 

o,3 

•90593 

'  53,6 

.00407 

.0808 

.00788 

53,9 

.00142 

0,4 

.90647 

53,5 

.09353 

.0809 

.00842 

53,8 

.00142 

0,4 

.90700 

53,4 

.09300 

0.0810 

8.00896 

53,7 

O.OOI42 

0,4 

8.90754 

53,4 

1.09246 

.0811 

.90950 

53,7 

.00143 

.90807 

53,3 

.09193 

.0812 

.91003 

53,6 

.00143 

.90860 

53,3 

.09140 

.0813 

.91057 

53,5 

.00143 

.90914 

53,2 

.09086 

.0814 

.91110 

53,5 

.00144 

.90967 

53,1 

.09033 

0.0815 

8.91164 

53,4 

0.00144 

0,4 

8.9IO2O 

53,1 

1.08980 

.0816 

.91217 

53,3 

.00144 

.91073 

53,0 

.08927 

.0817 

.91271 

53,3 

.00145 

.91126 

52,9 

.08874 

.0818 

.91324 

53,2 

.00145 

.91179 

52,9 

.08821 

.0819 

.91377 

53,1 

.00145 

.91231 

52,8 

.08769 

0.0820 

8.91430 

53,1 

0.00146 

0,4 

8.91284 

52,7 

1.08716 

.0821 

.91483 

53,0 

.00146 

.91337 

52,7 

.08663 

.0822 

.91536 

53,o 

.00147 

.91390 

52,6 

.08610 

.0823 

.91589 

52,9 

.00147 

.91442 

52,5 

.08558 

.0824 

.91642 

52,8 

.00147 

.91495 

52,5 

.08505 

0.0825 

8.91695 

52,8 

0.00148 

0,4 

8.91547 

52,4 

1.08453 

.0826 

.91747 

52,7 

.00148 

.91599 

52,3 

.08401 

.0827 

.91800 

52,6 

.00148 

.91652 

52,3 

.08348 

.0828 

.91853 

52,6 

.00149 

.91704 

52,2 

.08296 

.0829 

.91905 

52,5 

.00149 

.91756 

52,1 

.08244 

0.0830 

8.91958 

52,4 

0.00149 

0,4 

8.91808 

52,1 

1.08192 

.0831 

.92010 

52,4 

.00150 

.91860 

52,0 

.08140 

.0832 

.92062 

52,3 

.00150 

.91912 

52,0 

.08088 

.0833 

.92115 

52,3 

.00151 

.91964 

51,9 

.08036 

.0834 

.92167 

52,2 

.00151 

.92016 

51,8 

.07984 

0.0835 

8.92219 

52,1 

0.00151 

0,4 

8.92068 

5i,8 

1.07932 

.0836 

.92271 

52,1 

.00152 

.92120 

5i,7 

.07880 

.0837 

.92323 

52,0 

.00152 

.92171 

5i,6 

.07829 

.0838 

.92375 

5i,9 

.00152 

.92223 

5i,6 

.07777 

.0839 

.92427 

5i,9 

.00153 

.92274 

5i,5 

.07726 

0.0840 

8.02479 

51,8 

0.00153 

0,4 

8.92326 

51,5 

1.07674 

.0841 

.92531 

5i,8 

.00153 

.92377 

51,4 

.07623 

.0842 

.92583 

5i,7 

.00154 

.92429 

51,3 

•07571 

.0843 

.92634 

5i,6 

.00154 

.92480 

51,3 

.07520 

.0844 

.92686 

51,6 

.00154 

.92531 

51,2 

.07469 

0.0845 

8.92737 

51,5 

0.00155 

0,4 

8.92582 

51,2 

1.07418 

.0846 

.92789 

5i,5 

.00155 

.92634 

5i,i 

.07366 

.0847 

.92840 

5M 

.00156 

.92685 

51,0 

.07315 

.0848 

.92892 

51,3 

.00156 

.92736 

5i,o 

.07264 

.0849 

.92943 

51,3 

.00156 

.92787 

50,9 

.07213 

0.0850 

8.92994 

51,2 

0.00157 

0,4 

8.92837 

50,8 

1.07163 

u 

log  tin  fld  u 

-  Fo' 

log  tec  gd  u 

-  Fo' 

log  sin  gd  u 

-FO' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


18 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«F0' 

log  coth  u 

0.0850 

8.92994 

51,2 

0.00157 

0,4 

8.92837 

50,8 

1.07163 

.0851 

.93045 

51,2 

.00157 

.92888 

50,8 

.07112 

.0852 

.93096 

51,1 

.00157 

.92939 

50,7 

.07061 

.0853 

.93148 

51,0 

.00158 

.92990 

50,7 

.O7OIO 

.0854 

.93199 

51,0 

.00158 

.93040 

50,6 

.06960 

0.0855 

8.93250 

50,9 

0.00159 

0,4 

8.93091 

50,5 

1.06909 

.0856 

.93300 

50,9 

.00159 

.93141 

50,5 

.06859 

.0857 

.93351 

50,8 

.00159 

.93192 

50,4 

.06808 

.08^8 

.93402 

50,7 

.00160 

.93242 

50,4 

.06758 

.0859 

•93453 

50,7 

.00160 

.93293 

50,3 

.06707 

0.0860 

8.93503 

50,6 

0.00160 

0,4 

8.93343 

50,3 

1.06657 

.0861 

•93554 

50,6 

.00161 

•93393 

50,2 

.06607 

.0862 

.93604 

50,5 

.00161 

.93443 

50,1 

•06557 

.0863 

.93655 

50,4 

.00162 

•93493 

50,i 

.06507 

.0864 

.93705 

50,4 

.00162 

.93543 

50,o 

.06457 

0.0865 

8.93756 

50,3 

0.00162 

0,4 

8.93593 

50,o 

1.06407 

.0866 

.938o6 

50,3 

.00163 

.93643 

49,9 

.06357 

.0867 

.93856 

50,2 

.00163 

.93693 

49,8 

.06307 

.0868 

•93907 

50,2 

.00163 

•93743 

49,8 

.06257 

.0869 

•93957 

50,i 

.00164 

•93793 

49,7 

.06207 

0.0870 

8.94007 

50,o 

0.00164 

0,4 

8.93843 

49,7 

I.06I57 

.0871 

.94057 

50,0 

.00165 

.93892 

49,6 

.06108 

.0872 

.94107 

49,9 

.00165 

•93942 

49,6 

.0605? 

.0873 

.94157 

49,9 

.00165 

.93991 

49,5 

.06009 

.0874 

.94206 

49,8 

.00166 

.04041 

49,4 

.05959 

0.0875 

8.94256 

49,8 

0.00166 

0,4 

8.94090 

49,4 

1.05910 

.0876 

.94306 

49,7 

.00166 

.94140 

49,3 

.05860 

.0877 

.94356 

49,6 

.00167 

.04189 

49,3 

.05811 

.0878 

.94405 

49,6 

.00167 

.94238 

49,2 

.05762 

.0879 

.94455 

49,5 

.00168 

.94287 

49,2 

.05713 

0.0880 

8.94504 

49,5 

0.00168 

0,4 

8.94336 

49,1 

1.05664 

.0881 

.94554 

49,4 

.00168 

•94385 

49,0 

.05615 

.0882 

.94603 

49,4 

.00169 

•94434 

49,0 

.05566 

.0883 

.94652 

49,3 

.00169 

.94483 

48,9 

.05517 

.0884 

.94702 

49,3 

.00169 

•94532 

48,9 

.05468 

0.0885 

8.94751 

49,2 

0.00170 

0,4 

8.94581 

48,8 

1.05419 

.0886 

.94800 

49,1 

.06170 

.94630 

48,8 

.05370 

.0887 

.94849 

49,1 

.00171 

•94679 

48,7 

.05321 

.0888 

.94898 

49,0 

.00171 

.94727 

48,7 

.05273 

.0889 

.94947 

49,0 

.00171 

.94776 

48,6 

.05224 

0.0890 

8.94996 

48,9 

0.00172 

0,4 

8.94825 

48,5 

I.05I75 

.0891 

.95045 

48,9 

.00172 

.94873 

48,5 

.05127 

.0892 

.95094 

48,8 

.00173 

.94922 

48,4 

.05078 

.0893 

.95143 

48,8 

.00173 

.94970 

48,4 

.05030 

.0894 

.95192 

48,7 

.00173 

.95018 

48,3 

.04982 

0.0895 

8.95240 

48,7 

0.00174 

0,4 

8.95067 

48,3 

1.04933 

.0896 

.95289 

48,6 

.00174 

.95H5 

48,2 

.04885 

.0897 

•95337 

48,5 

.00174 

.95163 

48,2 

.04837 

.0898 

.95386 

48,5 

.00175 

.95211 

48,1 

.04789 

.0899 

•95434 

48,4 

.00175 

.95259 

48,0 

.04741 

0.0900 

8.95483 

48,4 

0.00176 

0,4 

8.95307 

48,0 

1.04693 

u 

log  tan  gd  u 

»  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F</ 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0900 

8.95483 

48,4 

0.00176 

0,4 

8.95307 

48,0 

1.04693 

.0901 

•95531 

48,3 

.00176 

•95355 

47,9 

.04645 

.0902 

.95580 

48,3 

.00176 

.95403 

47,9 

•04597 

.0903 

.95628 

48,2 

.00177 

•95451 

47,8 

.04549 

.0904 

.95676 

48>2 

.00177 

•95499 

47,8 

.04501 

0.0905 

8.95724 

48,1 

0.00178 

0,4 

8-95547 

47,7 

1.04453 

.0906 

•957/2 

48,1 

.00178 

•95594 

47,7 

.04406 

.0907 

.95820 

48,0 

.00178 

•95642 

47,6 

•04358 

.0908 

.95868 

48,0 

.00179 

.95689 

47,6 

.04311 

.0909 

.95916 

47,9 

.00179 

•95737 

47,5 

.04263 

0.0910 

8.95964 

47,9 

0.00180 

0,4 

8.95784 

47,5 

1.04216 

.0911 

.96012 

47,8 

.00180 

.95832 

47,4 

.04168 

.0912 

.96060 

47,8 

.00180 

.95879 

47,4 

.04121 

.0913 

.96107 

47,7 

.00181 

.95927 

47,3 

.04073 

.0914 

.96155 

47,6 

.00181 

•95974 

47,3 

.04026 

0.0915 

8.96203 

47,6 

0.00182 

0,4 

8.96021 

47,2 

1.03979 

.0910 

.96250 

47,5 

.00182 

.96068 

47,1 

.03932 

.0917 

.96298 

47,5 

.00182 

•96115 

47,1 

.03885 

.0918 

.96345 

47,4 

.00183 

•  96163 

47,0 

•03837 

.0919 

.96393 

47,4 

.00183 

.96210 

47,0 

.03790 

0.0920 

8.96440 

47,3 

0.00184 

0,4 

8.96256 

46,9 

1.03744 

.0921 

.96487 

47,3 

.00184 

•  96303 

46,9 

.03697 

.0922 

.96535 

47,2 

.00184 

.96350 

46,8 

.03650 

.0923 

.96582 

47,2 

.00185 

.96397 

46,8 

.03603 

.0924 

.96629 

47,1 

.00185 

.96444 

46,7 

.03556 

0.0925 

8.96676 

47,1 

0.00186 

0,4 

8.96491 

46,7 

1.03509 

.0926 

.96723 

47,0 

.00186 

•96537 

46,6 

•03463 

.0927 

.96770 

47,0 

.00186 

.96584 

46,6 

.03416 

.0928 

.96817 

46,9 

.00187 

.96630 

46,5 

•03370 

.0929 

.96864 

46,9 

.00187 

.96677 

46,5 

.03323 

0.0930 

8.96911 

46,8 

0.00188 

0,4 

8.96723 

46,4 

1.03277 

.0931 

.96958 

46,8 

.00188 

.96770 

46,4 

.03230 

.0932 

.97004 

46,7 

.00188 

.96816 

46,3 

.03184 

•  0933 

.97051 

46,7 

.00189 

.96862 

46,3 

.03138 

•  0934 

.97098 

46,6 

.00189 

.96909 

46,2 

.03091 

0.0935 

8.97144 

46,6 

0.00190 

0,4 

8.96955 

46,2 

1.03045 

.0936 

.97191 

46,5 

.00190 

.97001 

,46,1 

.02999 

•  0937 

.97237 

46,5 

.00190 

.97047 

46,1 

.02953 

.0938 

.97284 

46,4 

.00191 

•  97093 

46,0 

.02007 

•  0939 

•97330 

46,4 

.00191 

.97139 

46,0 

.02861 

0.0040 

8.97377 

46,3 

0.00192 

0,4 

8.97185 

45,9 

1.02815 

.0941 

.97423 

46,3 

.00102 

.97231 

45,9 

.02769 

.0942 

.97469 

46,2 

.OOI92 

.97277 

45,8 

.02723 

.0943 

.97516 

46,2 

.00193 

•97323 

45,8 

.02677 

.0944 

.97562 

46,1 

.00193 

.97368 

45,7 

.02632 

0.0945 

8.97608 

46,1 

O.OOT94 

0,4 

8.974M 

45,7 

1.02586 

.0946 

.97654 

46,0 

.00194 

.97460 

45,6 

.02540 

.0947 

•97700 

46,0 

.00194 

.97505 

45,6 

.02495 

.0948 

.97746 

45,9 

.00195 

•97551 

45,5 

.02449 

.0949 

•97792 

45,9 

.00195 

.97597 

45,5 

.02403 

0.0950 

8.97838 

45,9 

0.00106 

OA 

8.9764-' 

45,4 

1.02358 

u 

loo  tan  gd  u 

-Fo' 

loo  sec  gd  u 

«  Fo' 

log  sin  gd  u 

•  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


20 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.0950 

8.97838 

45,9 

0.00196 

0,4 

8.97642 

45,4 

1.02358 

.0951 

.97883 

45,8 

.00196 

.97687 

45,4 

.02313 

.0952 

.97929 

45,8 

.00197 

•97733 

45,3 

.02267 

.0953 

.97975 

45,7 

.00197 

.97778 

45,3 

.02222 

.0954 

.98021 

45,7 

.00197 

.97823 

45,2 

.02177 

0.0955 

8.98066 

45,6 

0.00198 

0,4 

8.97869 

45,2 

1.02131 

.0956 

.98112 

45,6 

.00198 

.979H 

45,2 

.02086 

.0957 

.98157 

45,5 

.00199 

.97959 

45,i 

.02041 

.0958 

.98203 

45,5 

.00199 

.98004 

45,1 

.01996 

.0959 

.98248 

45*4 

.00199 

.98049 

45,0 

.01951 

0.0960 

8.98294 

45,4 

0<O02po 

0,4 

8.98094 

45,0 

1.01906 

.0961 

.98339 

45,3 

.00200 

.98139 

44,9 

.01861 

.0962 

.98384 

45,3 

.OO2OI 

.98184 

44,9 

.01816 

.0963 

.98430 

45,2 

.00201 

.98229 

44,& 

.01771 

.0964 

.98475 

45,2 

.00201 

•98273 

44,8 

.01727 

0.0965 

8.98520 

45,1 

0.00202 

0,4 

8.98318 

44,7 

1.01682 

.0966 

.98565 

45,1 

.OO202 

.98363 

44,7 

.01637 

.0967 

.98610 

45,1 

.00203 

.98408 

44,6 

.01592 

.0968 

.98655 

45,o 

,  .00203 

.98452 

44,6 

.01548 

.0969 

.98700 

45,o 

.OO2O4 

.98497 

44,5 

.01503 

0.0970 

8.98745 

44,9 

O.O02O4 

0,4 

8.98541 

44,5 

1.  01459 

.0971 

.98790 

44,9 

.OO2O4 

.98586 

44,5 

.01414 

.0972 

.08835 

44,8 

.OO2O5 

.98630 

44,4 

.01370 

.0973 

.08880 

44,8 

.OO2O5 

.98675 

44,4 

.01325 

.0974 

.98925 

44,7 

.00206 

.98719 

44,3 

.01281 

0.0975 

8.98969 

44,7 

O.O0206 

0,4 

8.98763 

44,3 

1.01237 

.0976 

.90014 

44,6 

.00207 

.98807 

44,2 

.01193 

.0977 

.99059 

44,6 

.O02O7 

.98852 

44,2 

.01148 

.0978 

.99103 

44,5 

.OO2O7 

.98896 

44,1, 

.01104 

.0979 

.99148 

44,5 

.O0208 

.98940 

44,1 

.01060 

0.0980 

8.99192 

44,5 

O.OO2O8 

0,4 

8.98984 

44,0 

I.  01016 

.0981 

.99237 

44,4 

.00209 

.99028 

44,0 

.00972 

.0982 

.99281 

44,4 

.OO2O9 

.99072 

43,9 

.00928 

.0983 

•99325 

44,3 

.O02O9 

.99116 

43,9 

.00884 

.0984 

•99370 

44,3 

.00210 

.99160 

43,9 

.00840 

0.0985 

8.99414 

44,2 

0.00210 

0,4 

8.09203 

43,8 

1.00797 

.0986 

.99458 

44,2 

.OO2II 

.99247 

43,8 

.00753 

.0987 

.99502 

44,2 

.002  I  I 

.99291 

43,7 

.00709 

.0988 

.99546 

44,1 

.00212 

.99335 

43,7 

.0066,5 

.0989 

.99590 

44,1- 

.OO2I2 

.99378 

43,6 

.006*22 

0.0090 

8.99634 

44,0 

O.OO2I2 

0,4 

8.99422 

43,6 

1.00578 

.0991 

.99678 

44,0 

.00213 

.99466 

43,5 

.00534 

.0992 

.99722 

43,9 

.00213 

.99509 

43,5 

.00491 

.0993 

.99766 

43,9 

.OO2I4 

•99553 

43,4 

.00447 

.0994 

.99810 

43,8 

.00214 

.99596 

43,4 

.00404 

0.0095 

8.99854 

43,8 

0.00215 

0,4 

8.99639 

43,4 

1.00361 

.0096 

.99898 

43,7 

.00215 

.99683 

43,3 

.00317 

.0997 

.99941 

43,7 

.00215 

.99726 

43,2 

.00274 

.0098 

.99985 

43,7 

.002X6 

.99769 

43,2- 

.00231 

.0999 

9.00029 

43,6 

.00216 

.99812 

43,2. 

.00188 

O.IOOO 

9.00072 

43,6 

0.00217 

0,4 

8.99856 

43,1 

1.00144 

u 

log  tan  gd  u 

«  Fn' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


21 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

O.IOO 

9.00072 

435,7 

O.OO2I7 

4,3 

8.99856 

431,4 

1.00144 

.IOI 

.00506 

431,5 

.OO22I 

4,4 

9.00285 

427,1 

0.99715 

.102 

•00935 

427,3 

.00226 

4,4 

.00710 

422,8 

.99290 

.103 

.01360 

423,1 

.00230 

4,5 

.01131 

418,7 

.98869 

.104 

.01782 

419,1 

.00234 

4,5 

.01547 

414,6 

•98453 

0.105 

9.02199 

415,1 

0.00239 

4,5 

9.01960 

410,6 

0.98040 

.106 

.02612 

411,2 

.00244 

4,6 

.02368 

406,7 

.97632 

.107 

.03021 

407,4 

.00248 

4,6 

.02773 

402,8 

.97227 

.108 

.03427 

403,7 

.00253 

4,7 

.03174 

399,o 

.96826 

.109 

.03829 

400,0 

.00257 

4,7 

.03571 

395,3 

.96429 

O.IIO 

9.04227 

396,4 

0.00262 

4,8 

9.03965 

391,6 

0.96035 

.III 

.04621 

392,9 

.00267 

4,8 

-04354 

388,1 

.95646 

.112 

.05013 

389,4 

.00272 

4,8 

.04741 

384,5 

.95259 

•113 

.05400 

386,0 

.00277 

4,9 

.05124 

381,1 

.94876 

.114 

•05785 

382,6 

.00282 

4,9 

.05503 

377,7 

.94497 

O.IIS 

9.06165 

379,3 

O.O0287 

5,0 

9.05879 

374,3 

0.94121 

.116 

.06543 

376,1 

.OO292 

5,0 

.06252 

37i,i 

.93748 

.117 

.06918 

372,9 

.00297 

5,i 

.06621 

367,8 

.93379 

.118 

.07289 

309,8 

.00302 

5,1 

.06987 

364,7 

.93013 

.119 

.07657 

366,7 

.00307 

5,i 

.07350 

36i,5 

.92650 

O.I2O 

9.08022 

363,6 

0.00312 

5,2 

9.07710 

358,5 

0.92290 

.121 

.08384 

360,7 

.00317 

5,2 

.08067 

355,4 

.91933 

.122 

.08744 

357,7 

.00322 

5,3 

.08421 

352,5 

.91579 

.123 

.09100 

354,9 

.00328 

5,3 

.08772 

349,5 

.91228 

.124 

.09453 

352,0 

.00333 

5,4 

.09120 

346,7 

.90880 

O.I25 

9.09804 

349,2 

0.00338 

5,4 

9.09466 

343,8 

0.90534 

.126 

.10152 

346,5 

.00344 

5,4 

.09808 

34i,i 

.00192 

.127 

.  10497 

343,8 

.00349 

5,5 

.  10148 

338,3 

.89852 

.128 

.10840 

34M 

.00355 

5,5 

.  10485 

335,6 

.89515 

.129 

.11179 

338,5 

.00360 

5,6 

.10819 

333,0 

.89181 

0.130 

9.H5I7 

336,0 

0.00366 

5,6 

9.IH5I 

330,3 

0.88849 

.131 

.11851 

333,4 

.00372 

5,7 

.11480 

327,8 

.88520 

.132 

.12183 

330,9 

.00377 

5,7 

.11806 

325,2 

.88194 

.133 

.12513 

328,5 

.00383 

5,7 

.12130 

322,7 

.87870 

.134 

.12840 

326,0 

.00389 

5,8 

.12452 

320,3 

.87548 

0.135 

9.I3I65 

323,7 

0.00395 

5,8 

9.I277I 

317,8 

0.87229 

.136 

.13488 

321,3 

.00400 

5,9 

.13087 

315,4 

.86913 

.137 

.13808 

319,0 

.00406 

5,9 

.  13402 

3i3,i 

.86598 

.138 

.14126 

3i6,7 

.00412 

6,0 

.13713 

3io,7 

.86287 

.139 

.14441 

314,5 

.00418 

6,0 

.  14023 

308,5 

.85977 

0.140 

9-  14755 

312,2 

0.00424 

6,0 

9.14330 

306,2 

0.85670 

.141 

.15066 

310,0 

.00430 

6,1 

.14635 

304,0 

.85365 

.142 

.15375 

307,9 

.00436 

6,1 

.14938 

301,8 

.85062 

•  143 

.15682 

305,8 

.00443 

6,2 

.15239 

299,6 

.84761 

.144 

.15986 

303,7 

.00449 

6,2 

.15538 

297,5 

.84462 

0.145 

9.16289 

301,6 

0.00455 

6,3 

9.15834 

295,4 

0.84166 

.146 

.16589 

299,6 

.00461 

6,3 

.16128 

293,3 

.83872 

.147 

.16888 

297,6 

.00468 

6,3 

.16420 

291,2 

.83580 

.148 

.17185 

295,6 

.00474 

6,4 

.16711 

289,2 

.83289 

.149 

•  17479 

293,6 

.00480 

6,4 

.16999 

287,2 

.83001 

0.150 

9.17772 

291,7 

0.00487 

6,5 

9-17285 

285,2 

0.82715 

u 

log  tan  ad  u 

«  Fo' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

»  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


22 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F<>' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.150 

9-  17772 

291,7 

0.00487 

6,5 

9.17285 

285,2 

0.82715 

.151 

.18063 

289,8 

.00493 

6,5 

.17569 

283,3 

.82431 

.152 

.18351 

287,9 

.00500 

6,6 

.17852 

281,4 

.82148 

.153 

.18638 

286,1 

.00506 

6,6 

.  18132 

279,5 

.81868 

.154 

.18924 

284,2 

.00513 

6,6 

.18411 

277,6 

.81589 

0.155 

9.19207 

282,4 

0.00520 

6,7 

9.18687 

275,8 

0.81313 

.156 

.19488 

280,6 

.00526 

6,7 

.18962 

273,9 

.81038 

.157 

.19768 

278,9 

.00533 

6,8 

.  19235 

272,1 

.80765 

.158 

.20046 

277,1 

.00540 

6,8 

.19506 

270,3 

.80494 

.159 

.20323 

275,4 

.00547 

6,8 

.  19776 

268,6 

.80224 

0.160 

9.20597 

273,7 

0.00554 

6,9 

9.20044 

266,9 

0.79956 

.161 

.20870 

272,1 

.00560 

6,9 

.20310 

265,1 

.79690 

.162 

.21141 

270,4 

.00567 

7,o 

.20574 

263,4 

.79426 

.163 

.21411 

268,8 

.00574 

7,o 

.20837 

261,8 

.79163 

.164 

.21679 

267,2 

.00581 

7,i 

.21097 

260,1 

.78903 

0.165 

9.21945 

265,6 

0.00589 

7,i 

9.21357 

258,5 

0.78643 

.166 

.22210 

264,0 

.00506 

7,1 

.21614 

256,9 

.78386 

.167 

.22473 

262,5 

.00603 

7,2 

.21871 

255,3 

.78129 

.168 

.22735 

260,9 

.00610 

7,2 

.22125 

253,7 

.77875 

.169 

.22995 

259,4 

.00617 

7,3 

.22378 

252,2 

.77622 

0.170 

9.23254 

257,9 

0.00625 

7,3 

9.22629 

250,6 

0.77371 

.171 

.23511 

256,4 

.00632 

7,4 

.22879 

249,1 

.77121 

.172 

.23767 

255,0 

.00639 

7,4 

.23128 

247,6 

.76872 

.173 

.24021 

253,5 

.00647 

7,4 

.23374 

246,1 

.76626 

.174 

.24274 

252,1 

.00654 

7,5 

.23620 

244,6 

.76380 

0.175 

9.24525 

250,7 

0.00662 

7,5 

9.23864 

243,2 

0.76136 

.176 

.24775 

249,3 

.00669 

7,6 

.24106 

241,7 

.75894 

.177 

.25024. 

247,9 

.00677 

7,6 

.24347 

240,3 

.75653 

.178 

.25271 

246,5 

.00684 

7,6 

.24587 

238,9 

.75413 

.179 

.25517 

245,2 

.00692 

7,7 

.24825 

237,5 

.75175 

0.180 

9-25762 

243,9 

0.00700 

7,7 

9.25062 

236,1 

0.74938 

.181 

.26005 

242,5 

.00708 

7,8 

.25297 

234,8 

.74703 

.182 

.26247 

241,3 

.00715 

7,8 

.25531 

233,4 

.74469 

.183 

.26487 

240,0 

.00723 

7,9 

.25764 

232,1 

.74236 

.184 

.26727 

238,7 

.00731 

7,9 

.25996 

230,8 

.74004 

0.185 

9-26965 

237,4 

0.00739 

7,9 

9.26226 

229,5 

0.73774 

.186 

.27201 

236,2 

.00747 

8,0 

.26454 

228,2 

.73546 

.187 

.27437 

234,9 

.00755 

8,0 

.26682 

226,9 

.73318 

.188 

.27671 

233,7 

.00763 

8,1 

.26908 

225,7 

.73092 

.189 

.27904 

232,5 

.00771 

8,1 

.27133 

224,4 

.72867 

O.IOO 

9.28136 

231,3 

0.00779 

8,2 

9.27357 

223,2 

0.72643 

.191 

.28367 

230,1 

.00787 

8,2 

.27580 

221,9 

.72420 

.192 

.28597 

229,0 

.00796 

8,2 

.27801 

220,7 

.72109 

.193 

.28825 

227,8 

.00804 

8,3 

.28021 

219,5 

.71979 

.194 

.20052 

226,7 

.00812 

8,3 

.28240 

218,3 

.71760 

0.195 

9.29278 

225,5 

0.00821 

8,4 

9.28458 

217,2 

0.71542 

.196 

.29503 

224,4 

.00829 

8,4 

.28674 

216,0 

.71326 

.197 

.29727 

223,3 

.00837 

8,4 

.28890 

214,9 

.71110 

.198 

.20950 

222,2 

.00846 

8,5 

.29104 

213,7 

.70896 

.199 

.30172 

221,1 

.00854 

8,5 

.29317 

212,6 

.70683 

O.2OO 

9.30392 

22O,O 

0.00863 

8,6 

9.29529 

211,5 

0.70471 

U 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

O.200 

9.30392 

22O,0 

0.00863 

8,6 

9.29529 

211,5 

0.70471 

.201 

.30612 

219,0 

.00871 

8,6 

.29740 

210,4 

.70200 

.202 

.30830 

217,9 

.00880 

8,7 

.29950 

209,3 

.70050 

.203 

.31047 

2  1  6,9 

.00889 

8,7 

.30159 

208,2 

.69841 

.204 

.31264 

215,8 

.00897 

8,7 

.30366 

207,1 

.69634 

O.205 

9.31479 

214,8 

0.00906 

8,8 

9.30573 

206,0 

0.69427 

.206 

.31693 

213,8 

.00915 

8,8 

.30778 

205,0 

.69222 

.207 

.31907 

212,8 

.00924 

8,9 

.30983 

203,9 

.69017 

.208 

.32119 

211,8 

.00933 

8,9 

.31186 

202,9 

.68814 

.209 

.32330 

210,8 

.00942 

8,9 

.31389 

20  1,  9 

.68611 

0.2IO 

9.32541 

209,8 

0.00951 

9,0 

9.31590 

200,8 

0.68410 

.211 

.32750 

208,9 

.00960 

9,0 

.31790 

199,8 

.68210 

.212 

.32958 

207,9 

.00969 

9,i 

.31000 

198,8 

.68010 

.213 

.33166 

207,0 

.00978 

9,1 

.32188 

197,9 

.67812 

.214 

•33372 

206,0 

.00987 

9,2 

.32385 

196,9 

.67615 

O.2I5 

9.33578 

205,1 

0.00996 

9,2 

9.32582 

195,9 

0.67418 

.216 

.33783 

204,2 

.01005 

9,2 

.32777 

194,9 

.67223 

.217 

.33986 

203,3 

.OIOI5 

9,3 

.32972 

194,0 

.67028 

.218 

.34189 

202,4 

.01024 

9,3 

.33165 

I93,o 

.66835 

.219 

•34391 

201,5 

.01033 

9,4 

.33358 

192,1 

.66642 

O.220 

9-34592 

200,6 

0.01043 

9,4 

9-33549 

191,2 

0.66451 

.221 

•34792 

199,7 

.01052 

9,4 

•33740 

190,3 

.66260 

.222 

.34991 

198,8 

.01062 

9,5 

•33930 

189,3 

.66070 

.223 

.35190 

198,0 

.01071 

9,5 

.34119 

188,4 

.65881 

.224 

.35387 

197,1 

.01081 

9,6 

•34307 

187,5 

.65693 

O.225 

9.35584 

196,3 

O.OIOOO 

9,6 

9-34494 

186,7 

0.65506 

.226 

.35780 

195,4 

.OIIOO 

9,7 

.34680 

185,8 

.65320 

.227 

•35975 

194,6 

.01109 

9,7 

.34865 

184,9 

.65135 

.228 

.36169 

193,8 

.01119 

9,7 

.35050 

184,0 

.64950 

.229 

.36362 

193,0 

.OII2Q 

9,8 

.35234 

183,2 

.64766 

0.23O 

9.36555 

192,1 

O.OII39 

9,8 

9.35416 

182,3 

0.64584 

.231 

.36747 

I9i,3 

.OII49 

9,9 

.35598 

181,5 

.64402 

.232 

.36938 

190,5 

.OII58 

9,9 

•35779 

180,6 

.64221 

•233 

.37128 

189,8 

.01168 

9,9 

•35959 

179,8 

.64047 

•234 

.37317 

189,0 

.01178 

IO,O 

.36139 

179,0 

.63861 

0.235 

9.37506 

188,2 

O.OII88 

IO,O 

9-36317 

178,2 

0.63683 

.236 

.37694 

187,4 

.01198 

10,1 

.36495 

177,4 

.63505 

•237 

.37881 

186,7 

.OI208 

10,1 

.36672 

176,6 

.63328 

.238 

.38067 

185,9 

.OI2I9 

10,1 

.36848 

175,8 

.63152 

•239 

.38252 

185,2 

.01229 

IO,2 

.37024 

175,0 

.62976 

0.240 

9.38437 

184,4 

0.01239 

10,2 

9.37198 

174,2 

0.62802 

.241 

.38621 

183,7 

.01249 

10,3 

.37372 

173,4 

.62628 

.242 

.38805 

183,0 

.01259 

10,3 

.37545 

172,6 

.62455 

•243 

.38987 

182,2 

.01270 

10,4 

.37717 

I7L9 

.62283 

.244 

.39169 

181,5 

.01280 

10,4 

.37889 

171,1 

.62111 

0.245 

9.39350 

180,8 

0.01291 

10,4 

9.38060 

170,4 

0.61940 

.246 

.39531 

180,1 

.01301 

10,5 

.38230 

169,6 

.61770 

.247 

.39710 

179,4 

.01312 

10,5 

.38309 

168,9 

.61601 

.248 

.30889 

178,7 

.01322 

10,6 

.38567 

168,1 

.61433 

.249 

.40068 

178,0 

.01333 

10,6 

.38735 

167,4 

.61265 

0.250 

9.40245 

177,3 

0.01343 

10,6 

9.38002 

166,7 

0.61098 

u 

log  tan  od  u 

«  Fo' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

*>  Fo' 

log  cosh  u 

»Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.250 

9.40245 

177,3 

0.01343 

10,6 

9.38902 

166,7 

0.61098 

.251 

.40422 

170,0 

.01354 

10,7 

.39069 

166,0 

.60931 

.252 

.40599 

176,0 

.01365 

10,7 

.39234 

165,3 

.60766 

.253 

.40774 

175,3 

.01375 

10,8 

•39399 

164,5 

.60601 

•  254 

.40949 

174,6 

.01386 

10,8 

.39563 

163,8 

.60437 

0.255 

9.4H24 

174,0 

0.01397 

10,8 

9.39727 

163,1 

0.60273 

.256 

.41297 

173,3 

.01408 

10,9 

.39890 

162,5 

.60110 

.257 

.41470 

172,7 

.01419 

10,9 

.40052 

161,8 

.59948 

.258 

.41043 

172,0 

.01430 

II,O 

.40213 

161,1 

.59787 

.259 

.41814 

I7i,4 

.01441 

II,O 

•40374 

160,4 

.59626 

0.260 

9.41086 

170,8 

0.01452 

II,O 

9.40534 

159,7 

0.59466 

.261 

.42156 

170,2 

.01463 

n,  i 

.40693 

I59,i 

.59307 

.262 

.42326 

169,5 

.01474 

n,  i 

.40852 

158,4 

.59148 

.263 

.42495 

168,9 

.01485 

11,2 

.41010 

157,8 

.264 

.42664 

168,3 

.01496 

11,2 

.41168 

I57,i 

.58832 

0.265 

9.42832 

167,7 

0.01507 

11,2 

9.41324 

156,5 

0.58676 

.266 

.42999 

167,1 

.01519 

n,3 

.41480 

155,8 

.58520 

.267 

.43166 

166,5 

.01530 

n,3 

.41636 

155,2 

.58364 

.268 

•43332 

165,9 

.01541 

11,4 

.41791 

154,5 

.58209 

.269 

.43498 

165,3 

.01553 

11,4 

.41945 

153,9 

.58055 

0.270 

9.43663 

164,7 

0.01564 

11,4 

9.42099 

153,3 

0.57901 

.271 

.43827 

164,2 

.01576 

n,5 

.42252 

152,7 

.57748 

.272 

•43991 

163,6 

.01587 

n,5 

.42404 

152,1 

.57596 

.273 

.44154 

163,0 

.01599 

11,6 

.42556 

151,4 

•57444 

.274 

.44317 

162,4 

.01610 

11,6 

.42707 

150,8 

.57293 

0.275 

9.44479 

161,9 

0.01622 

n,7 

9.42857 

150,2 

0.57143 

.276 

.44641 

161,3 

.01634 

n,7 

.43007 

149,6 

.56993 

.277 

.44802 

160,8 

.01645 

n,7 

.43157 

149,0 

.56843 

.278 

.44962 

160,2 

.01657 

11,8 

.43305 

148,5 

.56695 

.279 

.45122 

159,7 

.01669 

11,8 

.43454 

147,9 

.56546 

0.280 

9.45282 

I59,i 

o.  01681 

11,9 

9.43601 

147,3 

0.56399 

.281 

.45441 

158,6 

.01693 

11,9 

.43748 

146,7 

.56252 

.282 

•45599 

158,1 

.01704 

11,9 

.43895 

146,1 

.56105 

.283 

.45757 

157,5 

.01716 

1  2,0 

.44040 

145,6 

.55960 

.284 

.45914 

I57,o 

.01728 

12,0 

.44186 

145,0 

.55814 

0.285 

9.46071 

156,5 

0.01740 

12,1 

9.44330 

144,4 

0.55670 

.286 

.46227 

156,0 

.01752 

12,1 

•  44475  . 

143,9 

.55525 

.287 

.46383 

155,5 

.01765 

12,1 

.44618 

143,3 

.55382 

.288 

.46538 

154,9 

.01777 

12,2 

.44761 

142,8 

.55239 

.289 

.46693 

154,4 

.01789 

12,2 

.44904 

142,2 

.55096 

0.290 

9.46847 

153,9 

0.01801 

12,3 

9.45046 

141,7 

0.54954 

.291 

.47001 

153,4 

.01813 

12,3 

.45187 

141,1 

.54813 

.292 

.47154 

152,9 

.01826 

12,3 

.45328 

140,6 

.54672 

.293 

.47306 

152,4 

.01838 

12,4 

.45468 

140,1 

.54532 

.294 

.47459 

152,0 

.01851 

12,4 

.45608 

139,5 

•  54392 

0.295 

9.47610 

I5i,5 

0.01863 

12,5 

9-45747 

139,0 

0.54253 

.296 

.47762 

151,0 

.01875 

12,5 

.45886 

138,5 

.54H4 

.297 

.47912 

150,5 

.01888 

12,5 

.46024 

138,0 

.53976 

.298 

.48063 

150,0 

.01900 

12,6 

.46162 

137,5 

.53838 

.299 

.48212 

149,6 

.01913 

12,6 

.46299 

136,9 

.53701 

0.300 

9.48362 

149,1 

0.01926 

12,7 

9.46436 

136,4 

0.53564 

u 

log  tan  gd  u 

«FO' 

log  sec  gd  u 

«F</ 

log  sin  gd  u 

«FO' 

logcscgdu 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«-  Fo' 

log  coth  u 

0.300 

9.48352 

149,1 

0.01926 

12,7 

9.40436 

136,4 

0.53564 

.301 

.48510 

148,6 

.01938 

12,7 

.46572 

135,9 

.53428 

.302 

.48J59 

148,2 

.01951 

12,7 

.46708 

135,4 

.53292 

.303 

.48807 

U7,7 

.01964 

12,8 

•46843 

134,9 

.53157 

.304 

.48954 

147,2 

.01977 

12,8 

.46978 

134,4 

•53022 

0.305 

9.49IOI 

146,8 

0.01989 

12,8 

9.47112 

133,9 

0.52888 

.306 

.49248 

146,3 

.02002 

12,9 

.47245 

133,4 

.52755 

.307 

•49394 

U5,9 

.02015 

12,9 

•47379 

133,0 

.52621 

.308 

•49540 

145,4 

.02028 

13,0 

•475II 

132,5 

.52489 

.309 

.49685 

145,0 

.02041 

13,0 

.47644 

132,0 

.52356 

0.310 

9.49830 

144,6 

0.02054 

13,0 

9-47775 

I3L5 

0.52225 

.311 

•49974 

I44,i 

.02067 

13,1 

.47007 

131,0 

.52093 

.312 

.50118 

H3,7 

.02080 

13,1 

.48037 

130,6 

.51963 

.313 

.50261 

143,3 

.02094 

13,2 

.48168 

130,1 

•51832 

.314 

.50404 

142,8 

.02107 

13,2 

.48298 

129,6 

.51702 

0.315 

9.50547 

142,4 

O.02I2O 

13,2 

9.48427 

129,2 

0.51573 

.316 

.50689 

142,0 

.02133 

13,3 

.48556 

128,7 

.51444 

.317 

.50831 

141,6 

.O2I4J 

13,3 

.48684 

128,2 

.51316 

.318 

.50972 

141,1 

.02l6o 

13,4 

.48812 

127,8 

.51188 

.319 

.51113 

140,7 

.02173 

13,4 

.48940 

127,3 

.51060 

0.320 

9.51254 

140,3 

O.O2I87 

13,4 

9.49067 

126,9 

0.50933 

.321 

.51394 

139,9 

.02200 

13,5 

.49194 

126,4 

.50806 

.322 

.51534 

139,5 

.O22I4 

13,5 

.49320 

126,0 

.50680 

.323 

.51673 

I39,i 

.O2227 

13,6 

.49446 

125,5 

.50554 

.324 

.51812 

138,7 

.02241 

13,6 

•49571 

125,1 

.50429 

0.325 

9.51950 

138,3 

O.O2254 

13,6 

9.49696 

124,7 

0.50304 

.326 

.52088 

137,9 

.02268 

13,7 

.49820 

124,2 

.50180 

.327 

.  52226 

137,5 

.O2282 

13,7 

.49944 

123,8 

.50056 

.328 

.52363 

I37,i 

.02295 

13,8 

.50068 

123,4 

•49932 

.329 

.52500 

136,7 

.02309 

13,8 

.50191 

122,9 

.49809 

0.330 

9-52637 

136,3 

O.02323 

13,8 

9.503U 

122,5 

0.49686 

.331 

.52773 

136,0 

.02337 

13,9 

.50436 

122,1 

.49564 

.332 

.52909 

135,6 

.02351 

13,9 

.50558 

121,7 

•49442 

•333 

•  53044 

135,2 

.02365 

14,0 

.50679 

121,3 

•49321 

•  334 

.53179 

134,8 

.02379 

14,0 

.50800 

120,8 

.49200 

0.335 

9.53314 

134,5 

0.02393 

14,0 

9.50921 

120,4 

0.40079 

•  336 

.53448 

-  I34,i 

.02407 

14,1 

.51041 

1  2O,O 

.48959 

•  337 

.53582 

133,7 

.02421 

14,1 

.51161 

119,6 

.48839 

.338 

.53715 

133,3 

•02435 

14,1 

.51281 

119,2 

.48719 

•  339 

.53849 

I33,o 

.02449 

14,2 

.51400 

118,8 

.48600 

0.340 

9.53981 

132,6 

0.02463 

14,2 

9.5I5I8 

1  1  8,4 

0.48482 

•  341 

.54114 

132,3 

.02478 

14,3 

.51636 

1  1  8,0 

.48364 

•  342 

.54246 

I3i,9 

.02492 

14,3 

.51754 

117,6 

.48246 

•  343 

.54378 

I3i,5 

.025O6 

14,3 

.51872 

117,2 

.48128 

•344 

.54509 

131,2 

.02520 

14,4 

.51989 

116,8 

.48011 

0.345 

9.54640 

130,8 

0.02535 

14,4 

9.52105 

116,4 

0.47895 

.346 

.54771 

130,5 

.02549 

14,5 

.52221 

116,0 

•47779 

•  347 

.54901 

130,1 

.02564 

14,5 

.52337 

H5,7 

•  47  '  3 

.348 

.55031 

129,8 

.02578 

i-l,5 

.52453 

"5,3 

•47547 

•  349 

.55l6l 

129,5 

•02593 

14,6 

.52568 

114,9 

•47432 

0.350 

9.55200 

129,1 

0.02607 

14,6 

9.52682 

"4,5 

0.47318 

u 

log  tan  gd  u 

«  Fo' 

log  tec  gd  u 

-Fo' 

log  sin  gd  u 

«Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.350 

9.55290 

129,1 

0.02607 

14,6 

9.52682 

114,5 

0.47318 

.351 

.55419 

128,8 

.02622 

14,6 

.52797 

114,1 

.47203 

.352 

.55547 

128,4 

.02637 

14,7 

.52911 

H3,7 

.47089 

.353 

.55676 

128,1 

.02651 

14,7 

.53024 

H3,4 

.46976 

.354 

.55804 

127,8 

.02666 

14,8 

.53137 

H3,O 

.46863 

0.355 

«F*rw 

9-55931 

127,4 

0.02681 

14,8 

9.53250 

112,6 

0.46750 

.356 

.56059 

127,1 

.02696 

14,8 

.53363 

112,3 

.46637 

•  357 

.56185 

.   126,8 

.02711 

14,9 

.53475 

111,9 

.   .46525 

•  358 

.56312 

126,5 

.02726 

14,9 

•53586 

m,5 

.46414 

.359 

.56438 

126,1 

.02740 

I5,o 

.53698 

111,2 

.46302 

0.360 

9-56564 

125,8 

0.02755 

I5,o 

9.53809 

no,8 

0.46191 

.361 

.56690 

125,5 

.02770 

I5,o 

.53919 

110,5 

.46081 

.362 

.56815 

125,2 

.02786 

15,1 

.54030 

no,  i 

•45970 

.363 

.56940 

124,8 

.02801 

15,1 

.54140 

109,7 

.45860 

.364 

.57065 

124,5 

.02816 

15,1 

.54249 

109,4 

•45751 

0.365 

9.57189 

124,2 

0.02831 

15,2 

9.54358 

109,0 

0.45642 

.366 

.57313 

123,9 

.02846 

15,2 

.54467 

108,7 

•45533 

.367 

•57437 

123,6 

.02861 

15,3 

.54576 

108,3 

.45424 

.368 

.5756i 

123,3 

.02877 

15,3 

.54684 

108,0 

.45316 

.369 

.57684 

123,0 

.02892 

15,3 

•54792 

107,7 

.45208 

0.370 

9.57807 

122,7 

0.02907 

15,4 

9.54899 

107,3 

0.45101 

•  371 

.57929 

122,4 

.02923 

15,4 

.55006 

107,0 

.44994 

•  372 

.58051 

122,1 

.02938 

15,4 

.55H3 

106,6 

.44887 

•  373 

.58173 

121,8 

•02954 

15,5 

.55220 

106,3 

.44780 

•  374 

.58295 

121,5 

.02969 

15,5 

.55326 

106,0 

.44674 

0.375 

9.58416 

121,2 

0.02985 

15,6 

9-55432 

105,6 

0.44568 

.376 

.58537 

120,9 

.03000 

15,6 

•55537 

105,3 

.44463 

•  377 

.58658 

120,6 

.03016 

15,6 

.55642 

105,0 

.44358 

.378 

.58779 

120,3 

.03031 

15,7 

.55747 

104,6 

.44253 

.379 

.58899 

1  20,0 

.03047 

15,7 

.55852 

104,3 

.44148 

0.380 

9.59019 

119,7 

0.03063 

15,8 

9.55956 

104,0 

0.44044 

.381 

.59138 

119,5 

.03079 

15,8 

.56059 

103,7 

.43941 

.382 

.59257 

110,2 

.03095 

15,8 

.56163 

103,3 

.43837 

.383 

.59377 

118,9 

.03110 

15,9 

.56266 

103,0 

.43734 

.384 

.59495 

118,6 

.03126 

15,9 

•56369 

102,7 

.43631 

0.385 

9.59614 

118,3 

0.03142 

15,9 

9-56472 

102,4 

0.43528 

.386 

•59732 

118,0 

.03158 

16,0 

.56574 

IO2,I 

.43426 

.387 

.59850 

117,8 

.03174 

16,0 

.56676 

101,8 

.43324 

.388 

.50967 

ii7,5 

.03190 

16,1 

.56777 

101,4 

.43223 

.389 

.60085 

117,2 

.03206 

16,1 

.56879 

101,1 

.43121 

0.390 

9.60202 

116,9 

0.03222 

16,1 

9-56980 

100,8 

0.43020 

•  391 

.60319 

116,7 

.03238 

16,2 

.57080 

100,5 

.42920 

•  392 

.60435 

116,4 

.03255 

16,2 

.57i8i 

100,2 

.42819 

•  393 

.60551 

116,1 

.03271 

16,2 

.57281 

99,9 

.42719 

•  394 

.60668 

H5,9 

.03287 

16,3 

.57380 

99,6 

.42620 

0.395 

9.60783 

H5,6 

0.03303 

16,3 

9.5748o 

99,3 

0.42520 

.396 

.60899 

H5,3 

.03320 

16,4 

•57579 

99,0 

.42421 

•  397 

.61014 

115,1 

.03336 

16,4 

.57678 

98,7 

.42322 

•  398 

.61129 

114,8 

.03353 

16,4 

•  57776 

98,4 

.42224 

•  399 

.61244 

114,6 

.03369 

16,5 

.57875 

98,1 

.42125 

0.400 

9.61358 

H4,3 

0.03385 

16,5 

9-57973 

97,8 

0.42027 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

w  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gdu 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

»Fo' 

log  coth  u 

0.400 

9.6I358 

114,3 

0.03385 

16,5 

9-57973 

97,8 

0.42027 

.401 

.61472 

114,0 

.03402 

16,5 

.58070 

97,5 

.41930 

.402 

.61586 

113,8 

.03419 

16,6 

.58168 

97,2 

.41832 

.403 

.61700 

H3,5 

•03435 

16,6 

.58265 

96,9 

.41735 

.404 

.61813 

H3,3 

.03452 

16,6 

.58361 

96,6 

.41639 

0.405 

9.61926 

H3,o 

0.03468 

16,7 

9.58458 

96,3 

0.41542 

.406 

.62039 

112,8 

.03485 

16,7 

.58554 

96,i 

.41446 

.407 

.62152 

112,5 

.03502 

16,8 

.58650 

95,8 

.41350 

.408 

.62264 

112,3 

.03519 

16,8 

.58746 

95,5 

.41254 

.409 

.62376 

112,0 

•03535 

16,8 

.58841 

95,2 

.4H59 

0.410 

9.62488 

in,8 

0.03552 

16,9 

9.58936 

94,9 

0.41064 

.411 

.62600 

111,6 

.03569 

16,9 

.50031 

94,6 

.40069 

.412 

.62711 

in,3 

.03586 

16,9 

.59125 

94,4 

.40875 

.413 

.62823 

in,  i 

.03603 

17,0 

.59220 

94,1 

.40780 

.414 

.62934 

110,8 

.03620 

17,0 

.593U 

93,8 

.40686 

0.415 

9.63044 

110,6 

0.03637 

I7,i 

9.59407 

93,5 

0.40593 

.416 

.63155 

110,4 

.03654 

I7,i 

•59501 

93,3 

.40499 

.417 

.63265 

no,  i 

.03671 

I7,i 

•59594 

93,0 

.40406 

.418 

.63375 

109,9 

.03688 

17,2 

.59687 

92,7 

.40313 

.419 

.63485 

109,6 

.03706 

17,2 

.59779 

92,4 

.40221 

0.420 

9.63594 

109,4 

0.03723 

17,2 

9.59871 

92,2 

0.40129 

.421 

.63704 

109,2 

.03740 

17,3 

.59963 

91,9 

.40037 

.422 

.63813 

109,0 

.03757 

17,3 

.60055 

91,6 

•39945 

.423 

.63922 

108,7 

.03775 

17,3 

.60147 

91,4 

.39853 

.424 

.64030 

108,5 

.03792 

17,4 

.60238 

91,1 

.39762 

0.425 

9.64139 

108,3 

0.03810 

17,4 

9.60329 

90,8 

0.30671 

.426 

.64247 

108,0 

.03827 

17,5 

.60420 

00,6 

.39580 

.427 

.64355 

107,8 

.03844 

17,5 

.60510 

90,3 

.39490 

.428 

.64462 

107,6 

.03862 

17,5 

.60600 

90,1 

•39400 

.429 

.64570 

107,4 

.03880 

17,6 

.60690 

89,8 

.39310 

0.430 

9.64677 

107,1 

0.03897 

17,6 

9.60780 

89,6 

0.39220 

.431 

.64784 

106,9 

.03915 

17,6 

.60869 

89,3 

.39131 

.432 

.64891 

106,7 

.03932 

17,7 

.60959 

89,0 

.39041 

•  433 

.64997 

106,5 

.03950 

17,7 

.61047 

88,8 

.38953 

•  434 

.65104 

106,3 

.03968 

17,7 

.61136 

88,5 

.38864 

0.435 

9.65210 

106,0 

0.03086 

17,8 

9.61224 

88,3 

0.38776 

.436 

.65316 

105,8 

.04003 

17,8 

.61313 

88,0 

.38687 

•  437 

.65422 

105,6 

.04021 

17,9 

.61401 

87,8 

.38599 

.438 

.65527 

105,4 

.04039 

17,9 

.61488 

87,5 

.38512 

•  439 

.65633 

105,2 

.04057 

17,9 

.61576 

87,3 

.38424 

0.440 

9.65738 

105,0 

0.04075 

18,0 

9.61663 

87,0 

0.38337 

.441 

.65843 

104,8 

.04093 

18,0 

.61750 

86,8 

.38250 

.442 

.65947 

104,6 

.04111 

18,0 

.61836 

86,5 

.38164 

•  443 

.66052 

104,4 

.04129 

18,1 

.61923 

86,3 

.38077 

.444 

.66156 

104,2 

.04147 

18,1 

.62009 

86,1 

.37091 

0.445 

9.66260 

104,0 

0.04165 

18,1 

9.62095 

85,8 

0.37005 

.446 

.66364 

103,7 

.04183 

18,2 

.62180 

85,6 

.37820 

•447 

.66468 

103,5 

.04202 

18,2 

.62266 

85,3 

•37734 

.448 

.66571 

103,3 

.04220 

18,3 

.62351 

85,1 

.37649 

.449 

.66674 

103,1 

.04238 

18,3 

.62436 

84,9 

•37564 

0.450 

9.66777 

102,9 

0.04256 

18,3 

9.62521 

84,6 

0.37479 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

<-  F,,' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLCS 


28 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

<-  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.450 

9.66777 

102,9 

0.04256 

18,3 

9.62521 

84,6 

0.37479 

.451 

.66880 

102,7 

.04275 

18,4 

.62605 

84,4 

.37395 

.452 

.66983 

102,5 

.04293 

18,4 

.62690 

84,I 

•37310 

•  453 

.67085 

102,3 

.04312 

18,4 

.62774 

83,9 

.37226 

•454 

.67187 

102,1 

.04330 

18,5 

.62857 

83,7 

.37143 

0.455 

9.67289 

101,9 

0.04348 

18,5 

9.62941 

83,4 

0.37059 

.456 

.67391 

101,8 

.04367 

18,5 

.63024 

83,2 

.36976 

•  457 

.67493 

101,6 

.04386 

18,6 

.63107 

83,0 

.36893 

•  458 

.67594 

101,4 

.04404 

18,6 

.63190 

82,8 

.36810 

•459 

.67696 

101,2 

.04423 

18,6 

.63273 

82,5 

.36727 

0.460 

9.67797 

101,0 

0.04441 

18,7 

9.63355 

82,3 

0.36645 

.461 

.67898 

100,8 

.04460 

18,7 

.63438 

82,1 

.36562 

.462 

.67998 

100,6 

.04479 

18,7 

.63519 

81,8 

.36481 

•  463 

.68099 

100,4 

.04498 

18,8 

.63601 

81,6 

.36399 

.464 

.68199 

100,2 

.04516 

18,8 

.63683 

81,4 

.36317 

0.465 

9.68299 

100,0 

0.04535 

18,9 

9.63764 

81,2 

0.36236 

.466 

.68399 

99,8 

.04554 

18,9 

.63845 

81,0 

.36155 

•  467 

.68499 

99,7 

.04573 

18,9 

.63926 

80,7 

.36074 

.468 

.68599 

99,5 

.04592 

19,0 

.64007 

80,5 

.35993 

.469 

.68698 

99,3 

.04611 

19,0 

.64087 

80,3 

.35913 

0.470 

9.68797 

99,i 

0.04630 

19,0 

9.64167 

80,1 

0.35833 

.471 

.68896 

98,9 

.04649 

19,1 

.64247 

79,9 

•35753 

.472 

.68995 

98,7 

.04668 

19,1 

.64327 

79,6 

.35673 

•473 

.69094 

98,6 

.04687 

19,1 

.64406 

79,4 

•35594 

•474 

.69192 

98,4 

.04706 

19,2 

.64486 

79,2 

.35514 

0.475 

9.69290 

98,2 

0.04726 

19,2 

9.64565 

79,0 

0.35435 

.476 

.69388 

98,0 

.04745 

19,2 

.64644 

78,8 

.35356 

•477 

.69486 

97,8 

.04764 

19,3 

.64722 

78,6 

.35278 

.478 

.69584 

97,7 

.04783 

19,3 

.64801 

78,4 

•35109 

•479 

.69682 

97,5 

.04803 

19,3 

.64879 

78,2 

•35I2I 

0.480 

9.69779 

97,3 

0.04822 

19,4 

9.64957 

77,9 

0.35043 

.481 

.69876 

97,i 

.04841 

19,4 

.65035 

77,7 

.34965 

.482 

.69973 

97,o 

.04861 

19,4 

.65H3 

77,5 

.34887 

.483 

.70070 

96,8 

.04880 

19,5 

.65190 

77,3 

.34810 

.484 

.70167 

96,6 

.04900 

19,5 

.65267 

77,i 

•34733 

0.485 

9.70264 

65,5 

0.04919 

19,6 

9.65344 

76,9 

0.34656 

.486 

.70360 

96,3 

.04939 

19,6 

.65421 

76,7 

•34579 

.487 

.70456 

96,1 

.04959 

19,6 

.65498 

76,5 

•34502 

.488 

.70552 

95,9 

.04978 

19,7 

.65574 

76,3 

.34426 

.489 

.70648 

95,8 

.04998 

19,7 

.65650 

76,1 

•34350 

0.490 

9.70744 

95,6 

0.05018 

19,7 

9.65726 

75,9 

0.34274 

•  491 

.70839 

95,4 

.05037 

19,8 

.65802 

75,7 

.34198 

.492 

•70935 

95,3 

.05057 

19,8 

.65878 

75,5 

.34122 

•493 

.71030 

95,i 

.05077 

19,8 

.65953 

75,3 

•34047 

.494 

.71125 

95,o 

.05097 

19,9 

.66028 

75,1 

.33972 

0.495 

9.71220 

94,8 

0.05117 

19,9 

9.66103 

74,9 

0.33897 

.496 

.71315 

94,6 

.05137 

19,9 

.66178 

74,7 

.33822 

•  497 

.71409 

94,5 

.05156 

20,0 

.66253 

74,5 

.33747 

.498 

.71503 

94,3 

.05176 

20,0 

.66327 

74,3 

.33673 

.499 

.71598 

94,1 

.05196 

20,0 

.66401 

74,i 

•33599 

0.500 

9.71692 

94,0 

0.05217 

20,1 

9.66475 

73,9 

0.33525 

u 

log  tan  gd  u 

«-  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

logcscgdu 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

»  Fo' 

log  cosh  u 

•  IV 

log  tanh  u 

-  Fo' 

log  coth  u 

0.500 

9.71692 

94,0 

0.05217 

20,1 

9.66475 

73,9 

0.33525 

.501 

.71786 

93,8 

.05237 

20,1 

.66549 

73,7 

•33451 

.502 

.71879 

93,7 

.05257 

20,1 

.66623 

73,5 

.33377  ; 

.503 

.71973 

93,5 

.05277 

2O,2 

.66696 

73,3 

.33304 

.504 

.72066 

93,3 

.05297 

20,2 

.66769 

73,1 

.33231 

0.505 

9.72160 

93,2 

0.05317 

2O,2 

9.66842 

72,9 

0.33158 

.506 

.72253 

93,0 

.05338 

20,3 

.66915 

72,8 

.33085 

.507 

.72346 

92,9 

.05358 

20,3 

.66988 

72,6 

.33012 

.508 

.72438 

92,7 

.05378 

20,3 

.67060 

72,4 

.32940 

.509 

.72531 

92,6 

.05399 

20,4 

.67133 

72,2 

.32867 

0.510 

9.72624 

92,4 

0.05419 

20,4 

9.67205 

72,0 

0.32795 

.511 

.72716 

92,3 

.05439 

20,4 

.67277 

7i,8 

•32723 

.512 

.72808 

92,1 

.05460 

20,5 

.67348 

7i,6 

.32652  , 

.513 

.72900 

92,0 

.05480 

20,5 

.67420 

7i,5 

.32580  ; 

.514 

.72992 

91,8 

.05501 

20,5 

.67491 

71,3 

.32509 

0.515 

9.73084 

91,7 

0.05521 

20,6 

9-67562 

7i,i 

0.32438  ; 

.516 

.73175 

9i,5 

.05542 

20,6 

.67633 

70,9 

.32367 

.517 

.73267 

91,4 

.05563 

20,6 

.67704 

70,7 

.32296 

.518 

.73358 

91,2 

.05583 

20,7 

.6/775 

70,5 

.32225 

.519 

•73449 

9i,i 

.05604 

20,7 

.67845 

70,3 

.32155 

0.520 

9-73540 

90,9 

0.05625 

20,7 

9.67916 

70,2 

0.32084 

.521 

.73631 

90,8 

.05645 

20,8 

.67986 

70,0 

.32014 

.522 

.73722 

90,6 

.05666 

20,8 

.68056 

69,8 

.31944 

.523 

.73812 

90,5 

.05687 

20,8 

.68125 

69,6 

.31875  ; 

.524 

.73903 

90,3 

.05708 

20,9 

.68195 

69,5 

.31805 

0.525 

9-73993 

90,2 

0.05729 

20,9 

9.68264 

69,3 

0.31736 

.526 

.74083 

90,o 

•05750 

20,9 

.68333 

69,1 

.31667 

.527 

.74173 

89,9 

.05771 

21,0 

.68402 

68,9 

.31598 

.528 

.74263 

89,8 

.05792 

2I,O 

.68471 

68,7 

.31529 

.529 

•74353 

89,6 

.05813 

2I,O 

.68540 

68,6 

.31460 

0.530 

9.74442 

89,5 

0.05834 

21,1 

9.68608 

68,4 

0.31392 

.531 

•74532 

89,3 

.05855 

21,1 

.68677 

68,2 

.31323 

.532 

.74621 

89,2 

.05876 

21,1 

.68745 

68,0 

.31255 

•533 

•74710 

89,1 

.05897 

21,2 

.68813 

67,9 

.31187 

•  534 

•74799 

88,9 

.05918 

21,2 

.68880 

67,7 

.31120 

0.535 

9.74888 

88,8 

0.05940 

21,2 

9.68948 

67,5 

0.31052 

.536 

.74976 

88,6 

.05961 

21,3 

.69016 

67,4 

.30984 

•  537 

.75065 

88,5 

.05982 

21,3 

.69083 

67,2 

•  538 

.75153 

88,4 

.06004 

21,3 

.69150 

67,0 

.30850 

•  539 

.75242 

88,2 

.06025 

21,4 

.69217 

66,9 

.30783 

0.540 

9-75330 

88,1 

0.06046 

21,4 

9.69284 

66,7 

0.30716 

•  541 

.75418 

88,0 

.06068 

21,4 

.69350 

66,5 

.30650 

.542 

.75506 

87,8 

.06089 

21,5 

.69417 

66,3 

.30583 

.543 

•75594 

87,7 

.06111 

21,5 

,69483 

66,2 

.30517 

•  544 

.75681 

87,6 

.06132 

21,5 

.69549 

66,0 

.30451 

0.545 

9.75769 

87,4 

0.06154 

21,6 

9.69615 

65,9 

0.30385 

.546 

.75856 

87,3 

.06175 

21,6 

.69681 

65,7 

.30319 

•  547 

•75943 

87,2 

.06197 

21,6 

.69746 

65,5 

.30254 

.548 

.76030 

87,0 

.06219 

21,7 

.69812 

65,4 

.30188 

•  549 

.76117 

86,9 

.06240 

21,7 

.69877 

65,2 

.30123 

0.550 

9.76204 

86,8 

0.06262 

21,7 

9.69942 

65,0 

0.30058 

u 

log  tan  gd  u 

-Fo' 

log  sec  gd  u 

•  Fo' 

log  sin  gd  u 

•  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.550 

9.76204 

86,8 

0.06262 

21,7 

9.69942 

65,0 

0.30058 

.551 

.76291 

86,6 

.06284 

21,8 

.70007 

64,9 

.29993 

.552 

.76377 

86,5 

.06306 

21,8 

.70072 

64,7 

.29928 

•  553 

.76464 

86,4 

.06327 

21,8 

.70137 

64,5 

.29863 

.554 

.76550 

86,3 

.06349 

21,9 

.  7O2OI 

64,4 

.29799 

0.555 

9.76636 

86,1 

0.06371 

21,9 

9.70265 

64,2 

0.29735 

.556 

.76722 

86,0 

.06393 

21,9 

.70329 

64,1 

.29671 

•  557 

.76808 

85,9 

.06415 

22,0 

.70393 

63,9 

.29607 

.558 

.76894 

85,7 

.06437 

22,0 

.70457 

63,7 

•29543 

•  559 

.76980 

85,6 

.06459 

22,0 

.70521 

63,6 

.29479 

0.560 

9.77065 

85,5 

0.06481 

22,1 

9.70584 

63,4 

0.29416 

.561 

.77151 

85,4 

.   .06503 

22,1 

.70648 

63,3 

.29352 

.562 

.77236 

85,2 

.06525 

22,1 

.70711 

63,1 

.29289 

•  563 

.77321 

85,1 

.06547 

22,2 

.70774 

63,0 

.29226 

•  564 

.77406 

85,0 

.06570 

22,2 

.70837 

62,8 

.29163 

0.565 

9-77491 

84,9 

0.06592 

22,2 

9.70900 

62,7 

.29100 

.566 

.77576 

84,8 

.06614 

22,3 

.70962 

62,5 

.29038 

.567 

.77661 

84,6 

.06636 

22,3 

.71025 

62,3 

.28975 

.568 

•77745 

84,5 

.06659 

22,3 

.71087 

62,2 

.28913 

.569 

.77830 

84,4 

.06681 

22,3 

.71149 

62,0 

.28851 

0.570 

9.77914 

84,3 

0.06703 

22,4 

9.7I2II 

61,9 

0.28789 

•  571 

.77998 

84,2 

.06726 

22,4 

.71273 

6i,7 

.28727 

•  572 

.78083 

84,0 

.06748 

22,4 

.71334 

61,6 

.28666 

•  573 

.78167 

83,9 

.06771 

22,5 

.71396 

61,4 

.28604 

•  574 

.78250 

83,8 

.06793 

22,5 

.71457 

61,3 

.28543 

0.575 

9.78334 

83,7 

O.o68l6 

22,5 

9.7I5I9 

61,1 

0.28481 

•  576 

.78418 

83,6 

.06838 

22,6 

.71580 

61,0 

.28420 

•  577 

.78501 

83,4 

.06861 

22,6 

.71641 

60,8 

.28359 

•  578 

.78585 

83,3 

.06883 

22,6 

.71701 

60,7 

.28299 

•  579 

.78668 

83,2 

.06906 

22,7 

.71762 

60,5 

.28238 

0.580 

9.78751 

83,1 

0.06329 

22,7 

9.71822 

60,4 

0.28178 

.581 

.78834 

83,0 

.06951 

22,7 

.71883 

60,2 

.28117 

.582 

.78917 

82,9 

.06974 

22,8 

.71943 

60,  i 

.28057 

.583 

.79000 

82,7 

.06097 

22,8 

.72003 

60,0 

.27997 

.584 

.79082 

82,6 

.07020 

22,8 

.72063 

59,8 

.27937 

0.585 

9.79165 

82,5 

0.07043 

22,9 

9.72123 

59,7 

0.27877 

.586 

.79247 

82,4 

.07065 

22,9 

.72182 

59,5 

.27818 

.587 

•79330 

82,3 

.07088 

22,9 

.72242 

59,4 

.27758 

.588 

.79412 

82,2 

.O7III 

23,0 

.72301 

59,2 

.27699 

.589 

.79494 

82,1 

.07134 

23,0 

.72360 

59,1 

.27640 

0.500 

9.79576 

82,0 

0.07157 

23,0 

9.72419 

58,9 

0.27581 

•  591 

.79658 

81,8 

.07180 

23,0 

.72478 

58,8 

.27522 

•  592 

•79740 

8i,7 

.07203 

23,1 

.72537 

58,7 

.27463 

•  593 

.79822 

81,6 

.07226 

23,1 

.72595 

58,5 

.27405 

•  594 

.79903 

8i,5 

.07249 

23,1 

.72654 

58,4 

.27346 

0.595 

9.79985 

81,4 

0.07273 

23,2 

9.72712 

58,2 

0.27288 

.596 

.80066 

81,3 

.07296 

23,2 

.72770 

58,1 

.27230 

•  597 

.80147 

81,2 

.07319 

23,2 

.72828 

58,0 

.27172 

.598 

.80228 

81,1 

23,3 

.72886 

57,8 

.27114 

.599 

.80309 

81,0 

.07366 

23,3 

•72944 

57,7 

.27056 

0.600 

9.80390 

80,9 

0.07389 

23,3 

9.73001 

57,5 

0.26099 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

a.  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

•  Fo' 

log  cosh  u 

-IV 

log  tanh  u 

«  Fo' 

log  coth  u 

0.600 

9.80300 

80,9 

0.07389 

23,3 

9-73001 

57,5 

0.26999 

.601 

.80471 

80,8 

.07412 

23,4 

.73059 

57,4 

.26941 

.602 

.80552 

80,7 

.07436 

23,4 

.73116 

57,3 

.26884 

.603 

.80632 

80,5 

.07459 

23,4 

.73173 

57,1 

.26827 

.604 

.80713 

80,4 

.07482 

23,4 

.73231 

57,o 

.26769 

0.605 

9.80793 

80,3 

0.07506 

23,5 

9.73287 

56,9 

0.26713 

.606 

.80$74 

8o,2 

.07529 

23,5 

.73344 

56,7 

.26656 

.607 

.80954 

80,  1 

•07553 

23,5 

•73401 

56,6 

.26599 

.608 

.81034 

8o,0 

.07576 

23,6 

•73457 

56,5 

.26543 

.609 

.81114 

79,9 

.07600 

23,6 

•73514 

56,3 

.26486 

0.610 

9.8II94 

79,8 

0.07624 

23,6 

9-73570 

56,2 

0.26430 

.611 

.81273 

79,7 

.07647 

23,7 

.  .73626 

56,0 

.26374 

.612 

.81353 

79,6 

.07671 

23,7 

.73682 

55,9 

.26318 

.613 

.81433 

79,5 

.07695 

23,7 

.73738 

55,8 

.26262 

.614 

.81512 

79,4 

.07718 

23,8 

•73794 

55,7 

.26206 

0.615 

9.8I59I 

79,3 

0.07742 

23,8 

9.73849 

55,5 

0.26151 

.616 

.81671 

79,2 

.07766 

23,8 

.73905 

55,4 

.26095 

.617 

.81750 

79,1 

.07790 

23,8 

.73960 

55,3 

.26040 

.618 

.81829 

79,0 

.07814 

23,9 

.74015 

55,1 

.25985 

.619 

.81908 

78,9 

.07838 

23,9 

.74070 

55,o 

.25930 

0.620 

9.81987 

78,8 

0.07861 

23,9 

9.74125 

54,9 

0.25875 

.621 

.82065 

78,7 

.07885 

24,0 

.74180 

54,7 

.25820 

.622 

.82144 

78,6 

.07909 

24,0 

•74235 

54,6 

.25765 

.623 

.82223 

78,5 

.07933 

24,0 

.74289 

54,5 

.257H 

.624 

.82301 

78,4 

.07957 

24,1 

•74344 

54,3 

.25656 

0.625 

9.82380 

78,3 

0.07982 

24,1 

9.74398 

54,2 

0.25602 

.626 

.82458 

78,2 

.08006 

24,1 

.74452 

54,i 

.25548 

.627 

.82536 

78,1 

.08030 

24,1 

.74506 

54,0 

.25494 

.628 

.82614 

78,0 

.08054 

24,2 

.74560 

53,8 

.25440 

.629 

.82692 

77,9 

.08078 

24,2 

.74614 

53,7 

.25386 

0.630 

9.82770 

77,8 

0.08162 

24,2 

9.74667 

53,6 

0.25333 

.631 

.82848 

77,7 

.08126 

24,3 

.74721 

53,5 

.25279 

.632 

.82925 

77,6 

.08151 

24,3 

53,3 

.25226 

.633 

.83003 

77,5 

.08175 

24,3 

.  74828 

53,2 

.25172 

.634 

.83080 

77,4 

.08200 

24,4 

.74881 

53,1 

.25119 

0.635 

9.83158 

77,3 

0.08224 

24,4 

9-74934 

53,0 

0.25066 

.636 

.83235 

77,3 

.08248 

24,4 

.74987 

52,8 

.25013 

•637 

.83312 

77,2 

.08273 

24,4 

.75040 

52,7 

.24060 

.638 

.83389 

77,i 

.08297 

24,5 

.75092 

52,6 

.24008 

.639 

.83466 

77,o 

.08322 

24,5 

-75I45 

52,5 

.24855 

0.640 

9.83543 

76,9 

0.08346 

24,5 

9.75197 

52,3 

0.24803 

.641 

.83620 

76,8 

.08371 

24,6 

.75249 

52,2 

.24751 

.642 

.83697 

76,7 

.08395 

24,6 

•75302 

52,1 

.24698 

.643 

.83774 

76,6 

.08420 

24,6 

•75354 

52,o 

.24646 

.644 

.83850 

76,5 

.08445 

24,7 

.75406 

51,9 

.24594 

0.645 

9.83927 

76,4 

0.08469 

24,7 

9-75457 

51,7 

0.24543 

.646 

.84003 

76,3 

.08494 

24,7 

.75509 

.24491 

.647 

.84079 

76,2 

.08519 

24,7 

.75561 

51,'s 

.24439 

.648 

.84155 

76,1 

.08543 

24,8 

.75612 

5i,4 

.24388 

.649 

.84232 

76,1 

.08568 

24,8 

.75663 

51,3 

.24337 

0.650 

9.84308 

76,0 

0.08593 

24,8 

9.75715 

Si.i 

0.24285 

u 

log  tan  gd  u 

•  FO' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

•  Fo' 

log  esc  gd  u 

SMITHSCNIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.650 

9.84308 

76,0 

0.08593 

24,8 

9.75715 

51,1 

0.24285 

.651 

.84383 

75,9 

.08618 

24,9 

.75766 

51,0 

.24234 

.652 

.84459 

75,8 

.08643 

24,9 

•75817 

50,9 

.24183 

.653 

.84535 

75,7 

.08668 

24,9 

.75867 

50,8 

.24133 

.654 

.84611 

75,6 

.08693 

24,9 

.75918 

50,7 

.24082 

0.655 

9.84686 

75,5 

0.08718 

25,0 

9.75969 

50,6 

0.24031 

.656 

.84762 

75,4 

.08742 

25,0 

.76019 

50,4 

.23981 

.657 

.84837 

75,4 

.08768 

25,0 

.76070 

50,3 

.23930 

.658 

.84912 

75,3 

.08793 

25,1 

.76120 

50,2 

.23880 

.659 

.84988 

75,2 

.08818 

25,1 

.76170 

50,i 

.23830 

0.660 

9.85063 

75,i 

0.08843 

25,1 

9.76220 

50,o 

0.23780 

.661 

.85138 

75,o 

.08868 

25,1 

.76270 

49,9 

.23730 

.662 

.85213 

74,9 

.08893 

25,2 

.76320 

49,7 

.23680 

.663 

.85288 

74,8 

.08918 

25,2 

.76369 

49,6 

.23631 

.664 

.85362 

74,7 

.08943 

25,2 

.76419 

49,5 

.23581 

o  665 

9.85437 

74,7 

0.08969 

25,3 

9.76469 

49,4 

0.23531 

!666 

.85512 

74,6 

.08994 

25,3 

.76518 

49,3 

.23482 

.667 

.85586 

74,5 

.09019 

25,3 

.76567 

49,2 

•23433 

.668 

.85661 

74,4 

.09045 

25,3 

.76616 

49,1 

.23384 

.669 

•85735 

74,3 

.09070 

25,4 

.76665 

48,9 

•23335 

0.670 

9.85809 

74,2 

0.09095 

25,4 

9.76714 

48,8 

0.23286 

.671 

.85884 

74,2 

.09121 

25,4 

.76763 

48,7 

.23237 

.672 

.85958 

74,1 

.09146 

25,5 

.76812 

48,6 

.23188 

.673 

.86032 

74,o 

.09172 

25,5 

.76860 

48,5 

.23140 

.674 

.86106 

73,9 

.09197 

25,5 

.76909 

48,4 

.23091 

0.675 

9.86180 

73,8 

0.09223 

25,5 

9.76957 

48,3 

0.23043 

.676 

.86253 

73,7 

.09248 

25,6 

•77005 

48,2 

.22995 

.677 

.86327 

73,7 

.09274 

25,6 

.77053 

48,1 

.22947 

.678 

.86401 

73,6 

.09300 

25,6 

.77101 

47,9 

.22899 

.679 

.86474 

73,5 

.09325 

25,7 

.77149 

47,8 

.22851 

0.680 

9.86548 

73,4 

0.09351 

25,7 

9.77197 

47,7 

0.22803 

.681 
.682 

.86621 
.86694 

73,3 
73,3 

.09377 
.09402 

25,7 
25,7 

.77245 
.77292 

47,6 

47,5 

.22755 
22708 

.683 

.86768 

73,2 

.09428 

25,8 

.77340 

47,4 

22660 

.684 

.86841 

73,i 

.09454 

25,8 

.77387 

47,3 

.22613 

0.685 

9.86914 

73,0 

0.09480 

25,8 

9-77434 

47,2 

0.22566 

.686 

.86987 

72,9 

.09505 

25,9 

.77481 

47,i 

.22519 

.687 

.87060 

72,9 

.09531 

25,9 

.77528 

47,o 

.22472 

.688 

.87133 

72,8 

.09557 

25,9 

.77575 

46,9 

.22425 

.689 

.87205 

72,7 

.09583 

25,9 

.77622 

46,8 

.22378 

0.690 

9.87278 

72,6 

0.09609 

26,0 

9.77669 

46,7 

0.22331 

.691 

.87351 

72,5 

.09635 

26,0 

.77715 

46,6 

.22285 

.692 

.87423 

72,5 

.09661 

26,0 

.77762 

46,4 

.22238 

.693 

.87495 

72,4 

.09687 

26,1 

.77808 

46,3 

.22192 

.694 

.87568 

72,3 

.09713 

26,1 

.77855 

46,2 

.22145 

0.695 

9.87640 

72,2 

0.09739 

26,1 

9.77901 

46,1 

O.22O99 

.696 

.87712 

72,2 

.09765 

26,1 

.77947 

46,0 

.22053 

.697 

.87784 

72,1 

.09792 

26,2 

.77993 

45,9 

.22OO7 

.698 

.87856 

72,0 

.09818 

26,2 

•78039 

45,8 

.21961 

.699 

.87928 

71,9 

.09844 

26,2 

.78084 

45,7 

.21916 

0.700 

9.88000 

7i,9 

0.09870 

26,2 

9.78130 

45,6 

0.21870 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«FO' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


33 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

<-  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.700 

9.88000 

71,9 

0.09870 

26,2 

9.78130 

45,6 

0.21870 

.701 

.88072 

7i,8 

.09895 

26,3 

.78176 

45,5 

.21824 

.702 

.88144 

7i,7 

.09923 

26,3 

.78221 

45,4 

.21779 

•  703 

.88216 

7i,6 

.09949 

26,3 

.78266 

45,3 

.21734 

.704 

.88287 

7i,6 

.09975 

26,4 

.78312 

45,2 

.21688 

0.705 

9.88359 

7i,5 

O.IOO02 

26,4 

9.78357 

45,i 

0.21643 

.706 

.88430 

7i,4 

.10028 

26,4 

.78402 

45,0 

.21598 

.707 

.88502 

7i,3 

.10055 

26,4 

.78447 

44,9 

•21553 

.708 

.88573 

7i,3 

.10081 

26,5 

.78492 

44,8 

.21508 

.709 

.88644 

71,2 

.10108 

26,5 

.78536 

447 

.21464 

0.710 

9.88715 

7i,i 

0.10134 

26,5 

9.78581 

44,6 

0.21419 

.711 

.88786 

71,0 

.10161 

26,5 

.78626 

44,5 

.21374 

.712 

.88857 

71,0 

.10187 

26,6 

.78670 

44,4 

.21330 

.713 

.88928 

70,9 

.10214 

26,6 

.78714 

44,3 

.21286 

.714 

.88999 

70,8 

.  10240 

26,6 

.78759 

44,2 

.21241 

0.715 

9.89070 

70,8 

0.10267 

26,7 

9.78803 

44,1 

0.21197 

.716 

.89141 

70,7 

.10294 

26,7 

.78847 

44,0 

•2II53 

.717 

.89211 

70,6 

.  10320 

26,7 

.78891 

43,9 

.21109 

.718 

.89282 

70,5 

.  10347 

26,7 

.78935 

43,8 

.21065 

.719 

.89352 

70,5 

.  10374 

26,8 

.78978 

43,7 

.21022 

0.720 

9.89423 

70,4 

O.I04QI 

26,8 

9-79022 

43,6 

0.20978 

.721 

.89493 

70,3 

.10427 

26,8 

.79066 

43,5 

.20934 

.722 

.89563 

70,3 

.  10454 

26,8 

.79109 

43,4 

.20891 

.723 

.89634 

70,2 

.10481 

26,9 

.79153 

43,3 

.20847 

.724 

.89704 

70,i 

.10508 

26,9 

.79196 

43,2 

.20804 

0.725 

9.89774 

70,0 

0.10535 

26,9 

9.79239 

43,1 

O.2O76I 

.726 

.89844 

70,o 

.  10562 

27,0 

.79282 

43,0 

.20718 

.727 

.89914 

69,9 

.10589 

x  27,0 

.79325 

42,9 

.20675 

.728 

.89984 

69,8 

.  10616 

27,0 

.79368 

42,8 

.20632 

.729 

.90054 

69,8 

.10643 

27,0 

.79411 

42,7 

.20589 

0.730 

9.90123 

69,7 

0.10670 

27,1 

9.79453 

42,6 

0.20547 

.731 

.90193 

69,6 

.id&97 

27,1 

.79496 

42,5 

.20504 

.732 

.90263 

69,6 

.  10724 

27,1 

.79538 

42,5 

.20462 

•  733 

.90332 

69,5 

.10751 

27,1 

.79581 

42,4 

.204^9 

.734 

.90402 

69,4 

.  10778 

27,2 

.79623 

42,3 

.20377 

0.735 

9.90471 

69,4 

o.io8o5 

27,2 

9.79665 

42,2 

0.20335 

.736 

.90540 

69,3 

.10833 

27,2 

.79708 

42,1 

.20292 

•  737 

.00610 

69,2 

.10860 

27,2 

•79750 

42,0 

.20250 

.738 

.00679 

69,2 

.10887 

27,3 

.79791 

41,9 

.20209 

•  739 

.90748 

69,1 

.10915 

27,3 

.79833 

41,8 

.20167 

0.740 

9.90817 

69,0 

0.10942 

27,3 

9.79875 

4L7 

0.20125 

.741 

.90886 

69,0 

.10969 

27,3 

.79917 

41,6 

.20083 

.742 

.90955 

68,9 

.10997 

27,4 

.79958 

41,5 

.20042 

•  743 

.91024 

68,8 

.  i  1024 

27,4 

.80000 

41,4 

.20000 

•  744 

.91092 

68,8 

.11051 

27,4 

.80041 

41,3 

.19959 

0.745 

9.9Il6l 

68,7 

0.11079 

27,5 

9.80082 

41,2 

O.I99l8 

.746 

.91230 

68,6 

.11106 

27,5 

.80124 

41,2 

.19876 

•  747 

.91298 

68,6 

•11134 

27,5 

.80165 

41,1 

.19835 

.748 

.91367 

68,5 

.11161 

27,5 

.80206 

41,0 

.19794 

•  749 

.91436 

r*s,4 

.11189 

27,6 

.80247 

40,9 

.  19753 

0.750 

9.91504 

68,4 

o.  11216 

27,6 

9.80288 

40,8 

0.19712 

u 

log  tan  od  u 

•  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

-  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


34 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

<-  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«F0' 

log  coth  u 

0.750 

9.91504 

68,4 

o.  11216 

27,6 

9.80288 

40,8 

0.19712 

.751 

.91572 

68,3 

.11244 

27,6 

.80328 

40,7 

.19672 

.752 

.91641 

68,2 

.11272 

27,6 

.80369 

40,6 

.19631 

•  753 

.91709 

68,2 

.11299 

27,7 

.80410 

40,5 

.19590 

•  754 

.91777 

68,1 

.11327 

27,7 

.80450 

40,4 

.  19550 

0.755 

9.91845 

68,1 

O.H355 

27,7 

9.80490 

40,3 

0.19510 

.756 

.91913 

68,0 

.  1.1382 

27,7 

.80531 

40,3 

.19469 

•  757 

.91981 

67,9 

.11410 

27,8 

.80571 

40,2 

.  19429  . 

•  758 

.92049 

67,9 

.11438 

27,8 

.80611 

40,1 

.19389 

•  759 

.92117 

67,8 

.11466 

27,8 

.80651 

40,0 

.19349 

0.760 

9.92185 

67,7 

O.H493 

27,8 

9.80691 

39,9 

0.19309 

.761 

.92252 

67,7 

.11521 

27,9 

.80731 

39,8 

.19269 

.762 

.92320 

67,6 

.11549 

27,9 

.80771 

39,7 

.19229 

.763 

.92387 

67,6 

.11577 

27,9 

.80810 

39,6 

.19100 

.764 

.92455 

67,5 

.11605 

27,9 

.80850 

39,6 

.19150 

0.765 

9.92522 

67,4 

0.11633 

28,0 

9.80889 

39,5 

0.19111 

.766 

.92590 

67,4 

.11661 

28,0 

.80929 

39,4 

.19071 

.92657 

67,3 

.11689 

28,0 

.80968 

39,3 

.19032 

768 

.92724 

67,3 

.11717 

28,0 

.81007 

39,2 

.18993 

.769 

.92792 

67,2 

.11745 

28,1 

.81047 

39,1 

.18953 

0.770 

9.92859 

67,1 

O.H773 

28,1 

9.81086 

39,0 

0.18914 

.771 

.92926 

67,1 

.11801 

28,1 

.81125 

39,o 

.18875 

.772 

.92993 

67,0 

.  i  1829 

28,1 

.81164 

38,9 

.18836 

•  773 

.93000 

67,0 

.11858 

28,2 

.81202 

38,8 

.18798 

•  774 

.93127 

66,9 

.11886 

28,2 

.81241 

38,7 

.  18759 

0.775 

9.93194 

66,8 

0.119)14 

28,2 

9.81280 

38,6 

o.  18720 

•  776 

.93261 

66,8 

.11942 

28,2 

.81318 

38,5 

.18682 

•  777 

.93327 

66,7 

.11970 

28,3 

.81357 

38,4 

.18643 

•  778 

•  93394 

66,7 

.H999 

28,3 

.81395 

38,4 

.18605 

•  779 

.93461 

66,6 

.  12027 

28,3 

.81434 

38,3 

.18566 

0.780 

9.93527 

66,5 

0.12055 

28,3 

9.81472 

38,2 

0.18528 

.781 

•93594 

66,5 

.12084 

28,4 

.81510 

38,1 

.18490 

.782 

.93660 

66,4 

.12112 

28,4 

.81548 

38,0 

.  18452 

.783 

.93727 

66,4 

.12141 

28,4 

.81586 

37,9 

.18414 

.784 

•93793 

66,3 

.I2IO9 

28,4 

.81624 

37,9 

.18376 

0.785 

9.93859 

66,2 

O.I2I97 

28,5 

9.81662 

37,8 

0.18338 

.786 

.93925 

66,2 

.12226 

28,5 

.81699 

37,7 

.  18301 

.787 

.93992 

66,1 

.  12254 

28,5 

.81737 

37,6 

.18263 

.788 

.94058 

66,1 

.12283 

28,5 

.81775 

37,5 

.  18225 

.789 

.94124 

66,0 

.12312 

28,6 

.81812 

37,4 

.18188 

0.790 

9.94190 

66,0 

0.12340 

28,6 

9.81850 

37,4 

0.18150 

.791 

.94256 

65,9 

.12369 

28,6 

.81887 

37,3 

.18113 

.792 

.94321 

65,8 

.12397 

28,6 

.81924 

37,2 

.18076 

•  793 

.94387 

65,8 

.  12426 

28,7 

.81961 

37,i 

.18039 

•  794 

•94453 

65,7 

.12455 

28,7 

.81998 

37,0 

.18002 

0.795 

9.94519 

65,7 

o.  12483 

28,7 

9-82035 

37,0 

0.17965 

•  796 

.94584 

65,6 

.12512 

28,7 

.82072 

36,9 

.  17928 

•  797 

.94650 

65,6 

.12541 

28,8 

.82109 

36,8 

.17891 

•  798 

.94716 

65,5 

.12570 

28,8 

.82146 

36,7 

.  17854 

•  799 

.94781 

65,5 

.12598 

28,8 

.82183 

36,6 

.17817 

0.800 

9.94846 

65,4 

o.  12627 

28,8 

9.82219 

36,6 

0.17781 

u 

tog  tan  gd  u 

a,  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


35 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fu' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.800 

9.94846 

65,4 

0.12627 

28,8 

9.82219 

36,6 

0.17781 

.801 

.94912 

65,3 

.12656 

28,9 

.82256 

36,5 

•17744 

.802 

•94977 

65,3 

.12685 

28,9 

.82292 

36,4 

.17708 

.803 

.95042 

65,2 

.  12714 

28,9 

.82329 

36,3 

.  17671 

.804 

.95io8 

65,2 

.  12743 

28,9 

.82365 

36,2 

•  17635 

0.805 

9-95173 

65,1 

0.12772 

29,0 

9.82401 

36,2 

o.  17599 

.806 

.95238 

65,1 

.12801 

29,0 

.82437 

36,1 

.  17563 

.  .807 

•95303 

65,0 

.  12830 

29,0 

.82473 

36,0 

.  17527 

.808 

.95368 

65,O 

.12859 

29,0 

.82509 

35,9 

.17491 

.809 

•95433 

64,9 

.12888 

29,1 

.82545 

35,9 

•  17455 

0.810 

9.95498 

04,9 

0.12917 

29,1 

9.82581 

35,8 

0.17419 

.811 

.95563 

64,8 

.  12946 

29,1 

.82617 

35,7 

.17383 

.812 

.95627 

64,8 

.  12975 

29,1 

.82652 

35,6 

.17348 

.813 

.95692 

64,7 

.13004 

29,2 

.82688 

35,5 

.17312 

.814 

•95757 

64,6 

.  13033 

29,2 

.82723 

35,5 

.17277 

0.815 

9.95821 

64,6 

0.13063 

29,2 

9.82759 

35,4 

0.17241 

.816 

.95886 

64,5 

.13092 

29,2 

.82794 

35,3 

.17206 

.817 

•95950 

64,5 

.13121 

29,2 

.82829 

35,2 

.17171 

.818 

.96015 

64,4 

.13150 

29,3 

.82865 

35,2 

.17135 

.819 

.96079 

64,4 

.13180 

29,3 

.82900 

35,1 

.17100 

0.820 

9.96144 

64,3 

o.  13209 

29,3 

9.82935 

35,0 

0.17065 

.821 

.96208 

64,3 

.13238 

29,3 

.82970 

34,9 

.  17030 

.822 

.96272 

64,2 

.13268 

29,4 

.83005 

34,9 

.16995 

.823 

.96336 

64,2 

.  13297 

29,4 

.  83040 

34,8 

.16960 

.824 

.96401 

64,1 

.  13326 

29,4 

.83074 

34,7 

.16926 

0.825 

9.96465 

64,1 

0.13356 

29,4 

9.83109 

34,6 

0.16891 

.826 

.96529 

64,0 

.13385 

29,5 

.83144 

34,6 

.16856 

.827 

.96593 

64,0 

.13415 

29,5 

.83178 

34,5 

.16822 

.828 

.96657 

63,9 

.13444 

29,5 

.83213 

34,4 

.  16787 

.829 

.96721 

63,9 

.13474 

29,5 

.83247 

34,3 

.16753 

0.830 

9.96784 

63,8 

0.13503 

29,6 

9.83281 

34,3 

0.16719 

.831 

.96848 

63,8 

.13533 

29,6 

.83316 

34,2 

.16684 

.832 

.96912 

63,7 

.13562 

29,6 

.83350 

34J 

.16650 

.833 

.96976 

63,7 

.13592 

29,6 

.83384 

34,o 

.16616 

.834 

.97039 

63,6 

.  13622 

29,6 

.83418 

34,0 

.  16582 

0.835 

9.97103 

63,6 

0.13651 

29,7 

9.83452 

33,9 

0.16548 

.836 

.97167 

63,5 

.13681 

29,7 

.83486 

33,8 

.16514 

.837 

.97230 

63,5 

.13711 

29,7 

.83519 

33,8 

.  16481 

.838 
.839 

.97293 
•97357 

63,4 
63,4 

.  13740 
.  13770 

29,7 

.83553 
.83587 

33,7 
33,6 

.  16447 
.16413 

0.840 

9.97420 

63,3 

0.13800 

29,8 

9.83620 

33,5 

o.  16380 

.841 

.97484 

63,3 

.  13830 

29,8 

•83654 

33,5 

.  16346 

.842 

.97547 

63,2 

.13860 

29,8 

.83687 

33,4 

.16313 

.843 

.97610 

63,2 

.13889 

29,9 

.83721 

33,3 

.  16279 

.844 

.97673 

63,I 

.13919 

29,9 

.83754 

33,3 

.  16246 

0.845 

9.97736 

63,1 

0.13949 

29,9 

9.83787 

33,2 

o.  16213 

.846 

.97799 

63,0 

•13979 

29,9 

.83820 

33,1 

.16180 

.847 

.97862 

63,0 

.14009 

29,9 

•83853 

33,0 

.16147 

.848 

.97925 

62,9 

.  T4039 

30,0 

.83886 

33,o 

.16114 

.849 

.97988 

62,9 

.14069 

30,0 

.83919 

32,9 

.16081 

0.850 

9.98051 

62,8 

0.14009 

30,0 

9.83952 

32,8 

o.  16048 

u 

loo  tan  gd  u 

«  Fo' 

log  tec  gd  u 

«F»' 

log  sin  gd  u 

-Fo' 

log  etc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.850 

9.98051 

62,8 

0.14099 

30,0 

9.83952 

32,8 

0.16048 

.851 

.98114 

62,8 

.  14129 

30,0 

•83985 

32,8 

.16015 

.852 

.98177 

62,7 

.14159 

30,1 

.84018 

32,7 

.  15982 

.853 

.98239 

62,7 

.14189 

30,1 

.84050 

32,6 

.15950 

.854 

.98302 

62,7 

.14219 

30,1 

.84083 

32,6 

.15917 

0.855 

9-98365 

62,6 

0.14249 

30,1 

9-84115 

32,5 

0.15885 

.856 

.98427 

62,6 

.  14279 

30,1 

.84148 

32,4 

.15852 

.857 

.98490 

62,5 

.14310 

30,2 

.84180 

32,3 

.15820 

.858 

.08552 

62,5 

.  14340 

30,2 

.84213 

32,3 

.15787 

.859 

.98615 

62,4 

.14370 

30,2 

.84245 

32,2 

.15755 

0.860 

9.98677 

62,4 

0.14400 

30,2 

9.84277 

32,1 

0.15723 

.861 

.98739 

62,3 

.14430 

30,3 

.84309 

32,1 

.15691 

.862 

.98802 

62,3 

.14461 

30,3 

.84341 

32,0 

.15659 

.863 

.98864 

62,2 

.14491 

30,3 

.84373 

31,9 

.  15627 

.864 

.98926 

62,2 

.  I452I 

30,3 

.84405 

31,9 

.15595 

0.865 

9.98988 

62,1 

0.14552 

30,3 

9.84437 

31,8 

o.  15563 

.866 

•99051 

62,1 

.14582 

30,4 

.84469 

31,7 

.15531 

.867 

.99113 

62,1 

.14612 

30,4 

.84500 

31,7 

.15500 

.868 

.99175 

62,0 

.  14643 

30,4 

.84532 

31,6 

.15468 

.§69 

.99237 

62,0 

.14673 

30,4 

.84563 

31,5 

.15437 

0.870 

9.99299 

61,9 

0.14704 

30,5 

9.84595 

31,5 

0.15405 

.871 

.99361 

61,9 

.  14734 

30,5 

.84626 

31,4 

.15374 

.872 

.99422 

61,8 

.  14765 

30,5 

.84658 

31,3 

.15342 

.873 

.99484 

61,8 

.14795 

30,5 

.84689 

31,3 

•I53II 

.874 

.99546 

6i,7 

.  14826 

30,5 

.84720 

31,2 

.15280 

0.875 

9.99608 

61,7 

o.  14856 

30,6 

9.84751 

3i,i 

0.  15249 

.876 

.99669 

6i,7 

.14887 

30,6 

.84783 

3IJ 

.15217 

.877 

.99731 

61,6 

.  I49I7 

30,6 

.84814 

31,0 

.15186 

.878 

•99793 

61,6 

.  14948 

30,6 

•84845 

30,9 

.15155 

.879 

.99854 

61,5 

.14979 

30,7 

.84875 

30,9 

.15125 

0.880 

9.99916 

6i,5 

0.15009 

30,7 

9.84006 

30,8 

0.15094 

.881 

.99977 

61,4 

.15040 

30,7 

.84937 

30,7 

.15063 

.882 

0.00038 

61,4 

.15071 

30,7 

.84968 

30,7 

.  15032 

.883 

.00100 

61,3 

.15101 

30,7 

.84998 

30,6 

.15002 

.884 

.00161 

61,3 

.15132 

30,8 

.85029 

30,5 

.  I497I 

0.885 

O.OO222 

61,3 

0.15163 

30,8 

9.85059 

30,5 

0.14941 

.886 

.00284 

61,2 

.15194 

30,8 

.85090 

30,4 

.  14910 

.887 

.00345 

61,2 

.15225 

30,8 

.85120 

30,3 

.14880 

.888 

.00406 

61,1 

.15255 

30,9 

.85151 

30,3 

.  14849 

.889 

.00467 

61,1 

.15286 

30,9 

.85181 

30,2 

.  14819 

0.890 

O.O0528 

61,0 

O.I53I7 

30,9 

9.85211 

30,2 

0.14789 

.891 

.00589 

61,0 

.15348 

30,9 

.85241 

30,1 

.14759 

.892 

.00650 

61,0 

.15379 

30,9 

.85271 

30,0 

.  14729 

.893 

.00711 

60,9 

.15410 

3i,o 

.85301 

30,0 

.14699 

.894 

.00772 

60,9 

.15441 

3i,o 

.85331 

29,9 

.14669 

0.895 

0.00833 

60,8 

0.15472 

3i,o 

9.85361 

29,8 

0.14639 

.896 

.00894 

60,8 

.  15503 

3i,o 

.85391 

29,8 

.14609 

.897 

.00955 

60,8 

.15534 

3i,o 

.85421 

29,7 

.  14579 

.898 

.01015 

60,7 

.15565 

3i,i 

.85450 

29,6 

.  14550 

.899 

.01076 

60,7 

.15596 

3i,i 

.85480 

29,6 

.14520 

o.eoo 

0.01137 

60,6 

o.  15627 

3i,i 

9.85509 

29,5 

o.  14491 

u 

log  tan  gd  u 

w  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

*>  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


37 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

»  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

•  FO' 

log  coth  u 

0.900 

O.OII37 

60,6 

0.15627 

31,1 

9.85509 

29,5 

O.I449I 

.901 

.01197 

60,6 

.15658 

31,1 

.85539 

29,5 

.14461 

.902 

.01258 

60,5 

.15689 

31,2 

.85568 

29,4 

.1443-' 

.903 

.01318 

60,5 

.15721 

31,2 

.85598 

29,3 

.14402 

.904 

.01379 

60,5 

•15752 

31,2 

.85627 

29,3 

•  14373 

0.905 

0.01439 

60,4 

0.15783 

31,2 

9.85656 

29,2 

0.14344 

.906 

.01500 

60,4 

.15814 

31,2 

.85685 

29,2 

.14315 

.907 

.01560 

60,3 

.15846 

31,3 

.85715 

29,1 

.14285 

.908 

.01620 

60,3 

.15877 

31,3 

•85744 

29,0 

.  14256 

.909 

.01681 

60,3 

.15908 

31,3 

•85773 

29,0 

.  14227 

0.910 

O.OI74I 

60,2 

0.15939 

31,3 

9.85801 

28,9 

O.I4I99 

.911 

.OlSoi 

60,2 

.15971 

31,3 

.85830 

28,8 

.14170 

.912 

.01861 

60,1 

.16002 

3M 

.85859 

28,8 

.  14141 

.913 

.01921 

60,1 

.16033 

31,4 

.85888 

28,7 

.14112 

.914 

.01981 

60,1 

.16065 

31,4 

.85917 

28,7 

.14083 

0.915 

0.02041 

60,0 

0.16096 

31,4 

9.85945 

28,6 

0.14055 

.916 

.02101 

60,0 

.16128 

31,4 

•85974 

28,5 

.  14026 

.917 

.02l6l 

59,9 

.16159 

31,5 

.86002 

28,5 

.13998 

.918 

.O222I 

59,9 

.16191 

31,5 

.86031 

28,4 

.13969 

.919 

.02281 

59,9 

.  16222 

31,5 

.85059 

28,4 

.13941 

0.920 

0.02341 

59,8 

0.16254 

31,5 

9.86088 

28,3 

0.13912 

.921 

.O240I 

59,8 

.  16285 

31,5 

.86116 

28,2 

.13884 

.922 

.02461 

59,8 

.16317 

31,6 

.86144 

28,2 

.13856 

.923 

.02520 

59,7 

.16348 

31,6 

.86172 

28,1 

.  13828 

.924 

.02580 

59,7 

.16380 

31,6 

.86200 

28,1 

.13800 

0.925 

O.O2640 

59,6 

0.16411 

3i,6 

9.86228 

28,0 

o.  13772 

.926 

.02699 

59,6 

.16443 

3i,6 

.86256 

27,9 

.13744 

.927 

.02759 

59,6 

.16475 

3i,7 

.86284 

27,9 

.13716 

.928 

.02819 

59,5 

.16506 

3i,7 

.86312 

27,8 

.13688 

.929 

.02878 

59,5 

.16538 

3i,7 

.86340 

27,8 

.13660 

0.930 

0.02937 

59,4 

0.16570 

31,7 

9.86368 

27,7 

0.13632 

.931 

.02997 

59,4 

.16602 

3i,7 

.86395 

27,7 

.13605 

.932 

.03056 

59,4 

.16633 

3i,8 

.86423 

27,6 

.  13577 

•933 

.03116 

59,3 

.16665 

3i,8 

.86450 

27,5 

.  13550 

•  934 

.03175 

59,3 

.16697 

31,8 

.86478 

27,5 

.  13522 

0.935 

0.03234 

59,3 

0.16729 

3i,8 

9-86505 

27,4 

0.13495 

.936 

.03293 

59,2 

.  16761 

3i,9 

.86533 

27,4 

.13467 

•937 

.03353 

59,2 

.16792 

3i,9 

.86560 

27,3 

.13440 

.938 

.03412 

59,1 

.16824 

3i,9 

.86587 

27,3 

.13413 

•939 

.03471 

59,1 

.16856 

3i,9 

.86615 

27,2 

.13385 

0.940 

0.03530 

59,1 

0.16888 

3i,9 

9.86642 

27,1 

o.  13358 

.941 

.03589 

59,0 

.16920 

32,0 

.86669 

27,1 

.13331 

•  942 

.03648 

59,0 

.16952 

32,0 

.86696 

27,0 

.  13304 

•943 

.03707 

59,0 

.16984 

32,0 

.86723 

27,0 

.  13277 

.944 

.03766 

58,9 

.17016 

32,0 

.86750 

26,9 

.  13250 

0.945 

0.03825 

58,9 

o.  17048 

32,0 

9.86777 

26,9 

0.13223 

.946 

.03884 

58,9 

.17080 

32,0 

.86804 

26,8 

.13196 

•947 

.03943 

58,8 

.17112 

32,1 

.86830 

26,7 

.13170 

.948 

.04001 

58,8 

.17144 

32,1 

.86857 

26,7 

.13143 

.949 

.04060 

58,7 

.17176 

32,1 

.86884 

26,6 

.13116 

0.950 

0.04119 

58,7 

0.17208 

32,1 

9.86910 

26,6 

0.13090 

u 

log  tan  gd  u 

-Fo' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

*  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLCS 


Logarithms  of  Hyperbolic  Functions. 


u 

loo  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

0.950 

0.04119 

58,7 

0.17208 

32,1 

9.86910 

26,6 

0.13090 

.951 

.04178 

58,7 

.  I724I 

32,1 

.86937 

26,5 

.13063 

.952 

.04236 

58,6 

•  17273 

32,2 

.86963 

26,5 

.13037 

•  953 

.04295 

58,6 

.17305 

32,2 

.86990 

26,4 

.13010 

•954 

.04353 

58,6 

.  17337 

32,2 

.87016 

26>4 

.12984 

0.955 

0.04412 

58,5 

0.17369 

32,2 

9.87043 

26,3 

0.12957 

.956 

.04470 

58,5 

.17402 

32,2 

.87069 

26,2 

.12931 

•957 

.04529 

58,5 

.17434 

32,3 

.87095 

26,2 

.12905 

.958 

.04587 

58,4 

.17466 

32,3 

.87121 

26,1 

.  12879 

•959 

.04646 

58,4 

.17498 

32,3 

.87147 

26,1 

.12853 

0.960 

0.04704 

58,4 

O.I753I 

32,3 

9.87173 

26,0 

o.  12827 

.961 

.04763 

58,3 

.  17563 

32,3 

.87199 

26,0 

.12801 

.962 

.04821 

58,3 

.17595 

32,4 

.87225 

25,9 

.12775 

.963 

.04879 

58,2 

.  17628 

32,4 

.87251 

25,9 

.  12749 

.964 

.04937 

58,2 

.17660. 

32,4 

.87277 

25,8 

.  12723 

0.965 

0.04996 

58,2 

0.17693 

32,4 

9.87303 

25,8 

0.12697 

.966 

.05054 

58,1 

.  17725 

32,4 

.87329 

25,7 

.12671 

.967 

.05112 

58,1 

•  17757 

32,5 

.87354 

25,7 

.12646 

.968 

.05170 

58,1 

.17790 

32,5 

.87380 

25,6 

.12620 

.969 

.05228 

58,0 

.  17822 

32,5 

.87406 

25,5 

.12594 

0.970 

0.05286 

58,0 

0.17855 

32,5 

9.87431 

25,5 

0.12569 

.971 

.05344 

58,0 

.17887 

32,5 

.87456 

25,4 

.12544 

•  972 

.05402 

57,9 

.  17920 

32,6 

.87482 

25A 

.12518 

•  973 

.05460 

57,9 

.  17953 

32,6 

.87507 

25,3 

.  12493 

•974 

.05518 

57,9 

.17985 

32,6 

•87533 

25,3 

.  12467 

0.975 

0.05576 

57,8 

o.  18018 

32,6 

9.87558 

25,2 

0.12442 

.976 

.05633 

57,8 

.18050 

32,6 

.87583 

25,2 

.12417 

•  977 

.05691 

57,8 

.18083 

32,6 

.87608 

25,1 

.  12392 

.978 

.05749 

57,7 

.18116 

32,7 

.87633 

25,1 

.  12367 

•  979 

.05807 

57,7 

.  18148 

32,7 

.87658 

25,0 

.12342 

0.980 

0.05864 

57,7 

0.18181 

32,7 

9.87683 

25,0 

0.12317 

.981 

.05922 

57,6 

.18214 

32,7 

.87708 

24,9 

.  12292 

.982 

.05980 

57,6 

.  18246 

32,7 

•87733 

24,9 

.12267 

.983 

.06037 

57,6 

.18279 

32,8 

.87758 

24,8 

.  12242 

.984 

.06095 

57,5 

.18312 

32,8 

.87783 

24,8 

.12217 

0.985 

0.06152 

57,5 

0.18345 

32,8 

9.87807 

24,7 

0.12193 

.986 

.06210 

57,5 

.18378 

32,8 

.87832 

24,7 

.12168 

.987 

.06267 

57,4 

.  18410 

32,8 

.87857 

24,6 

.  12143 

.988 

.06325 

57,4 

.18443 

32,9 

.87881 

24,6 

.12119 

.989 

.06382 

57,4 

.18476 

32,9 

.87906 

24,5 

.12094 

0.990 

0.06439 

57,3 

0.18509 

32,9 

9.87930 

24,5 

0.12070 

.991 

.06497 

57,3 

.18542 

32,9 

.87955 

24,4 

.12045 

.992 

.06554 

57,3 

.18575 

32,9 

.87979 

24,3 

.I2O2I 

•  993 

.06611 

57,2 

.18608 

32,9 

.88003 

24,3 

.11997 

.994 

.06669 

57,2 

.18641 

33,0 

.88028 

24,2 

.11972 

0.995 

0.06726 

57,2 

o.  18674 

33,0 

9.88052 

24,2 

O.II948 

.996 

.06783 

57,2 

.  18707 

33,o 

.88076 

24,1 

.11924 

•  997 

.06840 

57,i 

.  18740 

33,0 

.88100 

24,1 

.II90O 

.998 

.06897 

57,i 

.18773 

33,0 

.88124 

24,0 

.11876 

.999 

.06954 

57,i 

.18806 

33,1 

.88148 

24,0 

.11852 

I.OOO 

0.07011 

57,o 

0.18839 

33,1 

9.88172 

23,9 

O.II828 

u 

log  tan  gd  u 

«-  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

co  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


39 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.  000 

O.07OII 

57,o 

0.18839 

33,1 

9.88172 

23,9 

0.11828 

.001 

.07068 

57,o 

.18872 

33,1 

.88196 

23,9 

.11804 

.002 

.07125 

57,o 

.18905 

33,1 

.88220 

23,8 

.11780 

.003 

.07182 

56,9 

.18938 

33,1 

.88244 

23,8 

.11756 

.004 

.07239 

56,9 

.18971 

33,1 

.88268 

23,8 

.11732 

1.005 

0.07296 

56,9 

0.19004 

33,2 

9.88291 

23,7 

0.11709 

.006 

•07353 

56,8 

.19038 

33,2 

.88315 

23,7 

.11685 

.007 

.07410 

56,8 

.19071 

33,2 

.88339 

23,6 

.11661 

.008 

.07466 

56,8 

.  19104 

33,2 

.88362 

23,6 

.11638 

.009 

.07523 

56,7 

.18137 

33,2 

.88386 

23,5 

.11614 

1.  010 

0.07580 

56,7 

0.19171 

33,3 

9.88409 

23,5 

0.11591 

.Oil 

.07637 

56,7 

.  19204 

33,3 

.88433 

23,4 

.11567 

.012 

.07693 

56,7 

.19237 

33,3 

.88456 

23,4 

•II544 

.013 

.07750 

56,6 

.  19270 

33,3 

.88480 

23,3 

.11520 

.014 

.07807 

56,6 

.  19304 

33,3 

.88503 

23,3 

.11497 

1.  015 

0.07863 

56,6 

0.19337 

33,3 

9.88526 

23,2 

O.H474 

.016 

.07920 

56,5 

.  19370 

33,4 

.88549 

23,2 

.11451 

.017 

.07976 

56,5 

.19404 

33,4 

.88572 

23,1 

.  I  1428 

.018 

.08033 

56,5 

•  19437 

33,4 

.88595 

23,1 

.11405 

.019 

.08089 

56,4 

.  I947I 

33,4 

.88619 

23,0 

.11381 

I.O2O 

0.08146 

56,4 

0.19504 

33,4 

9.88642 

23,0 

0.11358 

.021 

.08202 

56,4 

.  19537 

33,5 

.88664 

22,9 

.11336 

.022 

.08258 

56,4 

.19571 

33,5 

.88687 

22,9 

.11313 

.023 

.08315 

56,3 

.19604 

33,5 

.88710 

22,8 

.11290 

.024 

.08371 

56,3 

.19638 

33,5 

.88733 

22,8 

.11267 

I.O25 

0.08427 

56,3 

0.19671 

33,5 

9.88756 

22,7 

0.11244 

.026 

.08483 

56,2 

.  1970S 

33,5 

.88779 

22,7 

.11221 

.027 

.08540 

56,2 

.  19738 

33,6 

.88801 

22,6 

.11109 

.028 

.08596 

56,2 

.  19772 

33,6 

.88824 

22,6 

.11176 

.029 

.08652 

56,i 

.19806 

33,6 

.88846 

22,6 

.11154 

1.030 

0.08708 

56,i 

0.19839 

33,6 

9.88869 

22,5 

0.11131 

.031 

.08764 

56,i 

.19873 

33,6 

.88891 

22,5 

.11109 

.032 

.08820 

56,i 

.19006 

33,6 

.88914 

22,4 

.11086 

.033 

.08876 

56,0 

.19940 

33,7 

.88936 

22,4 

.11064 

.034 

.08932 

56,0 

.19974 

33,7 

.88959 

22,3 

.11041 

1.035 

0.08988 

56,0 

0.20007 

33,7 

9.88981 

22,3 

0.11019 

.036 

.09044 

55,9 

.20041 

33,7 

.89003 

22,2 

.10997 

•  037 

.09100 

55,9 

.20075 

33,7 

.89025 

22,2 

.10975 

.038 

.09156 

55,9 

.20109 

33,7 

.89048 

22,1 

.10952 

.039 

.09212 

55,9 

.20142 

33,8 

.80070 

22,1 

.10930 

1.040 

0.09268 

55,8 

0.20176 

33,8 

9.89092 

22,0 

0.10008 

.041 

.09324 

55,8 

.20210 

33,8 

.89114 

22,0 

.  10886 

.042 

.09379 

55,8 

.20244 

33,8 

.89136 

22,0 

.10864 

.043 

.09435 

55,7 

.20278 

33,8 

.89158 

21,9 

.10842 

.044 

.09491 

55,7 

.20311 

33,9 

.89180 

21,9 

.10820 

1.045 

0.09547 

55,7 

0.20345 

33,9 

9.89201 

21,8 

0.  10799 

.046 

.09602 

55,7 

.20379 

33,9 

.89223 

21,8 

•  10777 

.047 

.09658 

55,6 

.20413 

33,9 

.89245 

21,7 

.  10755 

.048 

.097H 

55,6 

.20447 

33,9 

.89267 

21,7 

•  10733 

.049 

.09769 

55,6 

.20481 

33,9 

.89288 

21,6 

.10712 

1.050 

0.09825 

55,6 

0.20515 

34,0 

9.89310 

21,6 

0.10690 

u 

log  tan  gd  u 

-  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

•  Fflf 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

•  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.050 

0.09825 

55,6 

0.20515 

34,0 

9.89310 

21,6 

0.10690 

.051 

.09880 

55,5 

.20549 

34,0 

.89331 

21,6 

.10669 

.052 

.09936 

55,5 

.20583 

34,0 

.89353 

21,5 

.10647 

.053 

.09991 

55,5 

.20617 

34,0 

.89375 

21,5 

.10625 

•054 

.10047 

55,4 

.20651 

34,0 

.89396 

21,4 

.10604 

1.055 

0.  IOI02 

55,4 

0.20685 

34,0 

9.89417 

21,4 

0.10583 

.056 

.  10158 

55,4 

.20719 

34,1 

.89439 

21,3 

.  10561 

.057 

.10213 

55,4 

.20753 

34,1 

.89460 

21,3 

.  10540 

.058 

.10268 

55,3 

.20787 

34,1 

.89481 

21,2 

.10519 

•059 

.  10324 

55,3 

.20821 

34,1 

.89502 

21,2 

.10498 

i.  060 

0.10379 

55,3 

0.20855 

34,1 

9.89524 

21,2 

0.10476 

.061 

.  10434 

55,3 

.20889 

34J 

.89545 

21,1 

.10455 

.062 

.10489 

55,2 

.20924 

34,2 

.89566 

21,1 

.10434 

.063 

.  10545 

55,2 

.20958 

34,2 

.89587 

21,0 

.10413 

.064 

.10600 

55,2 

.20992 

34,2 

.89608 

21,0 

.  10392 

1.065 

0.10655 

55,1 

0.21026 

34,2 

9.89629 

20,9 

0.10371 

.066 

.  10710 

55,i 

.21060 

34,2 

.89650 

20,9 

.  10350 

.067 

.10765 

55,i 

.21094 

34,2 

.89671 

20,9 

.10329 

.068 

.10820 

55,1 

.21129 

34,3 

.89692 

20,8 

.10308 

.069 

.10875 

55,0 

.21163 

34,3 

.89712 

20,8 

.10288 

1.070 

o.  10930 

55,0 

0.21197 

34,3 

9.89733 

20,7 

0.10267 

.071 

.10985 

55,o 

.21232 

34,3 

.89754 

20,7 

.10246 

.072 

.  i  1040 

'55,o 

.21266 

34,3 

.89774 

2O,6 

.10226 

.073 

.11095 

54,9 

.21300 

34,3 

.89795 

2O,6 

.10205 

.074 

.11150 

54,9 

•21335 

34,4 

.89816 

20,6 

.10184 

1.075 

0.11205 

54,9 

0.21369 

34,4 

9.89836 

20,5 

0.10164 

.076 

.11260 

54,9 

.21403 

34,4 

.89857 

20,5 

.10143 

.077 

.11315 

54,8 

.21438 

34,4 

.89877 

20,4 

.10123 

.078 

.11370 

54,8 

.21472 

34,4 

.89898 

20,4 

.  IOI02 

.079 

.11424 

54,8 

.21507 

34,4 

.89918 

20,3 

.10082 

1.080 

0.11479 

54,8 

0.21541 

34,4 

9.89938 

20,3 

0.10062 

.081 

.11534 

54,7 

.21575 

34,5 

.89959 

20,3 

.IOO4I 

.082 

.11589 

54,7 

.21610 

34,5 

.89979 

20,2 

.IOO2I 

.083 

.11643 

54,7 

.21644 

34,5 

.89999 

20,2 

.IOOOI 

.084 

.11698 

54,7 

.21679 

34,5 

.90019 

20,1 

.09981 

1.085 

o.i  1753 

54,6 

0.21713 

34,5 

9.90039 

20,1 

0.09961 

.086 

.11807 

54,6 

.21748 

34,5 

.00059 

20,1 

.09941 

.087 

.11862 

54,6 

.21782 

34,6 

.90079 

20,0 

.09921 

.088 

.11916 

54,5 

.21817 

34,6 

.90099 

2O,O 

.09901 

.089 

.11971 

54,5 

.21852 

34,6 

.00119 

19,9 

.09881 

1.  000 

o.  12025 

54,5 

0.21886 

34,6 

9.00139 

19,9 

0.09861 

.091 

.12080 

54,5 

.21921 

34,6 

.90159 

19,9 

.09841 

.092 

.12134 

54,4 

.21955 

34,6 

.90179 

19,8 

.09821 

.093 

.12189 

54,4 

.21990 

34,7 

.90199 

19,8 

.09801 

.094 

.  12243 

54,4 

.22025 

34,7 

.90218 

19,7 

.09782 

1.095 

0.12298 

54,4 

0.22059 

34,7 

9.90238 

19,7 

0.09702 

.096 

.  12352 

54,4 

.22094 

34,7 

.90258 

19,6 

.09742 

.097 

.12406 

54,3 

.22129 

34,7 

.90277 

19,6 

.09723 

.098 

.  12461 

54,3 

.22164 

34,7 

.90297 

19,6 

.09703 

.099 

.12515 

54,3 

.22198 

34,7 

.90317 

19,5 

.09683 

1.  100 

0.12569 

54,3 

0.22233 

34,8 

9.90336 

19,5 

0.09664 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

•  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«FO' 

log  tanh  u 

«F0' 

log  coth  u 

I.IOO 

0.12569 

54,3 

0.22233 

34,8 

9.90336 

19,5 

0.09664 

.101 

.12623 

54,2 

.22268 

34,8 

•90356 

19,4 

.09644 

.102 

..12678 

54,2 

.22303 

34,8 

.90375 

19,4 

.09625 

.103 

.12732 

54,2 

.22337 

34,8 

.90394 

19,4 

.09606 

.104 

.12786 

54,2 

.22372 

34,8 

.90414 

19,3 

.09586 

I.IO5 

0.12840 

54,1 

0.22407 

34,8 

9.90433 

19,3 

0.09567 

.106 

.12894 

54,1 

.22442 

34,9 

.90452 

19,2 

.09548 

.107 

.12948 

54,1 

.22477 

34,9 

.90472 

19,2 

.09528 

.108 

.13002 

54,1 

.22512 

34,9 

.90491 

19,2 

.09509 

.109 

.13056 

54,0 

.22547 

34,9 

.00510 

19,1 

.09490 

I.  IIC 

O.I3III 

54,0 

0.22582 

34,9 

9.90529 

19,1 

0.09471 

.in 

.13165 

54,0 

.22616 

34,9 

.90548 

19,1 

.09452 

.112 

.13218 

54,0 

.22651 

35,0 

.90567 

19,0 

.09433 

.113 

.  13272 

53,9 

.22686 

35,0 

.90586 

19,0 

.09414 

.114 

.13326 

53,9 

.22721 

35,0 

.90605 

18,9 

•09395 

1.  115 

0.13380 

53,9 

0.22756 

35,0 

9.90624 

18,9 

0.09376 

.116 

.13434 

53,9 

.22791 

35,0 

.90643 

18,9 

.09357 

.117 

.13488 

53,8 

.22826 

35,o 

.90662 

18,8 

.09338 

.118 

•  13542 

53,8 

.22861 

35,o 

.90680 

18,8 

.09320 

.119 

.13596 

53,8 

.22896 

35,1 

.90609 

18,7 

.09301 

1.  120 

0.13649 

53,8 

0.22931 

35,i 

9.90718 

18,7 

0.09282 

.121 

•  13703 

53,8 

.22967 

35,i 

.90737 

18,7 

.09263 

.122 

.  13757 

53,7 

.23002 

35,1 

.90755 

18,6 

.09245 

.123 

.I38u 

53,7 

.23037 

35,1 

•90774 

18,6 

.09226 

.124 

.13864 

53,7 

.23072 

35,1 

.90792 

18,6 

.09208 

1.  125 

0.13918 

53,7 

0.23107 

35,1 

9.90811 

i8,5 

0.09189 

.126 

.  13972 

53,6 

.23142 

35,2 

.90830 

18,5 

.09170 

.127 

.14025 

53,6 

.23177 

35,2 

.90848 

18,4 

.09152 

.128 

.  14079 

53,6 

.23213 

35,2 

.90866 

18,4 

.09134 

.129 

.14133 

53,6 

.23248 

35,2 

.90885 

18,4 

.09115 

1.130 

0.14186 

53,5 

0.23283 

35,2 

9.90903 

18,3 

0.09097 

.131 

.14240 

53,5 

.23318 

35,2 

.90921 

18,3 

.00079 

.132 

.14293 

53,5 

.23353 

35,3 

.90040 

18,3 

.09060 

.133 

•14347 

53,5 

•23389 

35,3 

.90958 

18,2 

.09042 

.134 

.14400 

53,5 

.23424 

35,3 

.90976 

18,2 

.09024 

1.  135 

0.14454 

53,4 

0.23459 

35,3 

9.90004 

18,1 

0.09006 

.136 

.  14507 

53,4 

.23495 

35,3 

.91012 

18,1 

.08988 

.137 

.14560 

53,4 

.23530 

35,3 

.91030 

18,1 

.08970 

.138 

.  14614 

53,4 

.23565 

35,3 

.91049 

18,0 

.08951 

.139 

.  14667 

53,3 

.23601 

35,4 

.91067  . 

18,0 

.08933 

1.140 

0.14720 

53,3 

0.23636 

35,4 

9.91085 

18,0 

0.08915 

.141 

•  14774 

53,3 

.23671 

35,4 

.91102 

17,9 

.08898 

.142 

.  14827 

53,3 

.23707 

35,4 

.91120 

17,9 

.08880 

.143 

.14880 

53,3 

.23742 

35,4 

.9H38 

17,8 

.08862 

.144 

•  M934 

53,2 

.23778 

35,4 

.9H56 

17,8 

.08844 

1.  145 

o.  14987 

53,2 

0.23813 

35,4 

9.91174 

17,8 

0.08826 

.146 

.15040 

53,2 

.23848 

35,5 

.91192 

17,7 

.08808 

.147 

.15093 

53,2 

.23884 

35,5 

.91209 

17,7 

.08791 

.148 

.15146 

53,2 

.23919 

35,5 

.91227 

17,7 

.08773 

.149 

.15200 

53,1 

.23955 

35,5 

.91245 

17,6 

.08755 

1.150 

0.15253 

53,1 

0.23900 

35,5 

9.91262 

17,6 

0.08738 

u 

log  tan  ad  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

-Fo' 

logcscgdu 

SMITHSONIAN  TABLE* 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  F0' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.150 

0.15253 

53,i 

0.23990 

35,5 

9.91262 

17,6 

0.08738 

.151 

.15306 

53,i 

.24026 

35,5 

.91280 

17,6 

.08720 

.152 

•15359 

53,1 

.24061 

35,5 

.91297 

17,5 

.08703 

.153 

.15412 

53,o 

.24097 

35,6 

.91315 

17,5 

.08685 

•  154 

•  15465 

53,o 

.24133 

35,6 

.91332 

17,5 

.08668 

I.I55 

0.15518 

53,0 

0.24168 

35,6 

9.91350 

17,4 

0.08650 

.156 

.15571 

53,o 

.24204 

35,6 

.91367 

17,4 

.08633 

•  157 

.  15624 

53,o 

.24239 

35,6 

.91385 

17,3 

.08615 

.158 

•  15677 

52,9 

.24275 

35,6 

.91402 

17,3 

.08598 

.159 

.15730 

52,9 

.24311 

36,6 

.91419 

17,3 

.08581 

1.160 

0.15783 

52,9 

0.24346 

35,7 

9.91436 

17,2 

0.08564 

.161 

.15836 

52,9 

.24382 

35,7 

.91454 

17,2 

.08546 

.162 

.15888 

52,9 

.24418 

35,7 

.91471 

17,2 

.08529 

.163 

•I594I 

52,8 

.24453 

35,7 

.91488 

I7,i 

.08512 

.164 

.15994 

52,8 

.24489 

35,7 

.91505 

17,1 

.08495 

1.165 

0.16047 

52,8 

0.24525 

35,7 

9.91522 

I7,i 

0.08478 

.166 

.16100 

52,8 

.24560 

35,7 

.91539 

17,0 

.08461 

.167 

.16152 

52,7 

.24596 

35,8 

.91556 

17,0 

.08444 

.168 

.  16205 

52,7 

.24632 

35,8 

.91573 

17,0 

.08427 

.169 

.16258 

52,7 

.24668 

35,8 

.91590 

16,9 

.08410 

1.170 

0.16311 

52,7 

0.24703 

35,8 

9.91607 

16,9 

0.08393 

.171 

.  16363 

52,7 

.24739 

35,8 

.91624 

16,9 

.08376 

.172 

.  16416 

52,6 

.24775 

35,8 

.91641 

16,8 

•08359 

.173 

.16469 

52,6 

.24811 

35,8 

.91658 

16,8 

.08342 

.174 

.16521 

52,6 

.24847 

35,9 

.91674 

16,8 

.08326 

1.  175 

0.16574 

52,6 

0.24883 

35,9 

9.91691 

16,7 

0.08309 

.176 

.16626 

52,6 

.24919 

35,9 

.91708 

16,7 

.08292 

.177 

.16679 

52,5 

.24954 

35,9 

.91724 

16,7 

.08276 

.178 

.16731 

52,5 

.24990 

35,9 

.91741 

16,6 

.08259 

.179 

.  16784 

52,5 

.25026 

35,9 

.91758 

16,6 

.08242 

1.180 

0.16836 

52,5 

0.25062 

35,9 

9.91774 

16,6 

0.08226 

.181 

.16889 

52,5 

.25098 

35,9 

.91791 

16,5 

.08209 

.182 

.16941 

52,4 

.25134 

36,0 

.91807 

16,5 

.08193 

.183 

.16994 

52,4 

.25170 

36,0 

.91824 

16,4 

.08176 

.184 

.  17046 

52,4 

.25206 

36,0 

.91840 

16,4 

.08160 

1.185 

0.17009 

52,4 

0.25242 

36,0 

9.91857 

16,4 

0.08143 

.186 

.17151 

52,4 

.25278 

36,0 

.91873 

16,3 

.08127 

.187 

.  17203 

52,3 

.253U 

36,0 

.91889 

16,3 

.oSlII 

.188 

.  17256 

52,3 

.25350 

36,0 

.91906 

16,3 

.08094 

.189 

.17308 

52,3 

.25386 

36,1 

.91922 

16,2 

.08078 

1.190 

0.17360 

52,3 

0.25422 

36,1 

9.91938 

16,2 

0.08062 

.191 

.17413 

52,3 

.25458 

36,1 

.91954 

16,2 

.08046 

.192 

.17465 

52,2 

.25494 

36,1 

.91970 

16,2 

.08030 

.193 

.17517 

52,2 

.25530 

36,1 

.91987 

16,1 

.08013 

.194 

.17569 

52,2 

.25567 

36,1 

.92003 

16,1 

.07997 

1.  195 

0.17621 

52,2 

0.25603 

36,1 

9.92019 

16,1 

0.07981 

.196 

.  17674 

52,2 

.25639 

36,2 

.92035 

16,0 

.07965 

.197 

.  17726 

52,2 

.25675 

36,2 

.92051 

16,0 

.07949 

.198 

.17778 

52,1 

.257H 

36,2 

.92067 

16,0 

•07933 

.199 

.17830 

52,1 

.25747 

36,2 

.92083 

15,9 

.07917 

1.  200 

0.17882 

52,1 

0.25784 

36,2 

9.92009 

15,9 

0.07901 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

w  Fo' 

log  sin  gd  u 

«FO' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


43 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  IV 

log  tanh  u 

»  Fo' 

log  coth  u 

I.2OO 

0.17882 

52,1 

0.25784 

36,2 

9.92099 

15,9 

0.07901 

.2OI 

•  17934 

52,1 

.25820 

36,2 

.92114 

15,9 

.07886 

.202 

.17986 

52,1 

.25856 

36,2 

.92130 

15,8 

.07870 

.203 

.18038 

52,0 

.25892 

36,2 

.92146 

15,8 

.07854 

.204 

.18090 

52,0 

.25929 

36,3 

.92162 

15,8 

.07838 

1.205 

0.18142 

52,0 

0.25965 

36,3 

9.92178 

15,7 

0.07822 

.206 

.18194 

52,0 

.26001 

36,3 

.92193 

15,7 

.07807 

.207 

.  18246 

52,0 

.26037 

36,3 

.92209 

15,7 

.07791 

.208 

.18298 

5i,9 

.26074 

36,3 

.92225 

15,6 

.07775 

.209 

.18350 

5i,9 

.26110 

36,3 

.92240 

15,6 

.07760 

I.2IO 

0.18402 

51,9 

0.26146 

36,3 

9.92256 

15,6 

0.07744 

.211 

.  18454 

51,9 

.26183 

36,3 

.92271 

15,5 

.07729 

.212 

.18506 

5L9 

.26219 

36,4 

.92287 

15,5 

.07713 

.213 

.18558 

5i,9 

.26255 

36,4 

.92302 

15,5 

.07698 

.214 

.18610 

5i,8 

.26292 

36,4 

.92318 

15,4 

.07682 

1.  215 

0.18662 

5i,8 

0.26328 

36,4 

9.92333 

15,4 

0.07667 

.216 

.18713 

5i,8 

.26365 

36,4 

.92349 

15,4 

.07651 

.217 

.  18765 

5i,8 

.26401 

36,4 

.92364 

15,4 

.07636 

.218 

.18817 

5i,8 

.26437 

36,4 

.92379 

15,3 

.07621 

.219 

.18869 

51,7 

.26474 

36,5 

.92395 

15,3 

.07605 

1.220 

0.18920 

51,7 

0.26510 

36,5 

9.92410 

15,3 

0.07500 

.221 

.18972 

5i,7 

.26547 

36,5 

.92425 

15,2 

.07575 

.222 

.19024 

51,7 

.26583 

36,5 

.92440 

15,2 

.07560 

.223 

.19075 

51,7 

.26620 

36,5 

.92456 

15,2 

.07544 

.224 

.19127 

51,7 

.26656 

36,5 

.92471 

15,1 

.07529 

I.22S 

O.I9I79 

5i,6 

0.26693 

36,5 

9.92486 

I5,i 

0.07514 

.226 

.19230 

5i,6 

.26729 

36,5 

.92501 

I5,i 

.07499 

.227 

.  19282 

5i,6 

.26766 

36,6 

.92516 

I5,o 

.07484 

.228 

.19334 

5i,6 

.26802 

36,6 

.92531 

I5,o 

.07469 

.229 

.19385 

5i,6 

.26839 

36,6 

.92546 

I5,o 

.07454 

1.230 

0.19437 

5i,5 

0.26876 

36,6 

9.92561 

I5,o 

0.07439 

.231 

.19488 

5i,5 

.26912 

36,6 

.92576 

14,9 

.07424 

.232 

.  19540 

5i,5 

.20949 

36,6 

.92591 

H,9 

.07409 

•  233 

.  I959I 

51,5 

.26985 

36,6 

.92606 

14,9 

.07394 

.234 

.19643 

51,5 

.27022 

36,6 

.92621 

14,8 

.07379 

1.235 

0.19694 

51,5 

0.27059 

36,7 

9.92635 

14,8 

0.07365 

.236 

.  19746 

51,4 

.27095 

36,7 

.92650 

14,8 

.07350 

.237 

.  19797 

51,4 

.27132 

36,7 

.92665 

14,7 

.07335 

.238 

.19848 

51,4 

.27169 

36,7 

.92680 

14,7 

.07320 

•  239 

.19900 

51,4 

.27205 

36,7 

.92694 

14,7 

.07306 

1.240 

O.I995I 

51,4 

0.27242 

36,7 

9.92709 

14,7 

0.07291 

.241 

.20003 

5i,4 

.27279 

36,7 

.92724 

14,6 

.07276 

.242 

.20054 

5i,3 

.27316 

36,7 

.92738 

14,6 

.07262 

.243 

.20105 

51,3 

.27352 

36,8 

.92753 

14,6 

.07247 

.244 

.20157 

51,3 

.27389 

36,8 

.92767 

14,5 

.07233 

1.245 

0.20208 

51,3 

0.27426 

36,8 

9.92782 

14,5 

0.07218 

.246 

.20259 

51,3 

.27463 

36,8 

.92796 

14,5 

.07204 

.247 

.20310 

51,2 

.27499 

36,8 

.92811 

14,4 

.07189 

.248 

.20362 

51,2 

.27536 

36,8 

.92825 

14,4 

.07175 

.249 

.20413 

51,2 

•27573 

36,8 

.92840 

14,4 

.07160 

1.250 

0.20464 

51,2 

0.27610 

36,8 

9.92854 

14,4 

0.07146 

u 

log  tan  gd  u 

-Fo' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

-  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


44 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«F0' 

log  coth  u 

1.250 

0.20464 

51,2 

0.27610 

36,8 

9.92854 

14,4 

0.07146 

.251 

.20515 

51,2 

.27647 

36,9 

.92868 

14,3 

.07132 

.252 

.20566 

51,2 

.27684 

36,9 

.92883 

14,3 

.07117 

.253 

.20618 

51, 

.27721 

36,9 

.92897 

14,3 

.07103 

.254 

.20669 

51, 

•27757 

36,9 

.92911 

14,2 

.07089 

1.255 

0.20720 

Si, 

0.27794 

36,9 

9.92926 

14,2 

0.07074 

.256 

.20771 

51, 

.27831 

36,9 

.92940 

14,2 

.07060 

.257 

.20822 

5i, 

.27868 

36,9 

.92954 

14,2 

.07046 

.258 

.20873 

51, 

.27905 

36,9 

.92968 

14,1 

.07032 

.259 

.20924 

5i,o 

.27942 

36,9 

.92982 

14,1 

.07018 

1.260 

0.20975 

5i,o 

0.27979 

37,o 

9.92996 

14,1 

0.07004 

.261 

.21026 

5i,o 

.28016 

37,o 

.93010 

14,0 

.06990 

.262 

.21077 

5i,o 

.28053 

37,o 

.93024 

14,0 

.06976 

.263 

.21128 

5i,o 

.28090 

37,o 

.93038 

14,0 

.06962 

.264 

.21179 

5i,o 

.28127 

37,o 

.93052 

14,0 

.06948 

1.265 

0.21230 

50,9 

0.28164 

37,0 

9.93066 

13,9 

0.06934 

.266 

.21281 

50,9 

.28201 

37,0 

.93080 

13,9 

.06920 

.267 

.21332 

50,9 

.28238 

37,o 

.93094 

13,9 

.06906 

.268 

.21383 

50,9 

.28275 

37,1 

.93108 

13,8 

.06892 

.269 

.21434 

50,9 

.28312 

37,1 

.93122 

13,8 

.06878 

1.270 

0.21485 

50,9 

0.28349 

37,1 

9.93135 

13,8 

0.06865 

.271 

.21536 

50,9 

.28386 

37,i 

.93149 

13,8 

.06851 

.272 

.21586 

50,8 

.28423 

37,1 

.93163 

13,7 

.06837 

•  273 

.21637 

50,8 

.28460 

37,1 

.93177 

13,7 

.06823 

.274 

.21688 

50,8 

.28498 

37,1 

.93190 

13,7 

.06810 

1.275 

0.21739 

50,8 

0.28535 

37,1 

9.93204 

13,6 

0.06796 

.276 

.21790 

50,8 

.28572 

37,2 

.93218 

13,6 

.06782 

.277 

.21840 

50,8 

.28609 

37,2 

.93231 

13,6 

.06769 

.278 

.21891 

50,7 

.28646 

37,2 

.93245 

13,6 

•06755 

.279 

.21942 

50,7 

.28683 

37,2 

.93258 

13,5 

.06742 

1.280 

0.21993 

50,7 

0.28721 

37,2 

9.93272 

13,5 

0.06728 

.281 

.22043 

50,7 

.28758 

37,2 

.93285 

13,5 

.06715 

.282 

.22094 

50,7 

.28795 

37,2 

.93299 

13,5 

.06701 

.283 

.22145 

50,7 

.28832 

37,2 

.93312 

13,4 

.06688 

.284 

.22195 

50,6 

.28869 

37,2 

.93326 

13,4 

.06674 

1.285 

0.22246 

50,6 

0.28907 

37,3 

9-93339 

13,4 

O.o666l 

.286 

.22296 

50,6 

.28944 

37,3 

•93353 

13,3 

.06647 

.287 

.22347 

50,6 

.28981 

37,3 

.93366 

13,3 

.06634 

.288 

.22398 

50,6 

.29018 

37,3 

•93379 

13,3 

.06621 

.289 

.22448 

50,6 

.29056 

37,3 

•93392 

13,3 

.06608 

1.200 

0.22499 

50,6 

0.29093 

37,3 

9.93406 

13,2 

0.06594 

.291 

.22549 

50,5 

.29130 

37,3 

.93419 

13,2 

.06581 

.292 

.22600 

50,5 

.29168 

37,3 

.93432 

13,2 

.06568 

.293 

.22650 

50,5 

.29205 

37,3 

•93445 

13,2 

.06555 

.294 

.22701 

50,5 

.29242 

37,4 

.93458 

I3,i 

.06542 

1.295 

0.22751 

50,5 

0.29280 

37,4 

9.93472 

I3,i 

0.06528 

.296 

.22802 

50,5 

.29317 

37,4 

.93485 

13,1 

.06515 

.297 

.22852 

50,4 

.29355 

37,4 

.93498 

I3,i 

.06502 

.298 

.22003 

50,4 

.29392 

37,4 

•935II 

13,0 

.06489 

.299 

.22953 

50,4 

.29429 

37,4 

.93524 

I3,o 

.06476 

1.300 

0.23004 

50,4 

0.29467 

37,4 

9-93537 

I3,o 

0.06463 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

'«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


45 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

<o  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.300 

0.23004 

50,4 

0.29467 

37,4 

9-93537 

13,0 

0.06463 

.301 

•23054 

50,4 

.29504 

37,4 

•93550 

12,9 

.06450 

.302 

.23104 

50,4 

.29542 

37,4 

.93563 

12,9 

.06437 

.303 

.23155 

50,4 

.29579 

37,5 

.93576 

12,9 

.06424 

.304 

.23205 

50,3 

.29617 

37,5 

.93588 

12,9 

.06412 

1.305 

0.23255 

50,3 

0.29654 

37,5 

9.93601 

12,8 

0.06399 

.306 

.23306 

50,3 

.29692 

37,5 

.93614 

12,8 

.06386 

.307 

.23356 

50,3 

.29729 

37,5 

.93627 

12,8 

.06373 

.308 

.23406 

50,3 

.29767 

37,5 

.93640 

12,8 

.06360 

.309 

.23457 

50,3 

.29804 

37,5 

.93652 

12,7 

.06348 

1.310 

0.23507 

50,2 

0.29842 

37,5 

9.93665 

12,7 

0.06335 

.311 

.23557 

50,2 

•29879 

37,5 

.93678 

12,7 

.06322 

.312 

.23607 

50,2 

.29917 

37,6 

.93691 

12,7 

.06309 

.313 

•23657 

50,2 

.29954 

37,6 

.93703 

12,6 

.06297 

.314 

.23708 

50,2 

.29992 

37,6 

.93716 

12,6 

.06284 

1.315 

0.23758 

50,2 

0.30029 

3>,6 

9.93728 

12,6 

0.06272 

.316 

.23808 

50,2 

.30067 

37,6 

•93741 

12,6 

.06259 

.317 

.23858 

50,1 

.30105 

37,6 

•93754 

12,5 

.06246 

.318 

.23008 

50,1 

.30142 

37,6 

.93766 

12,5 

.06234 

.319 

.23958 

50,i 

.30180 

37,6 

•93779 

12,5 

.06221 

1.320 

0.24009 

50,1 

0.30217 

37,6 

9.93791 

12,5 

0.06209 

.321 

.24059 

50,1 

•30255 

37,7 

.93804 

12,4 

.06196 

.322 

.24109 

50,1 

.30293 

37,7 

.93816 

12,4 

.06184 

.323 

.24159 

50,1 

.30330 

37,7 

.93828 

12,4 

.06172 

.324 

.24209 

5o,o 

.30368 

37,7 

.93841 

12,4 

.06159 

1.325 

0.24259 

50,o 

0.30406 

37,7 

9.93853 

12,3 

0.06147 

.326 

.24309 

5o,o 

.30444 

37,7 

.93865 

12,3 

.06135 

.327 

.24359 

50,o 

.30481 

37,7 

.93878 

12,3 

.06122 

.328 

.24409 

50,0 

.30519 

37,7 

.93890 

12,3 

.06110 

.329 

.24459 

50,0 

•30557 

37,7 

.93902 

12,2 

.06098 

1.330 

0.24509 

50,o 

0-30594 

37,8 

9.93914 

12,2 

0.06086 

.331 

.24559 

49,9 

.30632 

37,8 

.93927 

12,2 

.00073 

.332 

.24609 

49,9 

.30670 

37,8 

•93939 

12,2 

.06061 

.333 

.24659 

49,9 

.30708 

37,8 

.93951 

12,1 

.06049 

•  334 

.24709 

49,9 

.30746 

37,8 

.93963 

12,1 

.06037 

1.335 

0.24759 

49,9 

0.30783 

37,8 

9-93975 

12,1 

0.06025 

.336 

.24808 

49,9 

.30821 

37,8 

.93987 

12,1 

.06013 

•  337 

.24858 

49,9 

.30859 

37,8 

•93999 

1  2,O 

.06001 

.338 

.24908 

49,9 

.30897 

37,8 

.94011 

1  2,O 

.05989 

•  339 

.24958 

49,8 

.30935 

37,8 

.04023 

12,0 

•05977 

1.340 

0.25008 

49,8 

0.30972 

37,9 

9.94035 

12,0 

0.05965 

•  341 

.25058 

49,8 

.31010 

37,9 

.94047 

11,9 

.05953 

.342 

.25107 

49,8 

.31048 

37,9 

.94059 

n,9 

.05941 

•  343 

.25157 

49,8 

.31086 

37,9 

.94071 

11,9 

.05929 

•  344 

.25207 

49,8 

.31124 

37,9 

•94083 

11,9 

.05917 

1-345 

0.25257 

49,8 

0.31162 

37,9 

9.94095 

11,8 

0.05905 

.346 

.25306 

49,7 

.31200 

37,9 

.94107 

11,8 

.05893 

•  347 

.25356 

49,7 

.31238 

37,9 

.94119 

n,8 

.05881 

.348 

.25406 

49,7 

.31276 

37,9 

•94130 

n,8 

.05870 

•  349 

.25456 

49,7 

.3I3U 

37,9 

.94142 

n,8 

.05858 

1.350 

0.25505 

49,7 

0.31352 

38,0 

9.04154 

ii,7 

0.05846 

u 

loo  tin  gd  u 

«  Fo' 

log  tec  gd  u 

•  Fo' 

log  sin  gd  u 

*.F0' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


46 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

»Fo' 

log  coth  u 

1.350 

0.25505 

49,7 

0.31352 

38,0 

9.94154 

n,7 

0.05846 

.351 

.25555 

49,7 

.31390 

38,0 

.94166 

u,7 

.05834 

.352 

.25605 

49,7 

.31428 

38,0 

.94177 

n,7 

.05823 

•  353 

.25654 

49,6 

.31465 

38,0 

.94189 

n,7 

.05811 

•  354 

.25704 

49,6 

.31503 

38,0 

.94201 

n,6 

.05799 

1-355 

0.25754 

49,6 

0.3I54I 

38,0 

9.94212 

11,6 

0.05788 

•  356 

.25803 

49,6 

.31580 

38,0 

.94224 

11,6 

.05776 

•  357 

.25853 

49,6 

.31618 

38,0 

.94235 

11,6 

.05765 

.358 

.25902 

49,6 

.31656 

38,0 

.94247 

n,5 

.05753 

•  359 

.25952 

49,6 

.31694 

38,1 

.94258 

n,5 

.05742 

1.360 

0.26002 

49,6 

0.31732 

38,1 

9.94270 

n,5 

0.05730 

.361 

.26051 

49,5 

.31770 

38,1 

.94281 

n,5 

.05719 

.362 

.26101 

49,5 

.31808 

38,1 

.94293 

11,4 

.05707 

.363 

.26150 

49,5 

.31846 

38,1 

.94304 

11,4 

.05696 

.364 

.26200 

49,5 

.31884 

38,1 

.94316 

11,4 

.05684 

1.365 

0.26249 

49,5 

0.31922 

38,1 

9.94327 

ii,4 

0.0567^3 

.366 

.26299 

49,5 

.31960 

38,1 

.94338 

11,4 

.05662 

.367 

.26348 

49,5 

.31998 

38,1 

•94350 

u,3 

.05650 

.368 

.26398 

49,5 

.32036 

38,1 

.94361 

n,3 

.05639 

.369 

.26447 

49,4 

.32075 

38,2 

•94372 

n,3 

.05628 

1.370 

0.26496 

49,4 

0.32113 

38,2 

9.94384 

n,3 

0.05616 

•  371 

.26546 

49,4 

.32151 

38,2 

•94395 

11,2 

.05605 

•  372 

.26595 

49,4 

.32189 

38,2 

.94406 

11,2 

•05594 

•  373 

.26645 

49,4 

.32227 

38,2 

.94417 

11,2 

.05583 

•  374 

.26694 

49,4 

.32266 

38,2 

.94429 

11,2 

.05571 

1-375 

0.26743 

49,4 

0.32304 

38,2 

9.94440 

11,2 

0,05560 

•  376 

.26793 

49,3 

.32342 

38,2 

•94451 

1  1,1 

•05549 

•  377 

.26842 

49,3 

.32380 

38,2 

.94462 

11,1 

.05538 

.378 

.26891 

49,3 

.32418 

38,2 

•94473 

11,1 

.05527 

•  379 

.26941 

49,3 

.32457 

38,2 

.94484 

11,1 

.05516 

1.380 

0.26990 

49,3 

0.32495 

38,3 

9-94495 

11,0 

0.05505 

.381 

.27039 

49,3 

.32533 

38,3 

.94506 

11,0 

.05494 

.382 

.27089 

49,3 

.32571 

38,3 

.94517 

11,0 

.05483 

.383 

.27138 

49,3 

.32610 

38,3 

.94528 

11,0 

.05472 

.384 

.27187 

49,2 

.32648 

38,3 

•94539 

11,0 

.05461 

1.385 

0.27236 

49,2 

0.32686 

38,3 

9-94550 

10,9 

0.05450 

.386 

.27286 

49,2 

.32725 

38,3 

.94561 

10,9 

.05439 

.387 

.27335 

49,2 

.32763 

38,3 

.94572 

10,9 

.05428 

.388 

.27384 

49,2 

.32801 

38,3 

.94583 

10,9 

.05417 

.389 

.27433 

49,2 

.32840 

38,3 

•94594 

10,8 

.05406 

1.390 

0.27482 

49,2 

0.32878 

38,4 

9.94604 

10,8 

0.05396 

•  391 

.27532 

49,2 

.32916 

38,4 

.94615 

10,8 

.05385 

.392 

.27581 

49,2 

.32955 

38,4 

.94626 

10,8 

.05374 

•  393 

.27630 

49,1 

.32993 

38,4 

.94637 

10,8 

.05363 

•  394 

.27679 

49,i 

.33031 

38,4 

.94648 

10,7 

.05352 

1-395 

0.27728 

49,1 

0.33070 

38,4 

9.94658 

10,7 

0.05342 

.396 

.27777 

49,1 

.33108 

38,4 

.94669 

10,7 

.05331 

•  397 

.27826 

49,1 

.33147 

38,4 

.94680 

10,7 

.05320 

.398 

.27875 

49,1 

.33185 

38,4 

.94690 

10,6 

.05310 

•  399 

.27925 

49,1 

.33224 

38,4 

.94701 

10,6 

.05299 

1.400 

0.27974 

49,1 

o  .  33262 

38,5 

9.94712 

10,6 

0.05288 

u    |  log  tan  gd  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«FO' 

logcscgdu 

SMITHSONIAN  TABLES 


47 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

-  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.400 

0.27974 

49,1 

0.33262 

38,5 

9.94712 

10,6 

0.05288 

.401 

.28023 

49,0 

•33300 

38,5 

.94722 

10,6 

.05278 

.402 

.28072 

49,0 

•33339 

38,5 

•94733 

10,6 

.05267 

.403 

.28121 

49,0 

.33377 

38,5 

.94743 

io,5 

.05257 

.404 

.28170 

49,0 

.33416 

38,5 

•94754 

10,5 

.05246 

1.405 

0.28219 

49,0 

0.33454 

38,5 

9.94764 

10,5 

0.05236 

.406 

.28268 

49,0 

•33493 

38,5 

•94775 

10,5 

.05225 

.407 

.28317 

49,0 

•33531 

38,5 

.94785 

10,5 

.05215 

.408 

.28366 

49,0 

.33570 

38,5 

.94796 

10,4 

.05204 

.409 

.284I5 

48,9 

.33608 

38,5 

.94806 

10,4 

.05194 

1.410 

0.28464 

48,9 

0.33647 

38,5 

9.94817 

10,4 

0.05183 

.411 

.28512 

48,9 

.33686 

38,6 

•94827 

10,4 

.05173 

.412 

.28561 

48,9 

.33724 

38,6 

.94837 

10,3 

.05163 

.413 

.28610 

48,9 

.33763 

38,6 

.94848 

10,3 

.05152 

.414 

.28659 

48,9 

.33801 

38,6 

.94858 

10,3 

.05142 

1.415 

0.28708 

48,9 

0.33840 

38,6 

9.94868 

10,3 

0.05132 

.416 

.28757 

48,9 

.33878 

38,6 

.94879 

10,3 

.05121 

.417 

.28806 

48,9 

.33917 

38,6 

.94889 

10,2 

.05111 

.418 

.28855 

48,8 

33956 

38,6 

.94899 

10,2 

.05101 

.419 

.28903 

48,8 

•33994 

38,6 

.94909 

10,2 

.05091 

1.420 

0.28952 

48,8 

0.34033 

38,6 

9.94919 

10,2 

0.05081 

.421 

.20001 

48,8 

.34071 

38,6 

.94930 

10,2 

.05070 

.422 

.29050 

48,8 

.34110 

38,7 

.94940 

IO,I 

.05060 

.423 

.29099 

48,8 

.34U9 

38,7 

.94950 

IO,I 

.05050 

.424 

.29147 

48,8 

.34187 

38,7 

.94960 

IO,I 

.05040 

1.425 

0.29196 

48,8 

0.34226 

38,7 

9.94970 

IO,I 

0.05030 

.426 

.29245 

48,8 

.34265 

38,7 

.94980 

10,1 

.05020 

.427 

.29294 

48,7 

.34304 

38,7 

.94990 

IQ,O 

.05010 

.428 

.29342 

48,7 

•34342 

38,7 

.95000 

IO,O 

.O5OOO 

.429 

.29391 

48,7 

.34381 

38,7 

.95010 

10,0 

.04990 

1.430 

0.29440 

48,7 

0.34420 

38,7 

9.95020 

IO,O 

0.04980 

.431 

.29489 

48,7 

.34458 

38,7 

.95030 

10,0 

.04970 

.432 

.29537 

48,7 

.34497 

38,7 

.95040 

9,9 

.04060 

.433 

.29586 

48,7 

•34536 

38,8 

.95050 

9,9 

.04950 

•434 

.29635 

48,7 

.34575 

38,8 

.95060 

9,9 

.04940 

1.435 

0.29683 

48,7 

0.34613 

38,8 

9.95070 

9,9 

0.04930 

.436 

.29732 

48,6 

•34652 

38,8 

.95080 

9,9 

.04920 

.437 

.29781 

48,6 

.34691 

38,8 

.95090 

9,8 

.04910 

.438 

.29829 

48,6 

•34730 

38,8 

.95009 

9,8 

.04901 

.439 

.29878 

48,6 

.34769 

38,8 

.95109 

9,8 

.04891 

1.440 

O.29926 

48,6 

0.34807 

38,8 

9.95119 

9,8 

0.04881 

.441 

.29975 

48,6 

.34846 

38,8 

.95129 

9,8 

.04871 

•  442 

.30024 

48,6 

.34885 

38,8 

.95139 

9,7 

.04861 

•  443 

.30072 

48,6 

.34924 

38,8 

.95148 

9,7 

.04852 

•  444 

.30121 

48,6 

.34963 

38,8 

.95158 

9,7 

.04842 

1.445 

0.30169 

48,5 

0.35002 

38,9 

9.95168 

9,7 

0.04832 

.446 

.30218 

48,5 

.35040 

38,9 

.95177 

9,7 

.04823 

.447 

.30266 

48,5 

.35079 

38,9 

.95187 

9,6 

.04813 

.448 

.30315 

48,5 

.35118 

38,9 

.95197 

9,6 

.04803 

.449 

.30363 

48,5 

.35157 

38,9 

.95206 

9,6 

.04794 

1.450 

O.3O4I2 

48,5 

0.35196 

38,9 

9.95216 

9,6 

0.04784 

u 

log  tan  ad  u 

«  Fo' 

log  iec  gd  u 

«  Fo' 

log  tin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


48 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0'  . 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.450 

0.30412 

48,5 

0.35196 

38,9 

9.95216 

9,6 

0.04784 

.451 

.30460 

48,5 

.35235 

38,9 

.95225 

9,6 

.04775 

.452 

.30509 

48,5 

.35274 

38,9 

.95235 

9,5 

.04765 

•453 

.30557 

48,5 

.35313 

38,9 

.95245 

9,5 

.04755 

•454 

.30606 

48,4 

•35352 

38,9 

.95254 

9,5 

.04746 

1.  455 

0.30654 

48,4 

0.35391 

38,9 

9.95264 

9,5 

0.04736 

.456 

.30703 

48,4 

.35429 

39,o 

.95273 

9,5 

.04727 

•457 

.30751 

48,4 

.35468 

39,0 

.95283 

9,5 

.04717 

.458 

•30799 

48,4 

.35507 

39,o 

.95292 

9,4 

.04708 

•459 

.30848 

48,4 

.35546 

39,0 

.95301 

9,4 

.04699 

1.460 

0.30896 

48,4 

0.35585 

39,0 

9.953H 

9,4 

0.04689 

.461 

.30945 

48,4 

.35624 

39,0 

•95320 

9,4 

.04680 

.462 

.30993 

48,4 

.35663 

39,0 

•95330 

9,4 

.04670 

.463 

.31041 

48,3 

.35702 

39,0 

.95339 

9,3 

.04661 

.464 

.31090 

48,3 

•35741 

39,0 

.95348 

9,3 

.04652 

1.465 

0.31138 

48,3 

0.35780 

39,0 

9.95358 

9,3 

0.04642 

.466 

.31186 

48,3 

.35819 

39,0 

.95367 

9,3 

.04633 

.467 

.31235 

48,3 

.35858 

39,0 

.95376 

9,3 

.04624 

.468 

.31283 

48,3 

.35897 

39,1 

.95385 

9,2 

.04615 

•  469 

.31331 

48,3 

.35937 

39,1 

.95395 

9,2 

.04605 

1.470 

0.31379 

48,3 

0.35976 

39,1 

9.95404 

9,2 

0.04506 

.471 

.31428 

48,3 

.36015 

39,1 

.95413 

9,2 

•04587 

.472 

.31476 

48,3 

.36054 

39,1 

•95422 

9,2 

.04578 

•  473 

.31524 

48,2 

.36093 

39,i 

•95431 

9,2 

.04569 

•474 

.31572 

48,2 

.36132 

39,1 

•95441 

9,i 

.04559 

1.  475 

0.31621 

48,2 

0.36171 

39,1 

9-95450 

9,i 

0.04550 

.476 

.31669 

48,2 

.36210 

39,1 

•95459 

9,i 

.04541 

•  477 

.31717 

48,2 

.36249 

39,i 

.95468 

9,i 

.04532 

.478 

•31765 

48,2 

.36288 

39,i 

•95477 

9,i 

.04523 

•479 

.31814 

48,2 

.36328 

39,1 

.95486 

9,o 

.04514 

1.480 

0.31862 

48,2 

0.36367 

39,2 

9-95495 

9,o 

0.04505 

.481 

.31910 

48,2 

.36406 

39,2 

.95504 

9,o 

.04496 

.482 

.31958 

48,2 

.36445 

39,2 

.95513 

9,o 

.04487 

.483 

.32006 

48,1 

.36484 

39,2 

.95522 

9,o 

.04478 

.484 

.32054 

48,1 

.36523 

39,2 

•95531 

9,0 

.04469 

1.485 

0.32102 

48,1 

0.36563 

39,2 

•95540 

8,9 

.04460 

.486 

.32151 

48,1 

.36602 

39,2 

•95549 

8,9 

.04451 

.487 

.32199 

48,1 

.36641 

39,2 

.95558 

8,9 

.04442 

.488 

.32247 

48,1 

.36680 

39,2 

.95567 

8,9 

.04433 

.489 

.32295 

48,1 

.36719 

39,2 

.95576 

8,9 

.04424 

1.490 

0.32343 

48,1 

0.36759 

39,2 

9.95584 

8,8 

0.04416 

.491 

.32391 

48,1 

.36798 

39,2 

.95593 

8,8 

.04407 

.492 

.32439 

48,1 

.36837 

39,2 

.95602 

8,8 

.04398 

.493 

.32487 

48,0 

.36876 

39,3 

.956n 

8,8 

.04389 

•494 

.32535 

48,0 

.36916 

39,3 

.95620 

8,8 

.04380 

1.495 

0.32583 

48,0 

0.36955 

39,3 

9-95628 

8,8 

0.04372 

.496 

.32631 

48,0 

.36994 

39,3 

.95637 

8,7 

.04363 

•497 

.32679 

48,0 

.37033 

39,3 

.95646 

8,7 

.04354 

.498 

.32727 

48,0 

.37073 

39,3 

.95655 

8,7 

.04345 

.499 

.32775 

48,0 

.37H2 

39,3 

•95663 

8,7 

.04337 

1.500 

0.32823 

48,0 

0.37I5I 

39,3 

9.95672 

8,7 

0.04328 

u 

loo  tan  gd  u 

«  Fo' 

log  sec  gd  u 

»Fo' 

log  sin  gd  u 

»Fo' 

1  og  esc  gd  u 

SMITHSONIAN  TABLES 


49 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.500 

0.32823 

48,0 

0.37I5I 

39,3 

9.95672 

8,7 

0.04328 

.501 

.32871 

48,0 

.37191 

39,3 

.95681 

8,7 

.04319 

.502 

.32919 

48,0 

.37230 

39,3 

.95689 

8,6 

.04311 

.503 

.32967 

48,0 

.37269 

39,3 

.95698 

8,6 

.04302 

.504 

.33015 

47,9 

.37309 

39,3 

-95707 

8,6 

.04293 

1.505 

0.33063 

47,9 

0.37348 

39,3 

9.95715 

8,6 

0.04285 

.506 

•33III 

47,9 

.37387 

39,4 

.95724 

8,6 

.04276 

.507 

.33159 

47,9 

•37427 

39,4 

•95732 

8,5 

.04268 

.508 

.33207 

47,9 

.37466 

39,4 

.95741 

8,5 

.04259 

.509 

.33255 

47,9 

.37505 

39,4 

•95749 

8,5 

.04251 

1.510 

0.33303 

47,9 

0.37545 

39,4 

9.95758 

8,5 

0.04242 

.511 

•33350 

47,9 

.37584 

39,4 

.95766 

8,5 

.04234 

.512 

.33398 

47,9 

.37624 

39,4 

•95775 

8,5 

.04225 

.513 

.33446 

47,9 

.37663 

39,4 

.95783 

8,4 

.04217 

.514 

•33494 

47,8 

.37702 

39,4 

•95792 

8,4 

.04208 

1.515 

0.33542 

47,8 

0-37742 

39,4 

9.958oo 

8,4 

0.04200 

.516 

•33590 

47,8 

.37781 

39,4 

.95808 

8,4 

.04192 

.517 

.33638 

47,8 

.37821 

39,4 

.95817 

8,4 

.04183 

.518 

.33685 

47,8 

.37860 

39,4 

.95825 

8,4 

.04175 

.519 

•33733 

47,8 

.37900 

39,5 

.95834 

8,3 

.04166 

1.520 

0.33781 

47,8 

0.37939 

39,5 

9.95842 

8,3 

0.04158 

.521 

.33829 

47,8 

•37979 

39,5 

.95850 

8,3 

.04150 

.522 

.33877 

47,8 

.38018 

39,5 

.95859 

8,3 

.04141 

.523 

.33924 

47,8 

.38057 

39,5 

.95867 

8,3 

.04133 

.524 

•33972 

47,8 

.38097 

39,5 

.95875 

8,3 

.04125 

1.525 

0.34020 

47,7 

0.38136 

39,5 

9.95883 

8,2 

0.04117 

.526 

.34068 

47,7 

.38176 

39,5 

.95892 

8,2 

.04108 

.527 

.34H5 

47,7 

.38215 

39,5 

•95900 

8,2 

.04100 

.528 

.34163 

47,7 

.38255 

39,5 

.95908 

8,2 

.04092 

.529 

.34211 

47,7 

.38295 

39,5 

.95916 

8,2 

.04084 

1.530 

0.34258 

47,7 

0.38334 

39,5 

9.95924 

8,2 

0.04076 

.531 

.34306 

47,7 

.38374 

39,5 

•95933 

8,1 

.04067 

.532 

•34354 

47,7 

.38413 

39,6 

•95941 

8,1 

.04059 

•  533 

.34402 

47,7 

.38453 

39,6 

•95949 

8,1 

.04051 

•  534 

•34449 

47,7 

.38492 

39,6 

.95957 

8,1 

.04043 

1.535 

0.34497 

47,7 

0.38532 

39,6 

9.95965 

8,1 

0.04035 

.536 

.34545 

47,6 

.38571 

39,6 

.95973 

8,1 

.04027 

•  537 

.34592 

47,6 

.38611 

39,6 

.95981 

8,0 

.04019 

.538 

.34640 

47,6 

.38651 

39,6 

.95989 

8,0 

.04011 

•  539 

.34687 

47,6 

.38690 

39,6 

•95997 

8,0 

.04003 

1.540 

0.34735 

47,6 

0.38730 

39,6 

9.06005 

8,0 

0.03995 

•  541 

.34783 

47,6 

.38769 

39,6 

.96013 

8,0 

.03987 

•  542 

•34830 

47,6 

.38809 

39,6 

.96021 

8,0 

.03979 

.543 

.34878 

47,6 

.38849 

39,6 

.96029 

8,0 

.03971 

.544 

.34925 

47,6 

.38888 

39,6 

.96037 

7,9 

.03963 

1.545 

0.34973 

47,6 

0.38928 

39,6 

9.96045 

7,9 

0.03955 

.546 

•35021 

47,6 

.38968 

39,7 

.96053 

7,9 

.03947 

.547 

.35068 

47,6 

.30007 

39,7 

.96061 

7,9 

.03939 

.548 

.35n6 

47,5 

.39047 

39,7 

.96069 

7,9 

.03931 

•  549 

.35163 

47,5 

.39087 

39,7 

.96077 

7,9 

.03923 

1.550 

0.35211 

47,5 

0.39126 

39,7 

9.96084 

7,8 

0.03916 

u 

log  tan  gd  u 

«F0' 

log  sec  gd  u 

stfV 

log  sin  gd  u 

-V 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

-Fo' 

log  coth  u 

1.550 

0.352II 

47,5 

0.39126 

39,7 

9.96084 

7,8 

0.03916 

.551 

.35258 

47,5 

.39166 

39,7 

.96092 

7,8 

.03908 

.552 

.35306 

47,5 

.39206 

39,7 

.96100 

7,8 

.03900 

•  553 

•35353 

47,5 

.39245 

39,7 

.96108 

7,8 

.03892 

•  554 

•35401 

47,5 

.39285 

39,7 

.96116 

7,8 

.03884 

1.555 

0.35448 

47,5 

0.39325 

39,7 

9.96123 

7,8 

0.03877 

.556 

.35496 

47,5 

.39365 

39,7 

.96131 

7,7 

.03869 

•  557 

•35543 

47,5 

.39404 

39,7 

'  .96139 

7,7 

.03861 

.558 
•  559 

•35591 
.35638 

47,5 
47,5 

.39444 
.39484 

39,7 
39,7 

.96147 
.96154 

7,7 
7,7 

.03853 
.03846 

1.560 

0.35686 

47,4 

0.39524 

39,8 

9.96162 

7,7 

0.03838 

.561 

.35733 

47,4 

.39563 

39,8 

.06170 

7,7 

.03830 

.562 

35780 

47,4 

.39603 

39,8 

.96177 

7,7 

.03823 

.563 

35828 

47,4 

.30643 

39,8 

.96185 

7,6 

.03815 

•  564 

.35875 

47,4 

.39683 

39,8 

.96193 

7,6 

.05807 

1.565 

0.35923 

47,4 

0.39722 

39,8 

9.96200 

7,6 

0.03800 

.566 

•35970 

%J+J^r* 

47,4 

.39762 

39,8 

.96208 

7,6 

.03792 

.567 

.36017 

47,4 

.39802 

39,8 

.96215 

7,6 

.03785 

.568 

.36065 

47,4 

.39842 

39,8 

.96223 

7,6 

.03777 

.569 

.36112 

47,4 

.39882 

39,8 

.06231 

7,5 

.03769 

1-570 

0.36160 

47,4 

0.39921 

39,8 

9-96238 

7,5 

0.03762 

•  571 

.36207 

47,4 

.39961 

39,8 

.96246 

7,5 

•03754 

•  572 

.36254 

47,3 

.40001 

39,8 

•96253 

7,5 

.03747 

•  573 

.36302 

47,3 

.40041 

39,8 

.96261 

7,5 

.03739 

•  574 

.36349 

47,3 

.40081 

39,9 

.96268 

7,5 

.03732 

1-575 

0.36396 

47,3 

0.40121 

39,9 

9.96276 

7,5 

0.03724 

.576 

.36444 

47,3 

.40161 

39,9 

.96283 

7,4 

.03717 

•  577 

.36491 

47,3 

'.40200 

39,9 

.96291 

7,4 

.03709 

.578 

.36538 

47,3 

.40240 

39,9 

.96298 

7,4 

.03702 

•5.79 

.36585 

47,3 

.40280 

39,9 

.96305 

7,4 

.03695 

1.580 

0.36633 

47,3 

0.40320 

39,9 

9.96313 

7,4 

0.03687 

.581 

.36680 

47,3 

.40360 

39,9 

.96320 

7,4 

.03680 

.582 

.36727 

47,3 

.40400 

39,9 

.96327 

7,4 

.03673 

.583 

.36775 

47,3 

.40440 

39,9 

.96335 

7,3 

.03665 

.584 

.36822 

47,2 

.40480 

39,9 

.96342 

7,3 

.03658 

1.585 

0.36869 

47,2 

0.40520 

39,9 

9.96349 

7,3 

0.03651 

.586 

.36916 

47,2 

.40560 

39,9 

.96357 

7,3 

.03643 

.587 

.36964 

47,2 

.40599 

39,9 

.96364 

7,3 

.03636 

.588 

•370II 

47,2 

.40639 

39,9 

.96371 

7,3 

.03629 

.589 

.37058 

47,2 

.40679 

40,0 

.96379 

7,3 

.03621 

1.590 

0.37105 

47,2 

0.40719 

40,0 

9.96386 

7,2 

0.03614 

•  591 

.37152 

47,2 

.40759 

40,0 

.96393 

7,2 

.03607 

•  592 

.37200 

47,2 

.40799 

40,0 

.96400 

7,2 

.03600 

•  593 

.37247 

47,2 

.40839 

40,0 

.96407 

7,2 

.03593 

.594 

.37294 

47,2 

.40879 

40,0 

.96415 

7,2 

.03585 

1-595 

0.37341 

47,2 

0.40919 

40,0 

9.06422 

7,2 

0.03578 

.596 

.37388 

47,2 

.40959 

40,0 

.96429 

7,2 

.03571 

•  597 

•37435 

47,1 

.40099 

40,0 

.96436 

7,i 

•03564 

.598 

.37482 

47,1 

.41039 

40,0 

.96443 

7,1 

.03557 

.599 

•37530 

47,1 

.41079 

40,0 

.96450 

7,i 

.03550 

T.  600 

0.37577 

47,1 

0.41119 

40,o 

9.96457 

7,1 

0.03543 

u 

log  tan  gd  u 

»F0' 

log  sec  gd  u 

»F0' 

log  sin  gd  u 

»  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms  of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

•  IV 

log  tanh  u 

«  Fo' 

log  coth  u 

1.  600 

0-37577 

47,1 

0.41119 

40,0 

9.96457 

7,i 

0.03543 

.601 

.37624 

.4H59 

.96465 

•03535 

.602 

.37671 

.41199 

.96472 

.03528 

.603 

.37718 

.41239 

.96479 

.03521 

.604 

.37765 

.41279 

40,1 

.96486 

7,o 

.03514 

1.605 

0.37812 

47,1 

0.4I3I9 

40,1 

9.96493 

7,0 

0.03507 

.606 

.37859 

.41360 

.96500 

.03500 

.607 

.37906 

.41400 

.96507 

.03493 

.608 

•37953 

.41440 

.96514 

.03486 

.609 

.38001 

.41480 

.96521 

.03479 

1.610 

0.38048 

47,0 

0.41520 

40,1 

9.96528 

7,o 

0.03472 

.611 

.38095 

.41560 

.06535 

6,9 

•03465 

.612 

.38142 

.41600 

.96542 

.03458 

.613 

.38189 

.41640 

.96548 

.03452 

.614 

.38236 

.41680 

.96555 

.03445 

1.615 

0.38283 

47,0 

0.41720 

40,1 

9-96562 

6,9 

0.03438 

.616 

.38330 

.41761 

.96569 

.03431 

.617 

.38377 

.418^1 

.96576 

.03424 

.618 

•38424 

.41841 

•96583 

6,8 

.03417 

.619 

.38471 

.41881 

.96590 

.03410 

1.620 

0.38518 

47,0 

0.41921 

40,2 

9.96597 

6,8 

0.03403 

.621 

.38565 

.41961 

.96603 

.03397 

.622 

.38612 

.42001 

.96610 

.03390 

.623 

.38659 

46,9 

.42042 

.96617 

•03383 

.624 

.38705 

.42082 

.96624 

.03376 

1.625 

0.38752 

46,9 

0.42122 

40,2 

9.96630 

6,7 

0.03370 

.626 

.38799 

.42162 

.96637 

.03363 

.627 

.38846 

.42202 

.96644 

.03356 

.628 

.38893 

.42243 

.96651 

.03349 

.629 

.38940 

.42283 

.96657 

.03343 

1.630 

0.38987 

46,9 

0.42323 

40,2 

9.96664 

6,7 

0.03336 

.631 

•39034 

•42363 

.96671 

.03329 

.632 

.39081 

.42403 

.96677 

.03323 

.633 

.39128 

.42444 

.96684 

6,6 

.03316 

.634 

.39175 

.42484 

.96691 

.03309 

1.635 

0.39221 

46,9 

0.42524 

40,2 

9.96697 

6,6 

0.03303 

.636 

.39268 

.42564 

40,3 

.96704 

.03296 

.637 

.39315 

46,8 

.42605 

.96710 

.03290 

.638 

.39362 

.42645 

.96717 

.03283 

•  639 

.39409 

.42685 

.96724 

.03276 

1.640 

0.39456 

46,8 

0.42725 

40,3 

9.96730 

6,5 

0.03270 

.641 

•39502 

.42766 

.96737 

.03263 

.642 

•39549 

.42806 

.96743 

.03257 

.643 

.39596 

.42846 

.06750 

.03250 

.644 

.39643 

.42887 

•96756 

.03244 

1.645 

0.39690 

46,8 

0.42927 

40,3 

9.96763 

6,5 

0.03237 

.646 

.39736 

.42967 

.96769 

.03231 

.647 

.39783 

.43008 

.96776 

.03224 

.648 

.39830 

.43048 

.96782 

6,4 

.03218 

.649 

.39877 

.43088 

.96788 

.03212 

1.650 

0.39923 

46,8 

0.43129 

40.3 

9.96795 

6,4 

0.03205 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

*»  Fo' 

\OQ  sin  gd  u 

»  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.650 

0.39923 

46,8 

0.43129 

40,3 

9.06795 

6,4 

0.03205 

.651 

.39970 

46,7 

.43169 

.96801 

.03199 

.652 

.40017 

.43209 

40,4 

.96808 

.03192 

.653 

.40064 

.43250 

.96814 

.03186 

.654 

.40110 

.43200 

.96820 

.03180 

1.655 

0.40157 

46,7 

0.43330 

40,4 

9.06827 

6,4 

0.03173 

.656 

.40204 

•43371 

.96833 

6,3 

.03167 

.657 

.40251 

•434II 

.96840 

.03160 

.658 

.40297 

.43451 

.96846 

.03154 

.659 

.40344 

•43492 

.96852 

.03148 

1.660 

0.40391 

46,7 

0.43532 

40,4 

9.96858 

6,3 

0.03142 

.661 

•40437 

•43573 

.96865 

.03135 

.662 

.40484 

.43613 

.96871 

.03129 

.663 

.40531 

.43653 

.96877 

.03123 

.664 

•40577 

.43694 

.96883 

6,2 

.03117 

1.665 

0.40624 

46,7 

0.43734 

40,4 

9.96890 

6,2 

0.03110 

.666 

.40671 

46,6 

•43775 

.96896 

.03104 

.667 

.40717 

.43815 

.96902 

.03098 

.668 

.40764 

.43856 

.96908 

.03092 

.669 

.40811 

.43896 

40,5 

.96915 

.03085 

1.670 

0.40857 

46,6 

0.43937 

40,5 

9.96921 

6,2 

0.03079 

.671 

.40004 

.43977 

.96927 

.03073 

.672 

.40950 

.44017 

.90933 

6,1 

.03067 

.673 

.40097 

.44058 

.96939 

.03061 

.674 

.41044 

.44098 

.96945 

.03055 

1.675 

0.41090 

46,6 

0.44139 

40,5 

9.96951 

6,1 

0.03049 

.676 

.4H37 

.44179 

.96957 

.03043 

•677 

.41183 

.44220 

.96964 

.03036 

.678 

.  .41230 

.44260 

.96970 

.03030 

.679 

.41277 

.44301 

.06976 

.03024 

i.  680 

0.41323 

46,6 

0.44341 

40,5 

9.06982 

6,0 

0.03018 

.681 

.41370 

46,5 

.44382 

.96988 

.03012 

.682 

.41416 

.44422 

.96994 

.03006 

.683 

.41463 

.44463 

.97000 

.03000 

.684 

.41509 

.44503 

.97006 

.02994 

1.685 

0.41556 

46,5 

0.44544 

40,5 

9.97012 

6,0 

0.02988 

.686 

.41602 

.44585 

.97018 

.02982 

.687 

.41649 

.44625 

40,6 

.97024 

.02976" 

.688 

.41695 

.44666 

.97030 

5,9 

.02970 

.689 

.41742 

.44706 

.97036 

.02964 

1.690 

0.41788 

46,5 

0.44747 

40,6 

9.97042 

5,9 

0.02958 

.691 

.41835 

.44787 

.97047 

.02953 

.692 

.41881 

.44828 

.97053 

.02947 

.693 

.41928 

.44869 

•97059 

.02941 

•694 

.41974 

.44909 

.97065 

•02935 

1.695 

0.42021 

46,5 

0.44950 

40,6 

9.97071 

5,9 

0.02929 

.696 

.42067 

.44990 

.97077 

.02923 

.697 

.42114 

46,4 

.45031 

.97083 

5,8 

.02917 

.608 

.42160 

.45072 

.97089 

.02911 

.699 

.42207 

•45II2 

.97094 

.02906 

1.700 

0.42253 

46,4 

0.45153 

40,6 

9.97100 

5,8 

0.02000 

u 

log  tan  gd  u 

«o  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


53 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.700 

0.42253 

46,4 

0.45153 

4O,6 

9-97100 

5,8 

0.02QOO 

.701 

.42299 

.45193 

.97106 

.02894 

.702 

.42346 

.45234 

.97112 

.02888 

.703 

.42392 

.45275 

.97118 

.02882 

.704 

.42439 

.45315 

.97123 

.02877 

1.705 

0.42485 

46,4 

0.45356 

40,7 

9.97129 

5,7 

0.02871 

.706 

.42531 

•45397 

.97135 

.02865 

.707 

.42578 

•45437 

.97141 

.02859 

.708 

.42624 

•45478 

.97146 

.02854 

.709 

.42671 

.45519 

.97152 

.02848 

1.710 

0.42717 

46,4 

0.45559 

40,7 

9.97158 

5,7 

0.02842 

.711 

.42763 

.45600 

.97163 

.02837 

.712 

.42810 

.45641 

.97169 

.02831 

.713 

.42856 

46,3 

.45681 

•97175 

.02825 

.714 

.42002 

•45722 

.97180 

5,6 

.02820 

1.715 

0.42949 

46,3 

0.45763 

40,7 

9.97186 

5,6 

0.02814 

.716 

.42995 

.45803 

.97192 

.02808 

.717 

.43041 

.45844 

.97197 

.02803 

.718 

.43088 

•45885 

•97203 

.02797 

.719 

•43134 

.45926 

.97208 

.02792 

1.720 

0.43180 

46,3 

0.45966 

40,7 

9.97214 

5,6 

0.02786 

.721 

.43227 

.46007 

.97220 

.02780 

.722 

.43273 

.46048 

.97225 

•02775 

.723 

.43319 

.46089 

.97231 

5,5 

.02769 

.724 

.43365 

.46129 

40,8 

.97236 

.02764 

1.725 

0.43412 

46,3 

0.46170 

40,8 

9.97242 

5,5 

0.02758 

.726 

.43458 

.46211 

•97247 

•02753 

.727 

-43504 

.46252 

•97253 

.02747 

.728 

•43551 

.46292 

.97258 

.02742 

.729 

•43597 

.46333 

.97264 

.02736 

1.730 

0.43643 

46,2 

0.46374 

40,8 

9.97269 

5,5 

0.02731 

.731 

.43689 

.46415 

•97275 

.02725 

.732 

.43736 

.46455 

.97280 

5,4 

.02720 

.733 

.43782 

.46496 

.97285 

.02715 

•  734 

.43828 

.46537 

.97291 

.02709 

1.735 

0.43874 

46,2 

0.46578 

40,8 

9.97206 

5,4 

0.02704 

.736 

.43920 

.46619 

•97302 

.02698 

•  737 

.43967 

.46660 

.97307 

.02693 

.738 

.44013 

.46700 

.97313 

.02687 

•  739 

.44059 

.46741 

.97318 

.02682 

1.740 

0.44105 

46,2 

0.46782 

40,8 

9.97323 

5,4 

0.02677 

.741 

.44151 

.46823 

.97329 

5,3 

.02671 

.742 

.44198 

.46864 

•97334 

.02666 

•  743 

.44244 

•46905 

•97339 

.02661 

.744 

.44290 

.46945 

40,9 

.97345 

.02^55 

1.745 

0.44336 

46,2 

0.46986 

40,9 

9-97350 

5,3 

0.02650 

.746 

.44382 

.47027 

•97355 

.02645 

•  747 

.44428 

.47068 

.97360 

.02640 

•  748 

•44475 

46,1 

.47109 

.97366 

.02634 

•  749 

•44521 

.47150 

•97371 

.02629 

1.750 

0.44567 

46,1 

0.47191 

40,9 

9.97376 

5,3 

0.02624 

u 

log  tan  gd  u 

«  Fo' 

log  tec  gd  u 

«  Fo' 

log  tin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITM«ONIA* 


54 


Logarithms  of  Hyperbolic  Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

-Fo' 

log  coth  u 

1.750 

0.44567 

46,1 

0.47I9I 

40,9 

9.97376 

5,3 

0.02624 

.751 

.44613 

.47231 

•  97382 

5,2 

.02618 

.752 

.44659 

.47272 

.97387 

.02613 

•  753 

•44705 

.47313 

•97392 

.02608 

•  754 

.44751 

•47354 

•97397 

.02603 

1.755 

0.44797 

46,1 

0.47395 

40,9 

9-97402 

5,3 

0.02598 

•  756 

.44844 

.47436 

.97408 

.02592 

.757 

.44890 

.47477 

•97413 

.02587 

•  758 

.44936 

.47518 

.97418 

.02582 

•  759 

.44982 

•47559 

.97423 

.02577 

1.760 

0.45028 

46,1 

0.47600 

40,9 

9.97428 

5,1 

0.02572 

.761 

•45074 

.47641 

•97433 

.02567 

.762 

.45120 

.47682 

•97439 

.02561 

.763 

.45166 

•47722 

•97444 

.02556 

.764 

.45212 

.47763 

41,0 

•97449 

.02551 

1.765 

0.45258 

46,1 

0.47804 

41,0 

9-97454 

5,1 

0.02546 

.766 

.45304 

46,0 

.47845 

•97459 

.02541 

.767 

•45350 

.47886 

.97464 

.02536 

.768 

.45396 

.47927 

.97469 

.02531 

.769 

.45442 

.47968 

•97474 

.02526 

1.770 

0.45488 

46,0 

0.48009 

41,0 

9-97479 

5,0 

0.02521 

•  771 

•45534 

.48050 

.97484 

.02516 

•  772 

.45580 

.48091 

.97489 

.02511 

•  773 

.45627 

.48132 

.97494 

.02506 

•  774 

.45673 

.48173 

.97499 

.02501 

1.775 

0.45719 

46,0 

0.48214 

41*0 

9.97504 

5,0 

0.02496 

•  776 

.45765 

.48255 

.97509 

.02491 

•  777 

.45810 

.48296 

.97514 

.02486 

.778 

.45856 

.48337 

.97519 

.02481 

•  779 

•45902 

.48378 

.97524 

.02476 

1.780 

0.45948 

46,0 

0.48419 

41,0 

9.97529 

40 

0.02471 

.781 

•45994 

.48460 

•97534 

.02466 

.782 

.46040 

.48501 

.   -97539 

.02461 

.783 

.46086 

.48542 

.97544 

.02456 

•  784 

.46132 

.48583 

.97549 

.02451 

1.785 

0.46178 

45,9 

0.48624 

4U 

9-97554 

4,9 

0.02446 

.786 

.46224 

.48666 

•97559 

.02441 

.787 

.46270 

.48707 

.97564 

.02436 

.788 

.46316 

.48748 

.97568 

.02432 

.789 

.46362 

.48789 

..97573 

.02427 

1.790 

0.46408 

45,9 

0.48830 

41,1 

9.97578 

48 

0.02422 

.791 

.46454 

.48871 

.97583 

.02417 

.792 

.46500 

.48912 

.97588 

.02412 

.793 

.46546 

.48953 

•97593 

.02407 

•  794 

.46592 

.48994 

•97597 

.02403 

1.795 

0.46637 

45,9 

0.49035 

41,1 

9.97602 

4,8 

0.02398 

.796 

.46683 

.49076 

.97607 

.02393 

•  797 

.46729 

.49H7 

.97612 

.02388 

.798 

.46775 

.49159 

.97617 

.02383 

•  799 

.46821 

.49200 

.97621 

.02379 

1.800 

0.46867 

45,9 

0.49241 

4LI 

9.97626 

4,8 

0.02374 

u 

log  tan  gd  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«FO' 

logcscgdu 

SMITHSONIAN  TABLES 


55 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

«F0' 

log  coth  u 

1.800 

0.46867 

45,9 

0.49241 

41,1 

9.97626 

4,8 

0.02374 

.801 

.46913 

.49282 

.97631 

4,7 

.02369 

.802 

.46959 

.49323 

.97636 

.02364 

.803 

.47004 

.49364 

.97640 

.02360 

.804 

.47050 

45,8 

.49405 

.97645 

•02355 

1.805 

0.47096 

45,8 

0.49446 

41,1 

9.97650 

4,7 

0.02350 

.806 

.47142 

.49488 

.97654 

.02346 

.807 

.47188 

.49529 

41,2 

.97659 

.02341 

.808 

.47234 

•49570 

.97664 

.02336 

.809 

.47279 

.49611 

.97668 

.02332 

1.810 

0.47325 

45,8 

0.49652 

41,2 

9.97673 

4,7 

0.02327 

.811 

•47371 

.49693 

.97678 

4,6 

.02322 

.812 

.47417 

•49734 

.97682 

.02318 

.813 

.47463 

.49776 

.97687 

.02313 

.814 

•47509 

.49817 

.97692 

.02308 

1.815 

0.47554 

45,8 

0.49858 

41,2 

9.97696 

4,6 

0.02304 

.816 

.47600 

.49899 

•97701 

.02299 

.817 

.47646 

.49940 

•97705 

.02295 

.818 

.47692 

.40982 

.97710 

.02200 

.819 

•47737 

.50023 

.97715 

.02285 

1.820 

0.47783 

45,8 

0.50064 

41,2 

9.97719 

4,6 

0.02281 

.821 

.47829 

.50105 

.97724 

.02276 

.822 

.47875 

.50146 

.97728 

4,5 

.02272 

.823 

.47921 

.50188 

•97733 

.02267 

.824 

.47966 

.50229 

•97737 

.02263 

1.825 

0.48012 

45,7 

0.50270 

41,2 

9-97742 

4,5 

0.02258 

.826 

.48058 

.50311 

.97746 

.02254 

.827 

.48104 

.50353 

•97751 

.02249 

.828 

.48149 

.50394 

•97755 

.02245 

.829 

.48195 

•50435 

.97760 

.02240 

1.830 

0.48241 

45,7 

0.50476 

41,3 

9.97764 

4,5 

0.02236 

.831 

.48286 

.50518 

.97769 

.02231 

.832 

.48332 

.  .50559 

•97773 

.02227 

.833 

.48378 

.50600 

.97778 

4,4 

.02222 

.834 

.48424 

.50641 

.97782 

.02218 

1.835 

0.48469 

45,7 

0.50683 

41,3 

9.97787 

4,4 

0.02213 

.836 

.48515 

.50724 

•97791 

.02209 

.837 

.48561 

.50765 

.97796 

.02204 

.838 

.48606 

.50806 

.97800 

.02200 

.839 

.48652 

.50848 

.97804 

.02196 

1.840 

0.48698 

45,7 

0.50889 

41,3 

9.97809 

4,4 

0.02191 

.841 

.48743 

.50930 

.97813 

.02187 

.842 

.48789 

.50972 

.97817 

.02183 

.843 

.48835 

.51013 

.97822 

.02178 

.844 

.48880 

.51054 

.97826 

4,3 

.02174 

1.845 

0.48926 

45,7 

0.51096 

41,3 

9.97831 

4,3 

0.02169 

.846 

.48972 

45,6 

.5H37 

.97835 

.02165 

.847 

.49017 

.5H78 

.97839 

.02161 

.848 

.40063 

.51219 

.97843 

.02157 

.849 

.49109 

.51261 

.97848 

.02152 

1.850 

0.49154 

45,6 

0.51302 

41,3 

9.97852 

4,3 

0.02148 

u 

log  tan  gd  u 

«  Fo' 

log  tec  gd  u 

-Fo' 

log  tin  gd  u 

-  Fo' 

log  esc  gd  u 

iMITHSONIAN 


Logarithms  of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«F0' 

log  coth  u 

1.850 

0.49IS4 

45,6 

0.51302 

41,3 

9.97852 

4,3 

0.02148 

.851 

.49200 

.51343 

.97856 

.02144 

.852 

.49246 

.51385 

.97861 

.02139 

.853 

.49291 

.51426 

.97865 

.02135 

.854 

•49337 

.51468 

4M 

.97869 

.02131 

1.855 

0.49382 

45,6 

0.51509 

4M 

9.97873 

4*3 

0.02127 

.856 

.49428 

.51550 

.97878 

4,2 

.O2I22 

.857 

.49474 

.51592 

.97882 

.02118 

.858 

.49519 

.51633 

.97886 

.02114 

.859 

.49565 

.51674 

.97890 

.02110 

1.860 

0.49610 

45,6 

0.51716 

41,4 

9.97895 

4,2 

0.02105 

.861 

.49656 

.51757 

.97899 

.02101 

.862 

.49702 

.51708 

.97903 

.02097 

.863 

•49747 

.51840 

.97907 

02093 

.864 

•49793 

.51881 

•  979II 

.02089 

1.865 

0.49838 

45,6 

0.51923 

41,4 

9.97916 

4,2 

0.02084 

.866 

.49884 

.51964 

.97920 

.02080 

.867 

.49929 

.52005 

.97924 

.02076 

.868 

•H9975 

.52047 

.97928 

4*1 

.O2072 

.869 

.50020 

45,5 

.52088 

•97932 

.02068 

1.870 

0.50066 

45,5 

0.52130 

41,4 

9.97936 

4,1 

O.O2O64 

.871 

.50112 

.52171 

.97940 

.02060 

.872 

•50157 

.52212 

•97945 

.02055 

.873 

.50203 

.52254 

•97949 

.02051 

.874 

.50248 

.52295 

•97953 

.02047 

1.875 

0.50294 

45,5 

0.52337 

41,4 

9-97957 

4,1 

0.02043 

.876 

.50339 

.52378 

.97961 

.02039 

.877 

.50385 

.52420 

.97965 

.02035 

.878 

.50430 

.52461 

.97969 

.02031 

.879 

.50476 

.52503 

.97973 

.02027 

i.  880 

0.50521 

45,5 

0.52544 

41,5 

9.97977 

4,0 

0.02023 

.881 

.50567 

.52585 

.9798i 

.02019 

.882 

.50612 

.52627 

.97985 

.02015 

.883 

.50658 

.52668 

.97989 

.0201  i 

.884 

.50703 

.52710 

•97993 

.02007 

1.885 

0.50749 

45,5 

0.52751 

41,5 

9-97997 

4,0 

0.02003 

.886 

.50704 

.52793 

.98001 

.01099 

.887 

.50840 

.52834 

.98005 

.01995 

.888 

.50885 

.52876 

.98009 

.01991 

.889 

.50931 

.52917 

.98013 

.01987 

1.890 

0.50976 

45,5 

0.52959 

41,5 

9.98017 

4,0 

0.01983 

.891 

.51021 

.53000 

.98021 

.01979 

.892 

.51067 

45,4 

.53042 

.98025 

.01975 

.893 

.51112 

.53083 

.98029 

3,9 

.01971 

.894 

.51158 

.53125 

•98033 

.01967 

1.895 

0.51203 

45,4 

0.53166 

4i,5 

9-98037 

3,9 

0.01963 

.896 

.51249 

.53208 

.98041 

.01959 

.897 

.51294 

.53249 

.98045 

.01955 

.898 

.51340 

.53291 

.98049 

.01951 

.899 

.51385 

.53332 

.98053 

.01947 

1.900 

0.51430 

45,4 

0.53374 

4i,5 

9.98057 

3,9 

0.01943 

u 

log  tan  gd  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

•W 

log  esc  gd  u 

SMITHSONIAN  TABLES 


57 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

«  Fo' 

log  eoth  u 

1.900 

0.51430 

45,4 

0.53374 

41,5 

9.98057 

3,9 

0.01943 

.901 

.51476 

.53415 

.98060 

.01940 

.902 

.51521 

.53457 

.98064 

.01936 

.903 

.51567 

.53498 

.98068 

.01932 

.  .904 

.51612 

•53540 

.98072 

.01928 

1.905 

0.51657 

45,4 

0.53581 

41,5 

9.98076 

3,8 

0.01924 

.906 

.51703 

.53623 

41,6 

.98080 

.01920 

.907 

.51748 

.53665 

.98084 

.01916 

.908 

.51794 

.53706 

.98087 

.01913 

.909 

.51839 

.53748 

.98091 

.01909 

1.910 

0.51884 

45,4 

0.53789 

41,6 

9.98095 

3,8 

0.01905 

.911 

.51930 

.53831 

.98099 

.OIOOI 

.912 

.51975 

. 

.53872 

.98103 

.01897 

.913 

.52020 

.53914 

.08106 

.01804 

.914 

.52066 

.53956 

.98110 

.01890 

1.915 

0.52III 

45,4 

0.53997 

41,6 

9.98114 

3,8 

0.01886 

.916 

.52157 

•54039 

.98118 

.01882 

.917 

.  52202 

45,3 

.54080 

.98122 

.01878 

.918 

•52247 

.54122 

.98125 

.01875 

.919 

.52293 

.54164 

.98129 

3,7 

.01871 

1.920 

0.52338 

45,3 

0.54205 

41,6 

9.98133 

3,7 

0.01867 

.921 

.52383 

.54247 

.98137 

.01863 

.922 

.52429 

.54288 

.98140 

.01860 

.923 

.52474 

.54330 

.98144 

.01856 

.924 

.52519 

.54372 

.98148 

.01852 

1.925 

0.52565 

45,3 

0.54413 

41,6 

9.98I5I 

3,7 

0.01849 

.926 

.52610 

.54455 

.98155 

.01845 

.927 

•52655 

.54496 

•08159 

.01841 

.928 

.52700 

.54538 

.98162 

.01838 

.929 

.52746 

.5458o 

.98166 

.01834 

1.930 

0.52791 

45,3 

0.54621 

41,6 

9.98170 

3,7 

0.01830 

.931 

.52836 

.54663 

.98173 

.01827 

.932 

.52882 

.54705 

.98177 

3,6 

.01823 

•  933 

.52927 

.54746 

.98181 

.01819 

.934 

.52972 

.54788 

41,7 

.98184 

.01816 

1.935 

0.53018 

45,3 

0.54830 

41,7 

9.98188 

3,6 

o.  01812 

.936 

.53063 

.54871 

.98192 

.01808 

•  937 

.53108 

.54913 

.98195 

.01805 

.938 

.53153 

•54955 

.98199 

.01801 

•939 

•53199 

.54996 

.98202 

.01798 

1.940 

0.53244 

45,3 

0.55038 

41,7 

9.98206 

3,6 

0.01794 

.941 

.53289 

.55080 

.98210 

.01700 

•  942 

•53334 

.55121 

.98213 

.01787 

•  943 

.5338o 

45,2 

.55163 

.98217 

.01783 

•944 

.53425 

.55205 

.98220 

.01780 

1-945 

0.53470 

45,2 

0.55246 

41,7 

9.98224 

3,6 

0.01776 

.946 

.53515 

.55288 

.98227 

3,5 

•QI773 

.947 

.53561 

.55330 

.98231 

.01769 

.948 

.53606 

.55371 

.98235 

.01765 

•  949 

.53651 

.55413 

.98238 

.01762 

1.950 

0.53696 

45,2 

0.55455 

41,7 

9.98242 

3,5 

0.01758 

u 

log  tan  ad  u 

*  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

1.950 

0.53696 

45,2 

0.55455 

41,7 

9.98242 

3,5 

0.01758 

.951 

.53742 

.55496 

.98245 

.01755 

.952 

.53787 

.55538 

.98249 

.01751 

•953 

.53832 

.55580 

.98252 

.01748 

•954 

.53877 

.55622 

.98256 

.01744 

1-955 

0.53922 

45,2 

0.55663 

41,7 

9.98259 

3,5 

0.01741 

.956 

.53968 

•55705 

.98263 

.01737 

•957 

.54013 

•55747 

.98266 

.01734 

.958 

.54058 

.55788 

.98269 

.01731 

•959 

.54103 

.55830 

.08273 

.01727 

1.960 

o'.  54148 

45,2 

0.55872 

41,7 

9.98276 

3,4 

0.01724 

.961 

.54194 

.55914 

.98280 

.01720 

.962 

.54239 

.55955 

.08283 

.01717 

.963 

.  54284 

•55997 

.98287 

.01713 

.964 

.54329 

•56039 

41,8 

.98290 

.01710 

1.965 

0.54374 

45,2 

0.56081 

41,8 

9.98294 

3,4 

0.01706 

.966 

.54419 

.56122 

.98297 

.01703 

.967 

.54465 

.56164 

.98300 

.01700 

.968 

.54510 

.56206 

.98304 

.01696 

.969 

•54555 

.56248 

.98307 

.01693 

1.970 

0.54600 

45,2 

0.56290 

41,8 

9.983II 

3,4 

0.01689 

.971 

.54645 

45,1 

.56331 

.98314 

.01686 

.972 

.54690 

.56373 

.98317 

.01683 

•  973 

.54736 

•56415 

.98321 

.01679 

•  974 

.54781 

.56457 

.98324 

.01676 

1.975 

0.54826 

45,1 

0.56498 

41,8 

9.98327 

3,3 

0.01673 

.976 

.54871 

.56540 

.98331 

.01669 

.977 

.54916 

.'56582 

.98334 

.01666 

.978 

.54961 

.98337 

.01663 

•  979 

.55006 

.56666 

•98341 

.01659 

1.080 

0.55051 

45,1 

0.56707 

41,8 

9.98344 

3,3 

0.01656 

.981 

.55097 

.56749 

.98347 

.01653 

.082 

.55142 

.56791 

.98351 

.01649 

.983 

.55187 

.56833 

.98354 

.01646 

.984 

.55232 

.56875 

.98357 

.01643 

1.985 

0.55277 

45,1 

0.56916 

41,8 

9.98360 

3,3 

0.01640 

.986 

.55322 

.56958 

.08364 

.01636 

.987 

.55367 

•57000 

.98367 

.01633 

.988 

.55412 

.57042 

.98370 

.01630 

.989 

•55457 

.57084 

.98374 

.01626 

1.900 

0.55502 

45,1 

0.57126 

41,8 

9.98377 

3,2 

0.01623 

•991 

•55547 

.57167 

.98380 

.01620 

.992 

.55593 

.57209 

•98383 

.01617 

•  993 

.55638 

.57251 

•98387 

.01613 

.994 

.55683 

•57293 

.98390 

.01610 

1.995 

0.55728 

45,1 

0.57335 

4i,9 

9.98393 

3,2 

0.01607 

.996 

.55773 

•57377 

.98396 

.01604 

.997 

.55818 

•57419 

.08399 

.01601 

.998 

.55863 

.57460 

.08403 

.01597 

.999 

.55908 

•57502 

.98406 

.01594 

2.000 

0.55953 

45,o 

0.57544 

41,9 

9.98409 

3,2 

0.01591 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

»  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


59 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

»F</ 

log  tanh  u 

«  Fo' 

log  coth  u 

2.0OO 

0.55953 

45,o 

0.57544 

41,9 

9.98409 

3,2 

0.01591 

.OOI 

.55998 

.57586 

.98412 

.01588 

.002 

.57628 

.98415 

.01585 

.003 

.56088 

.57670 

.98418 

.01582 

.004 

.56133 

•57712 

.98422 

.01578 

2.OO5 

0.56178 

45,o 

0.57754 

41,9 

9.98425 

3,2 

0.01575 

.006 

.56223 

•  57795 

.98428 

3.1 

.01572 

.007 

.56268 

.57837 

.98431 

.01569 

.008 

.56313 

.57879 

.98434 

.01566 

.009 

.56358 

•57921 

.98437 

.01563 

2.0IO 

0.56403 

45,o 

0.57963 

41,9 

9.98440 

3,1 

0.01560 

.Oil 

.56448 

.58005 

.98444 

.01556 

.012 

.56493 

.58047 

.98447 

.01553 

.013 

.56538 

.58089 

-98450 

.01550 

.OI4 

.56583 

.58131 

.98453 

.01547 

2.OIS 

0.56628 

45,0 

0.58172 

41,9 

9.98456 

3,1 

0.01544 

.Ol6 

.56673 

.58214 

.98459 

.01541 

.017 

.56718 

.58256 

.98462 

.01538 

.018 

•56723 

.58298 

.98465 

.01535 

.OIQ 

.56808 

.58340 

.98468 

.01532 

2.020 

0.56853 

45,0 

0.58382 

41,9 

9.98471 

3,1 

0.01529 

.021 

.56898 

.58424 

.98474 

.01526 

.022 

.58466 

•98477 

3,0 

.01523 

.023 

.56988 

.58508 

.98480 

.01520 

.024 

.57033 

.58550 

.98484 

.01516 

2.O25 

0.57078 

45,0 

0.58592 

41,9 

9.98487 

3,0 

0.01513 

.026 

.57123 

.58634 

.98490 

.01510 

.027 

.57168 

.58676 

.98493 

.01507 

.028 

.57213 

.58718 

42,0 

.98496 

.01504 

.029 

.57258 

.58760 

•98499 

.01501 

2.030 
.031 

0.57303 
.57348 

45,0 

0.58802 

.58843 

42,0 

9.98502 
.98505 

3,o 

0.01498 
.01495 

.032 

.57393 

44,9 

.58885 

.98508 

.01492 

•033 

.57438 

.58927 

.98511 

.01489 

.034 

.57483 

.58969 

.98514 

.01486 

2.035 

0.57528 

44,9 

0.59011 

42,0 

9.98517 

3,0 

0.01483 

.036 

•57573 

.59053 

.98519 

.01481 

•  037 

.57618 

.59095 

.98522 

.01478 

.038 

.57663 

.59137 

.98525 

2,9 

.01475 

.039 

.57708 

.59179 

.98528 

.01472 

2.040 

0.57753 

44,9 

0.59221 

42,0 

9.98531 

2,9 

0.01469 

.041 

.57797 

.59263 

.98534 

.01466 

.042 

.57842 

.59305 

.98537 

.01463 

.043 

.57887 

.59347 

.98540 

.01460 

•044 

•57932 

.59389 

.98543 

.01457 

2.045 

0.57977 

44,9 

0.59431 

42,0 

9.98546 

2,9 

0.01454 

.046 

.58022 

.59473 

.98549 

.01451 

.047 

.58067 

.59515 

.98552 

.01448 

.048 

.58112 

.59557 

.98555 

.01445 

.049 

.58157 

•59599 

.98558 

.01442 

2.050 

0.58202 

44,9 

0.50641 

42,0 

9.98560 

2,9 

0.01440 

u     log  tin  gd  u 

-Fo' 

log  sec  gd  u 

»tv 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


60 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  eoth  u 

2.050 

0.58202 

44,9 

0.59641 

42,0 

9-98560 

2,9 

0.01440 

.051 

.58246 

.59683 

.98563 

.01437 

.052 

.58291 

•59725 

.98566 

.01434 

.053 

.58336 

.59767 

.98569 

.01431 

.054 

.58381 

.59809 

.98572 

.01428 

2.055 

0.58426 

44,9 

0.59851 

42,0 

9.98575 

2,9 

0.01425 

.056 

.58471 

.59893 

.98578 

2,8 

.01422 

•  057 

.58516 

.59935 

.98580 

.01420 

.058 

.58561 

•59977 

.98583 

.01417 

.059 

.58606 

.60019 

.98586 

.01414 

2.060 

0.58650 

44,9 

0.60061 

42,0 

9.98589 

2,8 

0.01411 

.061 

.58695 

.60104 

.98592 

.01408 

.062 

.58740 

.60146 

.08595 

.01405 

.063 

.58785 

.60188 

.98597 

.01403 

.064 

.58830 

.60230 

42,1 

.98600 

.01400 

2.065 

0.58875 

44,8 

0.60272 

42,1 

9.98603 

2,8 

0.01397 

.066 

.58920 

.60314 

.98606 

.01394 

.067 

.58964 

.60356 

.98609 

.01391 

.068 

.59009 

.60398 

.98611 

.01389 

.069 

•59054 

.60440 

.98614 

.01386 

2.070 

0.59009 

44,8 

0.60482 

42,1 

9.98617 

2,8 

0.01383 

.071 

.59144 

.60524 

.98620 

.01380 

.072 

.59189 

.60566 

.98622 

.01378 

.073 

.59233 

.60608 

.98625 

.01375 

.074 

.59278 

.60650 

.98628 

2,7 

.01372 

2.075 

0.59323 

44,8 

0.60692 

42,1 

9-98631 

2,7 

0.01369 

.076 

.59368 

.60734 

.98633 

.01367 

•  077 

.59413 

.60777 

.98636 

.01364 

.078 

•59457 

.60819 

.98639 

.01361 

.079 

.59502 

.60861 

.98642 

.01358 

2.080 

0.59547 

44,8 

0.60903 

42,1 

9.98644 

2,7 

0.01356 

.081 

•59592 

.60945 

.98647 

.01353 

.082 

.59637 

.60987 

.98650 

.01350 

.083 

.59681 

.61029 

.98652 

.01348 

.084 

.59726 

.61071 

.98655 

.01345 

2.085 

0.59771 

44,8 

0.61113 

42,1 

9-98658 

2,7 

0.01342 

.086 

.59816 

.61155 

.98660 

.01340 

.087 

.59861 

.61198 

.98663 

.01337 

.088 

.59905 

.61240 

.98666 

.01334 

.089 

.59950 

.61282 

.98668 

.01332 

2.000 

0.59995 

44,8 

0.61324 

42,1 

•  9.98671 

2,7 

0.01329 

.091 

.60040 

.61366 

.98674 

.01326 

.092 

.60085 

.61408 

.98676 

2,6 

.01324 

.093 

.60129 

.61450 

.98679 

.01321 

.094 

.60174 

.61492 

.98682 

.01318 

2.095 

0.60219 

44,8 

0.61535 

42,1 

9.98684 

2,6 

0.01316 

.096 

.60264 

.61577 

.98687 

.01313 

.097 

.60308 

.61619 

.98690 

.01310 

.098 

.60353 

.61661 

.98692 

.01308 

•099 

.60398 

.61703 

.98695 

.01305 

2.  TOO 

0.60443 

44,8 

o.6i745 

42,1 

9.98697 

2,6 

0.01303 

U 

log  tan  gd  u 

*>  Fo' 

log  sec  gd  u 

w  Fo' 

log  sin  gd  u 

«FO' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


61 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.IOO 

0.60443 

44,8 

0.61745 

42,1 

9.98697 

2,6 

0.01303 

.101 

.60487 

44,7 

.61787 

.98700 

.01300 

.102 

.60532 

.61830 

42,2 

.98703 

.01297 

.103 

.00577 

.61872 

.08705 

.01295 

.104 

.60622 

.61914 

.98708 

.01292 

2.105 

0.6o666 

447 

0.61956 

42,2 

9.98710 

2,6 

0.01290 

.106 

.60711 

.61998 

.98713 

.01287 

.107 

.60756 

.62040 

.98716 

.01284 

.108 

.60801 

.62083 

.98718 

.01282 

.109 

.60845 

.62125 

.98721 

.01279 

2.  no 

0.6o8oo 

44,7 

0.62167 

42,2 

9.98723 

2,6 

0.01277 

.in 

.60935 

.62209 

.98726 

2,5 

.01274 

.112 

.60979 

.62251 

.98728 

.01272 

.113 

.61024 

.62293 

.98731 

.01269 

.114 

.61069 

.62336 

•98733 

.01267 

2.II5 

0.61114 

447 

0.62378 

42,2 

9.98736 

2,5 

0.01264 

.116 

.61158 

.62420 

.98738 

.01262 

.117 

.61203 

.62462 

.98741 

.01259 

.118 

.61248 

.62504 

.98743 

.01257 

.Up 

.61292 

.62546 

.98746 

.01254 

2.I2O 

0.61337 

447 

0.62589 

42,2 

9.98748 

2,5 

0.01252 

.121 

.61382 

.62631 

.98751 

.01249 

.122 

.61427 

.62673 

.98753 

.01247 

.123 

.61471 

.62715 

.98756 

.01244 

.124 

.61516 

.62757 

.98758 

.01242 

2.125 

0.61561 

447 

0.62800 

42,2 

9.98761 

2,5 

0.01239 

.126 

.61605 

.62842 

.98763 

.01237 

.127 

.61650 

.62884 

.98766 

.01234 

.128 

.61695 

.62926 

.98768 

.01232 

.I2Q 

.61739 

.62969 

.98771 

.01229 

2.130 

0.61784 

447 

0.63011 

42,2 

9.98773 

2,5 

0.01227 

.131 

.61829 

.63053 

.98776 

2,4 

.01224 

.132 

.61873 

.63095 

.98778 

.01222 

•133 

.61918 

.63137 

.98781 

.01219 

.134 

.61963 

.63180 

.98783 

.01217 

2.I3S 

0.62007 

447 

0.63222 

42,2 

9.98785 

2,4 

0.01215 

.136 

.62052 

.63264 

.98788 

.01212 

.137 

.62097 

.63306 

.98790 

.OI2IO 

.138 

.62141 

.63349 

.98793 

.01207 

.139 

.62186 

.63391 

.98795 

.01205 

2.140 

0.62231 

446 

•0.63433 

42,2 

9.98798 

2,4 

O.OI2O2 

.141 

.62275 

.63475 

.98800 

.OI2OO 

.142 

.62320 

.63518 

.98802 

.OIIOjS 

•  143 

.62365 

.63560 

42,3 

.98805 

.01195 

.144 

.62409 

.63602 

.98807 

.01193 

2.145 

0.62454 

44,6 

0.63644 

4?,3 

9.98810 

2,4 

0.01190 

.146 

.62498 

.63687 

.08812 

.01188 

.147 

.62543 

.63729 

.98814 

.01186 

.148 

.62588 

.63771 

.98817 

.01183 

.149 

.62632 

.63813 

.98819 

.01181 

2.150 

0.62677 

446 

0.63856 

42,3 

9.98821 

24 

0.01179 

u 

loo  tan  gd  u 

-FO' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


62 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

<-  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.150 

0.62677 

44,6 

0.63856 

42,3 

9.98821 

2,4 

O.OII79 

.151 

.62722 

.63898 

.98824 

.01176 

.152 

.62766 

.63940 

.98826 

2,3 

.01174 

.153 

.62811 

.63982 

.98828 

.01172 

.154 

.62855 

.64025 

.98831 

.01169 

2.155 

0.62900 

44,6 

0.64067 

42,3 

9.98833 

2,3 

0.01167 

.156 

.62945 

.64109 

.98835 

.01165 

.157 

.62989 

.64152 

.98838 

.01162 

.158 

•63034 

.64194 

.98840 

.01100 

.159 

.63079 

.64236 

.98842 

.01158 

2.160 

0.63123 

44,6 

0.64278 

42,3 

9.98845 

2,3 

O.OII55 

.161 

.63168 

.64321 

.98847 

.01153 

.162 

.63212 

.64363 

.98849 

.01151 

.163 

.63257 

.64405 

.98852 

.01148 

.164 

.63302 

.64448 

.98854 

.01146 

2.165 

0.63346 

44,6 

0.64490 

42,3 

9.98856 

2,3 

0.01144 

.166 

.63391 

.64532 

.98859 

.01141 

.167 

.63435 

.64574 

.98861 

.01139 

.168 

.63480 

.64617 

.98863 

.01137 

.169 

.63524 

.64659 

.98865 

.01135 

2.170 

0.63569 

44,6 

0.64701 

42,3 

9.98868 

2,3 

0.01132 

.171 

.64744 

.98870 

.01130 

.172 

.63658 

.64786 

.98872 

.01128 

.173 

.63703 

.64828 

.98874 

.01126 

.174 

.63747 

.64871 

.98877 

2,2 

.01123 

2.175 

0.63792 

44,6 

0.64913 

42,3 

9.98879 

2,2 

O.OII2I 

.176 

.63836 

.64955 

.98881 

.OIII9 

.177 

.63881 

.64998 

.98883 

.OIII7 

.178 

.63926 

.65040 

.98886 

.01114 

.179 

.63970 

.65082 

.98888 

.01112 

2.180 

0.64015 

44,6 

0.65125 

42,3 

9.98890 

2,2 

O.OIIIO 

.181 

.64059 

.65167 

.98892 

.OIIOS 

.182 

.64104 

44,5 

.65209 

.98894 

.01106 

.183 

.64148 

.65252 

.98897 

.OII03 

.184 

.64193 

.65294 

.98899 

.01101 

2.185 

0.64237 

44,5 

0.65336 

42,3 

9.98901 

2,2 

0.01099 

.186 

.64282 

.65379 

.98903 

.01097 

.187 

.64326 

.65421 

42,4 

.98905 

.01095 

.188 

.64371 

.65463 

.98908 

.01092 

.189 

.64416 

.65506 

.98910 

.01090 

2.190 

0.64460 

44,5 

0.65548 

42,4 

9.98912 

2,2 

0.01088 

.191 

.64505 

.65590 

.98914 

.01086 

.192 

.64549 

.65633 

.98916 

.01084 

.193 

.64594 

.65675 

.98919 

.01081 

.194 

.64638 

.65718 

.98921 

.01079 

2.195 

0.64683 

44,5 

0.65760 

42,4 

9.98923 

2,2 

0.01077 

.196 

.64727 

.65802 

.98925 

.01075 

.197 

.64772 

•65845 

.98927 

2,1 

.01073 

.198 

.64816 

.65887 

.98929 

.01071 

.199 

.64861 

.65929 

.98931 

.01069 

2.  2OO 

0.64005 

44,5 

0.65972 

42,4 

9.98934 

2,1 

0.01066 

U 

log  tan  gd  u 

»  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

«FV 

log  tanh  u 

«FO' 

log  coth  u 

2.2OO 

0.64905 

44,5 

0.65972 

42,4 

9.98934 

2,1 

0.01066 

.2OI 

.64950 

.66014 

.98936 

.01064 

.202 

.64994 

.66056 

.98938 

.01062 

.203 

.65039 

.66099 

.98940 

.01060 

.204 

.65083 

.66141 

.98942 

.01058 

2.2O5 

0.65128 

44.5 

0.66184 

42,4 

9.98944 

2,1 

O.OIO56 

.206 

.65172 

.66226 

.98946 

.01054 

.207 

.65217 

.66268 

.98948 

.01052 

.208 

.65261 

.66311 

.98950 

.01050 

.209 

.65306 

.66353 

.98953 

.01047 

2.210 

0.65350 

445 

0.66396 

42,4 

9.98955 

2,1 

0.01045 

.211 

.65395 

.66438 

.98957 

.01043 

.212 

.65439 

.66480 

.98959 

.01041 

.213 

.65484 

.66523 

.98961 

.01039 

.214 

.65528 

.66565 

.98963 

.01037 

2.215 

0.65573 

44,5 

0.666o8 

42,4 

9.98965 

2,1 

0.01035 

.216 

.65617 

.66650 

.98967 

.01033 

.217 

.65662 

.66692 

.98969 

.01031 

.218 

.65706 

.66735 

.98971 

.01029 

.219 

.65751 

.66777 

.98973 

.01027 

2.22O 

0.65795 

44,5 

0.66820 

42,4 

9.98975 

2,0 

0.01025 

.221 

.65840 

.66862 

.98977 

.01023 

.222 

.65884 

.66905 

.98979 

.0102  I 

.223 

.65928 

.66947 

.98982 

.01018 

.224 

.65973 

.66989 

.98084 

.01016 

2.225 

O.66OI7 

44,5 

0.67032 

42,4 

9.98986 

2,0 

0.01014 

.225 

.66062 

.67074 

.98988 

.OIOI2 

.227 

.66106 

.67117 

.98990 

.OIOIO 

.223 

.66151 

44A 

.67159 

.98992 

.01008 

.229 

.66195 

.67202 

.98994 

.01006 

2.230 

0.66240 

444 

0.67244 

42,4 

9.98996 

2,0 

O.OIO04 

.231 

.66284 

.67286 

.98998 

.01002 

.232 

.66328 

.67329 

.99000 

.01000 

.233 

.66373 

.67371 

.09002 

.00998 

•234 

.66417 

.674U 

.99004 

.00996 

2.235 

0.66462 

444 

0.67456 

42,4 

9.99006 

2,0 

0.00994 

.236 

.66506 

.67499 

.99008 

.00992 

•237 

.66551 

.67541 

42,5 

.99010 

.00990 

.238 

.66595 

.67583 

.99012 

.00988 

.239 

.66640 

.67626 

.99014 

.00986 

2.240 

0.66684 

444 

0.67668 

42,5 

9.99016 

2,0 

0.00984 

.241 

.66728 

.67711 

.99018 

.00982 

.242 

.66773 

.67753 

.90019 

.00981 

.243 

.66817 

.67796 

.99021 

.00979 

.244 

.66862 

.67838 

.99023 

.00977 

2.245 

0.66906 

44,4 

0.67881 

42,5 

9.90025 

1,9 

0.00975 

.246 

.66950 

.67923 

.99027 

.00973 

.247 

.66995 

.67966 

.99029 

.00971 

.248 

.67039 

.68008 

.99031 

.00969 

.249 

.67084. 

.68051 

.99033 

.00967 

2.250 

0.67128 

444 

0.68093 

42,5 

9.00035 

1,9 

0.00965 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


64 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  eoth  u 

2.250 

0.67128 

MA 

0.68093 

42,5 

9.99035 

1,9 

0.00965 

.251 

.67173 

.68136 

.09037 

.00963 

.252 

.67217 

.68178 

.99039 

.00961 

.253 

.67261 

.68220 

.99041 

.00959 

.254 

.67306 

.68263 

.99043 

.00957 

2.255 

0.67350 

44*4 

0.68305 

42,5 

9.99045 

1,9 

0.00955 

.256 

.67394 

.68348 

.99047 

.00953 

.257 

.67439 

.68390 

.09048 

.00952 

.258 

.67483 

.68433 

.99050 

.00950 

.259 

.67528 

.68475 

.99052 

.00948 

2.260 

0.67572 

44,4 

0.68518 

42,5 

9.99054 

1,9 

0.00946 

.261 

.67616 

.68560 

.99056 

.00944 

.262 

.67661 

.68603 

.09058 

.00942 

.263 

.67705 

.68645 

;99o6o 

.00940 

.264 

.67750 

.68688 

.09062 

.00938 

2.265 

0.67794 

44,4 

0.68730 

42,5 

9.09064 

1,9 

0.00936 

.266 

.67838 

.68773 

.99065 

.00935 

.267 

.67883 

.68815 

.99067 

.00933 

.268 

.67927 

.68858 

.99069 

.00931 

.269 

.67971 

.68900 

.99071 

.00929 

2.270 

0.68016 

MA 

0.68943 

42,5 

9.99073 

1,9 

0.00927 

.271 
.272 

.68060 
.68105 

.68985 
.69028 

.99075 
.99077 

1,8 

.00925 
.00923 

•  273 

.68149 

.69070 

.09078 

.00922 

.274 

.68193 

.69113 

.99080 

.00920 

2.275 

0.68238 

MA 

0.69156 

42,5 

9.99082 

1,8 

0.00918 

.276 

.68282 

.69198 

.99084 

.00916 

.277 

.68326 

.69241 

.99086 

.00914 

.278 

.68371 

.69283 

.99088 

.00912 

.279 

.68415 

44,3 

.69326 

.99089 

.00911 

2.280 

0.68459 

44,3 

0.69368 

42,5 

9.99091 

1,8 

0.00909 

.281 

.68504 

.69411 

.99093 

.00907 

.282 

.68548 

.69453 

.99095 

.00905 

.283 

.68592 

.69496 

.99097 

.00903 

.284 

.68637 

.69538 

.99098 

.00902 

2.285 

0.68681 

44,3 

.0.69581 

42,5 

9.99100 

1,8 

0.00900 

.286 

.68725 

.69623 

.99102 

.00898 

.287 

.68770 

.69666 

.99104 

.00896 

.288 

.68814 

.69708 

.09106 

.00894 

.289 

.68858 

.69751 

.99107 

.00893 

2.  20O 

0.68903 

44,3 

0.69794 

42,5 

9.09109 

1,8 

0.00891 

.291 

.68947 

.69836 

.99111 

.00889 

.292 

.68991 

.69879 

42,6 

.99H3 

.00887 

•293 

.60036 

.69921 

.99H5 

.00885 

.294 

.69080 

.69964 

.99116 

.00884 

2.295 

0.69124 

44,3 

0.70006 

42,6 

9.99118 

1,8 

0.00882 

.296 

.69169 

.70049 

.99120 

.00880 

.297 

.69213 

.70091 

.99122 

.00878 

.298 

.69257 

.70134 

.99123 

.00877 

.299 

.69302 

.70177 

.99125 

i,7 

.00875 

2.3OO 

0.69346 

44,3 

0.70219 

42,6 

9.99127 

i,7 

0.00873 

U 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.300 

0.69346 

44,3 

0.70219 

42,6 

9.99127 

1,7 

0.00873 

.301 

.69390 

.70262 

.99129 

.00871 

.302 

.69435 

.70304 

•99130 

.00870 

.303 

.69479 

.70347 

.99132 

.00868 

.304 

.69523 

•70389 

.99134 

.00866 

2.305 

0.69568 

44,3 

0.70432 

42,6 

9.99136 

1,7 

0.00864 

.306 

.69612 

•70475 

.99137 

.00863 

.307 

.69656 

.70517 

•99139 

.00861 

.308 

.69700 

.70560 

.99141 

.00859 

.309 

.69745 

.70602 

.99142 

.00858 

2.310 

0.69789 

443 

0.70645 

42,6 

9.99144 

1,7 

0.00856 

.311 

.69833 

.70687 

.99146 

.00854 

.312 

.69878 

.70730 

.99148 

.00852 

.313 

.69922 

.70773 

.99149 

.00851 

.314 

.69966 

.70815 

.99151 

.00849 

2.315 

O.7OOIO 

443 

0.70858 

42,6 

9.99153 

1,7 

0.00847 

.316 

.70055 

.70900 

.99154 

.00846 

.317 

.70099 

.70943 

.99156 

.00844 

.318 

.70143 

.70986 

.99158 

.00842 

.319 

.70188 

.71028 

•99159 

.00841 

2.320 

0.70232 

44,3 

0.71071 

42,6 

9.99l6l 

1,7 

0.00839 

.321 

.70276 

.7IH3 

.99163 

.00837 

.322 

.70320 

.71156 

.99164 

.00836 

.323 

.70365 

.71199 

.99166 

.00834 

.324 

.70409 

.71241 

.99168 

.00832 

2.325 

0.70453 

44,3 

0.71284 

42,6 

9.99169 

1,7 

0.00831 

.326 

•70497 

.71326 

.99171 

.00829 

.327 

.70542 

.71369 

.99173 

.00827 

.328 

.70586 

.71412 

.99174 

.00826 

.329 

.70630 

-.71454 

.99176 

1,6 

.00824 

2.330 

0.70675 

443 

0.7U97 

42,6 

9.99178 

1,6 

0.00822 

.331 

.70719 

.71539 

.99179 

.00821 

.332 

.70763 

.71582 

.99181 

.00819 

.333 

.70807 

.71625 

.99183 

.00817 

•  334 

.70852 

.71667 

•99184 

.00816 

2.335 

0.70896 

443 

0.7I7IO 

42,6 

9.99186 

1,6 

0.00814 

.336 

.70940 

442 

.71753 

.99188 

.008'I2 

•  337 

.70984 

.71795 

.99189 

.00811 

.338 

.71029 

.71838 

.99191 

.00809 

•  339 

.71073 

.71880 

.99192 

.00808 

2.340 

0.7IH7 

44,2 

0.71923 

42,6 

9.99194 

1,6 

0.00806 

.341 

.71161 

.71966 

.99196 

.00804 

•  342 

.71206 

.72008 

.99197 

.00803 

•  343 

.71250 

.72051 

.99199 

.00801 

•344 

.71294 

.72094 

.99200 

.00800 

2-345 

O.7I338 

44,2 

0.72136 

42,6 

9.99202 

1,6 

0.00798 

•  346 

.71382 

.72179 

.99204 

.00706 

•  347 

.71427 

.72221 

.09205 

.00795 

.348 

.71471 

.72264 

.99207 

\ 

.00793 

•  349 

.71515 

.72307 

.99208 

.00792 

2.350 

0.71559 

44,2 

0.72349 

42,6 

9.99210 

1,6 

0.00790 

u 

log  tin  ad  u 

«  Fo' 

log  fee  gd  u 

«  Fo' 

log  sin  gd  u 

«F</ 

log  esc  gd  u 

SMITHSONIAN  TABLCS 


66 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

u,  Fo' 

log  cosh  u 

»F0' 

log  tanh  u 

»Fo' 

log  coth  u 

2.350 

0.71559 

44,2 

0.72349 

42,6 

9.99210 

1,6 

0.00790 

.351 

.71604 

.72392 

.99212 

.00788 

.352 

.71648 

.72435 

.99213 

.00787 

.353 
•  354 

.71692 
.71736 

.72477 
.72520 

42,7 

.99215 
.99216 

.00785 
.00784 

2.355 
.356 

0.71781 
.71825 

44,2 

0.72563 
.72605 

42,7 

9.99218 
.99219 

1,6 

0.00782 
.00781 

•  357 

.71869 

.72648 

.99221 

.00779 

•  358 

.71913 

.72691 

.99223 

.00777 

•  359 

.71957 

.72733 

.99224 

.00776 

2.360 

O.720O2 

44,2 

0.72776 

42,7 

9.99226 

1,5 

0.00774 

.361 

.72046 

.72819 

.99227 

.00773 

.362 

.72000 

.72861 

.99229 

.00771 

.363 

.72134 

.72904 

.99230 

.00770 

ST\ 

.364 

.72178 

.72947 

.99232 

.00768 

2.365 

0.72223 

44,2 

0.72989 

42,7 

9.99233 

1,5 

O.O0767 

.366 

.72267 

.73032 

.99235 

.00765 

.367 

.723H 

.73075 

.99236 

.00764 

.368 

.72355 

.73H7 

.99238 

.OO762 

.369 

.72399 

.73160 

.99239 

.00761 

2.370 

0.72444 

44,2 

0.73203 

42,7 

9.99241 

1,5 

0.00759 

•  371 

•  372 

.72488 
.72532 

.73245 
.73288 

.99242 
.99244 

.00758 
.00756 

•  373 

.72576 

•73331 

.99245 

.00755 

•  374 

.72620 

•73373 

.99247 

.00753 

2.375 

0.72665 

44,2 

0.73416 

42,7 

9.99249 

1,5 

0.00751 

.376 

.72709 

•73459 

.99250 

.00750 

•  377 

.72753 

.73501 

.99252 

.00748 

•  378 

.72797 

.73544 

.99253 

.00747 

.379 

.72841 

.73587 

.99254 

.00746 

2.380 

0.72885 

44,2 

0.73630 

42,7 

9.99256 

i,5 

0.00744 

.381 

.72930 

.73672 

.99257 

.00743 

.382 

.72974 

.73715 

.99259 

.00741 

.383 

.73018 

.73758 

.99260 

.00740 

.384 

.73062 

.73800 

.99262 

.00738 

2.385 

0.73106 

44,2 

0.73843 

42,7 

9.99263 

1,5 

0.00737 

.386 

.73151 

.73886 

.99265 

.00735 

.387 

.73195 

.73928 

.99266 

.00734 

.388 

.73239 

.73971 

.99268 

.00732 

.389 

.73283 

.74014 

.99269 

.00731 

2.390 

0.73327 

44,2 

0.74056 

42,7 

9.99271 

i,5 

0.00729 

.391 

•73371 

.74099 

.99272 

.00728 

•  392 

.73416 

.74142 

.99274 

.00726 

.393 

.73460 

.74185 

.99275 

1,4 

.00725 

•  394 

.73504 

.74227 

.99277 

.00723 

2.395 

0.73548 

44,2 

0.74270 

42,7 

9.99278 

1,4 

0.00722 

.396 

•73592 

.74313 

.99279 

.00721 

•  397 

.73636 

.74355 

.99281 

.00719 

.398 

.73680 

.74398 

.99282 

.00718 

•  399 

.73725 

.74441 

.99284 

.00716 

2.400 

0.73769 

44,2 

0.74484 

42,7 

9.99285 

1,4 

0.00715 

u 

log  tan  grf  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


67 


Logarithms   of   Hyperbolic   Functions. 


u 

loo  sinh  u 

»jy 

log  cosh  u 

-FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.400 

0.73709 

44,2 

0.74484 

42,7 

9.99285 

1,4 

0.00715 

.401 

.73813 

44,1 

.74526 

.99287 

.00713 

.402 

.73857 

.74569 

.99288 

.00712 

.403 

•73901 

.74612 

.99289 

.00711 

.404 

•73945 

.74655 

.99291 

.00709 

2.405 

0.73990 

44,1 

0.74697 

42,7 

9.99292 

1,4 

0.00708 

.406 

.74934 

•74740 

.99294 

.00706 

.407 

.74078 

.74783 

.99295 

.00705 

.408 

.74122 

.74825 

.99297 

.00703 

.409 

.74166 

.74868 

.99298 

.00702 

2.410 

0.74210 

441 

0.749H 

42,7 

9.99299 

1,4 

0.00701 

.411 

.74254 

.74954 

•99301 

.00699 

.412 

•74298 

.74996 

.99302 

.00698 

.413 

.74343 

.75039 

.09304 

.00696 

.414 

.74387 

.75082 

.99305 

.00695 

2.415 

0.74431 

44,1 

0.75125 

42,7 

9.99306 

1,4 

0.00694 

.416 

•74475 

.75167 

.99308 

.00692 

.417 

.74519 

.75210 

.99309 

.00691 

.418 

.74563 

.75253 

.99310 

.00690 

.419 

.74607 

.75296 

.99312 

.00688 

2.420 

0.74652 

44,1 

0.75338 

42,7 

9.99313 

1,4 

0.00687 

.421 

.74696 

.75381 

.99315 

.00685 

.422 

.74740 

.75424 

42,8 

.99316 

.00684 

.423 

.74784 

.75467 

.99317 

.00683 

.424 

.74828 

.75509 

.99319 

.00681 

2.425 

0.74872 

44,1 

0.75552 

42,8 

9.99320 

1,4 

0.0068o 

.426 

.74916 

.75595 

•99321 

.00679 

.427 

.74960 

.75638 

.99323 

.00677 

.428 

.75004 

.75680 

•99324 

.00676 

.429 

.75049 

.75723 

.99325 

1,3 

.00675 

2.430 

0.75093 

44,1 

0.75766 

42,8 

9.99327 

1,3 

0.00673 

.431 

.75137 

.75809 

.99328 

.00672 

.432 

.75i8i 

.75851 

.99329 

.00671 

•  433 

.75225 

.75894 

•99331 

.00669 

•434 

.75269 

.75937 

.99332 

.00668 

2.435 

0.75313 

44,1 

0.75980 

42,8 

9-99333 

1,3 

0.00667 

.436 

.75357 

.76022 

.99335 

.00665 

•  437 

.75401 

.76065 

.99336 

.00664 

-438 

.75445 

.76108 

•99337 

.00663 

•  439 

•75490 

.76151 

•99339 

.00661 

2.440 

0.75534 

44,1 

0.76104 

42,8 

9.99340 

1,3 

0.00660 

.441 

.75578 

.76236 

•99341 

.00659 

.442 

.75622 

.76279 

•99343 

.00657 

•  443 

.75666 

.76322 

•99344 

.00656 

.444 

•75710 

.76365 

.99345 

.00655 

2.445 

0.75754 

44,1 

0.76407 

42,8 

9-99347 

1,3 

0.00653 

.446 

.75798 

.76450 

.99348 

.00652 

•447 

.75842 

.76493 

•99349 

.00651 

.448 

.75886 

.76536 

.99351 

.00649 

.449 

•75930 

.76579 

.99352 

.00648 

2.450 

0.75975 

44,1 

0.76621 

42,8 

9-99353 

1,3 

o.oo6Li7 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

»4V 

log  esc  gd  u 

SMITHSJONIMN  TABLES 


68 


Logarithms   of  Hyperbolic   Functions. 


u 

loo  sinh  u 

«  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

«F0' 

log  coth  u 

2.450 

0.75975 

44,1 

0.76621 

42,8 

9-99353 

1,3 

0.00647 

.451 

.76019 

.76664 

•99354 

.00646 

.452 

.76063 

.76707 

.99356 

.00644 

•453 

.76107 

.76750 

•99357 

.00643 

•454 

.76151 

.76793 

•99358 

.00642 

2.455 

0.76195 

44,1 

0.76835 

42,8 

9.99360 

1,3 

0.00640 

•  456 

.76239 

.76878 

.09361 

.00639 

•  457 

.76283 

.76921 

.99362 

.00638 

.458 

.76327 

.76964 

•99363 

.00637 

•459 

.76371 

.77006 

.99365 

.00635 

2.460 

0.76415 

44,1 

0.77049 

42,8 

9.99366 

1,3 

0.00634 

.461 

.76459 

•77092 

•99367 

.00633 

.462 

.76503 

.77135 

.99369 

.00631 

•  463 

.76547 

.77178 

.99370 

.00630 

.464 

.76592 

.77220 

•99371 

.00629 

2.465 

0.76636 

44,1 

0.77263 

42,8 

9.99372 

1,3 

0.00628 

.466 

.76680 

.77306 

•99374 

.00626 

.467 

.76724 

•77349 

.99375 

.00625 

.468 

.76768 

•77392 

.99376 

1,2 

.00624 

.469 

.76812 

•77435 

•99377 

.00623 

2.470 

0.76856 

44.1 

0.77477 

42,8 

9-99379 

1,2 

0.00621 

.471 

.76900 

•77520 

.99380 

.00620 

.472 

.76944 

.77563 

.9938i 

.00619 

•473 

.76988 

.77606 

.99382 

.00618 

•474 

.77032 

.77649 

.99384 

.00616 

2.475 

0.77076 

44*0 

0.77691 

42,8 

9.99385 

1,2 

0.00615 

.476 

.77120 

•77734 

.99386 

.00614 

•477 

.77164 

•77777 

.99387 

.00613 

.478 

.77208 

.77820 

.99388 

.00612 

•479 

.77252 

.77863 

.99390 

.00610 

2.480 

0.77296 

44,0 

0.77906 

42,8 

9.99391 

1,2 

0.00609 

.481 

.77340 

.77948 

•99392 

.00608 

.482 

.77384 

.77991 

.99393 

.00607 

•  483 

.77429 

.78034 

.00606 

.484 

•77473 

.78077 

.99396 

.00604 

2.485 

0.77517 

44,0 

0.78120 

42,8 

9-99397 

1,2 

0.00603 

.486 

.77561 

.78163 

.99398 

.00602 

.487 

.77605 

.78205 

•99399 

.00601 

.488 

.77649 

.78248 

.09401 

•00599 

.489 

.77693 

.78292 

.99402 

.00598 

2.490 

0.77737 

44,0 

0.78334 

42,8 

9.99403 

1,2 

0.00597 

.491 

.77781 

.78377 

.99404 

.00596 

.492 

.77825 

.78420 

.99405 

•00595 

.493 

.77869 

.78462 

.99406 

.00594 

.494 

.77913 

.78505 

.99408 

.00592 

2.495 

0.77957 

44,0 

0.78548 

42,8 

9.99409 

1,2 

0.00591 

.496 

.78001 

.78591 

.09410 

.00590 

•497 

.78045 

.78634 

.99411 

.00589 

.498 

.78089 

.78677 

.99412 

.00588 

.499 

.78133 

.78719 

.99414 

.00586 

2.500 

<  0.78177 

44,0 

0.78762 

42,8 

9.99415 

1,2 

0.00585 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«FO' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


69 


Logarithms   of   Hyperbolic   Functions. 


u 

loo  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.500 

0.78177 

44,0 

0.78762 

42,8 

9.99415 

1,2 

0.00585 

.501 

.78221 

.78805 

.99416 

.00584 

.502 

.78265 

.78848 

42,9 

•99417 

.00583 

.503 

.78309 

.78891 

.99418 

.00582 

.504 

.78353 

.78934 

.99419 

.00581 

2.505 

0.78397 

44,0 

0.78977 

42,9 

9.99421 

1,2 

0.00579 

.506 

.78441 

.79019 

.99422 

.00578 

.507 

.78485 

.79062 

.99423 

•00577 

.508 

.78529 

•79105 

.99424 

.00576 

.509 

.78573 

.79148 

•99425 

1,1 

.00575 

2.510 

0.78617 

44,0 

0.79I9I 

42,9 

9.99426 

1,1 

0.00574 

.511 

.78661 

.79234 

•99427 

.00573 

.512 

.78705 

.79277 

.99429 

.00571 

.513 

.78749 

.79319 

.99430 

.00570 

.514 

.78793 

.79362 

.99431 

.00569 

2.515 

0.78837 

44,0 

0.79405 

42,9 

9-99432 

1,1 

0.00568 

.516 

.78881 

.79448 

•99433 

.00567 

.517 

.78925 

•79491 

•99434 

.00566 

.518 

.78969 

.79534 

•99435 

.00565 

.519 

.79013 

.79577 

•99437 

.00563 

2.520 

0.79057 

44,0 

0.79619 

42,9 

9.99438 

1,1 

0.00562 

.521 

.79101 

.79662 

•99439 

.00561 

.522 

.79145 

•79705 

.99440 

.00560 

.523 

.79189 

.79748 

•99441 

.00559 

.524 

.79233 

.79791 

.99442 

.00558 

2.525 

0.79277 

44,0 

0.79834 

42,9 

9-99443 

1,1 

0.00557 

.526 

•79321 

.79877 

•99444 

.00556 

.527 

.79365 

.79920 

.99446 

.00554 

.528 

.79409 

.79962 

•99447 

•00553 

.529 

•79453 

.80005 

.99448 

•00552 

2.530 

0.79497 

44,0 

0.80048 

42,9 

9.09449 

1,1 

0.00551 

.531 

•79541 

.80091 

•99450 

.00550 

.532 

.79585 

.80134 

•99451 

.00549 

•533 

.79629 

.80177 

.99452 

.00548 

•534 

.79673 

.80220 

.99453 

.00547 

2.535 

0.79717 

44,0 

0.80263 

42,9 

9-99454 

1,1 

0.00546 

.536 

.79761 

.80306 

•99455 

.00545 

•  537 

.79805 

.80348 

•99456 

.00544 

.538 

.70849 

.80391 

.99458 

.00542 

•  539 

.79893 

.80434 

•99459 

.00541 

2.540 

0.79937 

44,0 

0.80477 

42,9 

9.99460 

1,1 

0.00540 

•  541 

.79981 

.80520 

.99461 

.00539 

•  542 

.80025 

.80563 

.99462 

.00538 

•  543 

.80069 

.80606 

.99463 

.00537 

•  544 

.80113 

.80649 

.99464 

.00536 

2.545 

0.80157 

44,0 

0.80692 

42,9 

9.99465 

1,1 

0.00535 

•  546 

.80201 

.80734 

.99466 

•00534 

.547 

.80245 

.80777 

.99467 

•00533 

.548 

.80289 

.80820 

.99468 

.00532 

•  549 

.80333 

.80863 

.99469 

.00531 

2.550 

0.80377 

44,0 

0.80906 

42,9 

9.99470 

1,1 

0.00530 

u 

log  tan  <jd  u 

«F0' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«F0' 

log  coth  u 

2.550 

0.80377 

44,0 

0.80906 

42,9 

9-99470 

1,1 

0.00530 

.551 

.80420 

.80949 

.99471 

.00529 

•  552 

.80464 

:8o992 

•99473 

.00527 

•  553 

.80508 

.81035 

•99474 

.00526 

•  554 

.80552 

.81078 

•99475 

.00525 

2.555 

0.80596 

44,0 

o.  81121 

42,9 

9.99476 

1,0 

0.00524 

.556 

.80640 

.81164 

•99477 

.00523 

•  557 

.80684 

..81206 

.99478 

.00522 

.558 

.80728 

.81249 

•99479 

.00521 

•  559 

.80772 

.81292 

.99480 

.00520 

2.560 

0.8o8l6 

44,0 

0.81335 

42,9 

9.99481 

1,0 

0.00519 

.561 

.80860 

.81378 

.99482 

.00518 

.562 

.80904 

43,9 

.81421 

.99483 

.00517 

.563 

.80948 

.81464 

.99484 

.00516 

.564 

.80992 

.81507 

.99485 

.00515 

2.565 

0.81036 

43,9 

0.81550 

42,9 

9.99486 

I,O 

0.00514 

.566 

.81080 

.81593 

.99487 

.00513 

.567 

.81124 

.81636 

.99488 

.00512 

.568 

.81168 

.81678 

.99489 

.00511 

.569 

.81212 

.81721 

•99490 

.00510 

2.570 

0.81256 

43,9 

0.81764 

42,9 

9.99491 

1,0 

0.00509 

•  571 

.81299 

.81807 

•99492 

.00508 

•  572 

.81343 

.81850 

•99493 

.00507 

•  573 

.81387 

.81893 

.99494 

.00506 

•  574 

.81431 

.81936 

•99495 

.00505 

2.575 

0.81475 

43,9 

0.81979 

42,9 

9.99496 

1,0 

0.00504 

.576 

.81519 

.82022 

•99497 

.00503 

•  577 

.81563 

.82065 

.99498 

.00502 

•  578 

.81607 

.82108 

•99499 

.00501 

•  579 

.81651 

.82151 

•99500 

.00500 

2.580 

0.81695 

43,9 

0.82194 

42,9 

9.99501 

1,0 

0.00499 

.581 

.81739 

.82237 

.99502 

.00498 

.582 

.81783 

.82279 

•99503 

.00497 

.583 

.81827 

.82322 

.99504 

.00496 

.584 

.81871 

.82365 

.99505 

.00495 

2.585 

0.81915 

43,9 

0.82408 

42,9 

9.99506 

1,0 

0.00494 

.586 

.81958 

.82451 

•99507 

.00493 

.587 

.82002 

.82494 

.99508 

.00492 

.588 

.82046 

.82537 

.99509 

.00491 

.589 

.82090 

.82580 

•99510 

.00490 

2.590 
.591 

0.82134 
.82178 

43,9 

0.82623 

.82666 

42,9 

9.995II 
•99512 

1,0 

0.00489 

.00488 

•  592 

.82222 

.82709 

.99513 

.00487 

•  593 

.82266 

.82752 

.99514 

.00486 

•  594 

.82310 

.82795 

.99515 

.00485 

2.595 
.596 

0.82354 
.82398 

43,9 

0.82838 
.82881 

42,9 

9.99516 
.99517 

1,0 

0.00484 
.00483 

.597 
.598 

.82442 
.82485 

.82924 
.82967 

43,0 

.99518 
.99519 

.00482 
.00481 

•  599 

.82529 

.83010 

.99520 

.00480 

2.600 

0.82573 

43,9 

0.83052 

43,o 

9.99521 

1,0 

0.00479 

u 

log  tan  gd  u 

w  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

»fV 

log  cosh  u 

«Fo' 

log  tanh  u 

«F0' 

log  coth  u 

2.600 

0.82573 

43,9 

0.83052 

43,0 

9.99521 

1,0 

0.00479 

.601 

.82617 

.83095 

.99522 

.00478 

.602 

.82661 

.83138 

.99523 

.00477 

.603 

.82705 

.83181 

.99524 

.00476 

.604 

.82749 

.83224 

.99525 

.00475 

2.605 

0.82793 

43,9 

0.83267 

43,0 

9.99526 

o,9 

0.00474 

.606 

.82837 

.83310 

.99527 

.00473 

.607 

.82881 

.83353 

• 

•99527 

.00473 

.608 

.82925 

.83396 

.99528 

.00472 

.609 

.82968 

.83439 

.99529 

.00471 

2.610 

0.83012 

43,9 

0.83482 

43,0 

9.99530 

0,9 

0.00470 

.611 

.83056 

.83525 

.99531 

.00469 

.612 

.83100 

.83568 

•99532 

.00468 

.613 

.83144 

.83611 

•99533 

.00467 

.614 

.83188 

.83654 

•99534 

.00466 

2.615 

0.83232 

43,9 

0.83697 

43,0 

9-99535 

0,9 

0.00465 

.6l6 

.83276 

.83740 

.99536 

.00464 

.617 

.83320 

.83783 

.99537 

.00463 

.6l8 

.83364 

.83826 

.99538 

.00462 

.619 

.83407 

.83869 

•99539 

.00461 

2.620 

0.83451 

43,9 

0.83912 

43,0 

9.99540 

0,9 

0.00460 

.621 

.83495 

.83955 

.99541 

.00459 

.622 

.83539 

.83998 

.99541 

.00459 

.623 

.83583 

.84041 

.99542 

.00458 

.624 

.83627 

.84084 

•99543 

.00457 

2.625 

0.83671 

43,9 

0.84127 

43,0 

9-99544 

0,9 

0.00456 

.626 

.83715 

.84170 

.99545 

.00455 

.627 

.83759 

.84213 

.99546 

.00454 

.628 

.83802 

.84256 

•99547 

.00453 

.629 

.83846 

.84299 

.99548 

.00452 

2.630 

0.83800 

43,9 

0.84341 

43,o 

9.99549 

0,9 

0.00451 

.631 

.83934 

.84384 

•99550 

.00450 

.632 

.83978 

.84427 

.99551 

.00449 

.633 

.84022 

.84470 

•99551 

.00449 

.634 

.84066 

.84513 

.99552 

.00448 

2.635 

0.84110 

43,9 

0.84556 

43,0 

9-99553 

0,9 

0.00447 

.636 

.84154 

.84599 

.99554 

.00446 

.637 

.84197 

.99555 

.00445 

.638 

.84241 

^84685 

.99556 

.00444 

.639 

.84285 

.84728 

•99557 

.00443 

2.640 

0.84329 

43,9 

0.84771 

43,0 

9.99558 

0,9 

0.00442 

.641 

.84373 

.84814 

•99559 

.00441 

.642 

.84417 

.84857 

•99559 

.00441 

.643 

.84461 

.84900 

.99560 

.00440 

.644 

.84505 

.84943 

.99561 

.00439 

2.645 

0.84548 

43,9 

0.84086 

43,0 

9.99562 

0,9 

0.00438 

.646 

.84592 

.85029 

.99563 

.00437 

.647 

.84636 

.85072 

.99504 

.00436 

.648 

.84680 

.85115 

.99565 

.00435 

.649 

.84724 

.85158 

.99566 

.00434 

2.650 

0.84768 

43,9 

0.85201 

43,0 

9.99566 

0,9 

0.00434 

u 

log  tan  gd  u 

-Fo' 

log  sec  gd  u 

-Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.650 

0.84768 

43,9 

0.85201 

43,0 

9.99566 

0,9 

0.00434 

.651 

.84812 

.85244 

.99567 

•00433 

.652 

.84855 

.85287 

.99568 

.00432 

653 

.84899 

.85330 

.99509 

.00431 

.654 

.84943 

.85373 

•99570 

.00430 

2.655 

0.84987 

43,9 

0.85416 

43,0 

9.99571 

0,9 

0.00429 

.656 

.85031 

.85459 

•99572 

.00428 

.657 

.85075 

.85502 

•99572 

.00428 

.658 

.85119 

.85545 

.99573 

.00427 

.659 

.85162 

.85588 

•99574 

.00426 

2.660 

0.85206 

43,9 

0.85631 

43,0 

9-99575 

0,8 

0.00425 

.661 

.85250 

.85674 

.99576 

.00424 

.662 

.85294 

.85717 

.99577 

.00423 

.663 

.85338 

.85760 

.99578 

.00422 

.664 

.85382 

.85803 

.99578 

.00422 

2.665 

0.85426 

43,9 

;o.  85846 

43,0 

9-99579 

0,8 

0.00421 

.666 

.85469 

.85889 

.9958o 

.00420 

.667 

.85513 

.85932 

.99581 

.00419 

.668 

.85557 

43,8 

.85975 

.99582 

.00418 

.669 

.85601 

.86018 

.99583 

.00417 

2.670 

0.85645 

43,8 

0.86061 

43,0 

9.99583 

0,8 

0.00417 

.671 

.85689 

.86104 

.99584 

.00416 

.672 

.85733 

.86147 

.99585 

.00415 

.673 

.85776 

.86190 

.99586 

.00414 

.674 

.85820 

.86233 

.99587 

.00413 

2.675 

0.85864 

43,8 

0.86276 

43,0 

9.99588 

0,8 

0.00412 

.676 

.85908 

.86320 

.99588 

.00412 

.677 

.85952 

.86363 

.99589 

.00411 

.678 

.85996 

.86406 

.99590 

.00410 

.679 

.86039 

.86449 

•99591 

.00409 

2.680 

0.86083 

43,8 

0.86492 

43,0 

9.99592 

0,8 

0.00408 

.681 

.86127 

.86535 

•  99592 

.00408 

.682 

.86171 

.86578 

•99593 

.00407 

.683 

.86215 

.86621 

•99594 

.00406 

.684 

.86259 

.83664 

•99595 

.00405 

2.685 

0.86302 

43,8 

0.86707 

43,0 

9.99596 

0,8 

0.00404 

.686 

.86346 

.86750 

.99597 

.00403 

.687 

.86300 

.86793 

•99597 

.00403 

.688 

.86434 

.86836 

.99598 

.00402 

.689 

.86478 

.86879 

•99599 

.00401 

2.690 

0.86522 

43,8 

0.86922 

43,0 

9.99600 

0,8 

0.00400 

.691 

.86565 

.86955 

.99601 

.00399 

.692 

.86609 

.87008 

.99601 

.00399 

.693 

.86653 

.87051 

.99602 

.00398 

.694 

.86697 

.87094 

.99603 

.00397 

2.695 

0.86741 

43,8 

0.87137 

43,o 

9.99604 

0,8 

0.00396 

.696 

.86785 

.87180 

.99605 

.00395 

.697 

.86828 

.87223 

.99605 

•00395 

.698 

.86872 

.87266 

.99606 

.00394 

.699 

.86916 

.87309 

.99607 

.00393 

2.700 

0.86960 

43,8 

0.87352 

43,o 

9.99608 

0,8 

0.00392 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

w  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


73 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

-W 

log  cosh  u 

•Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.700 

0.86960 

43,8 

0.87352 

43,0 

9.99608 

0,8 

0.00392 

.701 

.87004 

.87395 

.99608 

.00392 

.702 

.87048 

.87438 

.99609 

.00391 

.703 

.87091 

.87481 

.99610 

.00390 

.704 

.87135 

.8/524 

.99611 

.00389 

2.705 

0.87179 

43,8 

0.87567 

43,0 

9.99612 

0,8 

0.00388 

.706 

.87223 

.87610 

.99612 

.00388 

.707 

.87267 

.87654 

.99613 

.00387 

.708 

.87310 

.87697 

.99614 

.00386 

.709 

.87354 

.87740 

.99615 

.00385 

2.710 

0.87398 

43,8 

0.87783 

43,o 

9.99615 

0,8 

0.00385 

.711 

.87442 

.8782(1 

.99616 

.00384 

.712 

.87486 

.87869 

.99617 

.00383 

.713 

.87530 

.87912 

.99618 

.00382 

.714 

.87573 

.87955 

.90619 

.00381 

2.715 

0.87617 

43,8 

0.87998 

43,1 

9.99619 

0,8 

0.00381 

.716 

.87661 

.88041 

.99620 

.00380 

.717 

.87705 

.88084 

.99621 

.00379 

.718 

.87749 

.88127 

.99622 

.00378 

.719 

.87792 

.881/0 

.99622 

.00378 

2.720 

0.87836 

43,8 

0.88213 

43,1 

9.99623 

0,8 

0.00377 

.721 

.87880 

.88256 

.99624 

.00376 

.722 

.87924 

.88299 

.99625 

.00375 

.723 

.87968 

.88342 

.99625 

o,7 

.00375 

.724 

.88011 

.88385 

.99626 

.00374 

2.725 

0.88055 

43,8 

0.88428 

43,1 

9.99627 

o,7 

0.00373 

.726 

.88099 

.88471 

.99628 

.00372 

.88143 

.88515 

.99628 

.00372 

.728 

.88187 

.88558 

.99629 

.00371 

.729 

.88230 

.88601 

.99630 

.00370 

2.730 

0.88274 

43,8 

0.88644 

43,1 

9.99631 

o,7 

0.00369 

.731 

.88318 

.88687 

.99631 

.00369 

.732 

.88362 

.88730 

.99632 

.00368 

•  733 

.88406 

.88773 

.99633 

.00367 

•  734 

.88449 

.88816 

.99633 

.00367 

2.735 

o.  88493 

43,8 

0.88859 

43,1 

9.99634 

o,7 

0.00366 

.736 

.88537 

.88002 

.99635 

.00365 

•  737 

.88581 

.88945 

.99636 

.00364 

.738 

.88625 

.88988 

.99636 

.00364 

•  739 

.88668 

.89031 

.99637 

.00363 

2.740 

0.88712 

43,8 

0.89074 

43,1 

9.99638 

o,7 

0.00362 

.741 

.88756 

.89117 

•09639 

.00361 

.742 

.88800 

.89161 

.99639 

.00361 

.743 

.888*4 

.89204 

.99640 

.00360 

•  744 

.88887 

.89247 

.99641 

.00359 

2.745 

0.88931 

43,8 

0.89290 

43,1 

9.99641 

o,7 

0.00359 

.746 

.88975 

.89333 

.99642 

.00358 

.89019 

.89376 

.99643 

.00357 

.748 

.89063 

.89419 

.99644 

.00356 

.749 

.89106 

.89462 

.99644 

.00356 

2.750 

0.89150 

43,8 

0.89505 

43J 

9.99645 

0,7 

0.00355 

u 

log  tan  od  u 

-Fo' 

log  sec  gd  u 

•*  Fo' 

log  sin  gd  u 

,w 

log  esc  gd  u 

SMITHSONIAN  TABLE* 


74 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

-Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.750 

0.89150 

43,8 

0.89505 

43,1 

9.99645 

o,7 

0.00355 

.751 

.89194 

.89548 

.99646 

.00354 

.752 

.89238 

.89591 

.99646 

.00354 

.753 

.89281 

.89634 

.99647 

.00353 

•  754 

.89325 

.89677 

.99648 

.00352 

2.755 

0.89369 

43,8 

0.89720 

43,1 

9.99649 

o,7 

0.00351 

.756 

.89413 

.89764 

.99649 

.00351 

•  757 

.89457 

.89807 

.99650 

.00350 

•  758, 

j 

.89500 

.89850 

•99651 

.00349 

•  759 

.89544 

.89893 

.99651 

.00349 

2.760 

0.89588 

43,8 

0.89936 

43,1 

9.99652 

o,7 

0.00348 

.761 

.89632 

.89979 

.99653 

.00347 

.762 

.89676 

.90022 

.99653 

.00347 

.763 

.89719 

.90065 

.99654 

.00346 

.764 

.89763 

.90108 

.99655 

.00345 

2.765 

0.89807 

43,8 

0.90151 

43,1 

9.99656 

o,7 

0.00344 

.766 

.89851 

.90194 

.99656 

.00344 

.767 

.89894 

.90237 

.99657 

.00343 

.768 

.89938 

.90281 

.99658 

.00342 

.769 

.89982 

.90324 

.99658 

.00342 

2.770 

0.90026 

43,8 

0.90367 

43,1 

9.99659 

o,7 

0.00341 

.771 

.90069 

.90410 

.99660 

.00340 

.772 

.90113 

.90453 

.99660 

.00340 

•  773 

.90157 

.90496 

.99661 

.00339 

•  774 

.90201 

.90539 

.99662 

.00338 

2-775 

0.90245 

43,8 

0.90582 

43,1 

9.99662 

o,7 

0.00338 

.776 

.90288 

.90625 

.99663 

.00337 

•  777 

.90332 

.90668 

.99664 

.00336 

.778 

.90376 

.90712 

.99664 

.00336 

•  779 

.90420 

.90755 

.99665 

.00335 

2.780 

0.90463 

43,8 

0.90798 

43,1 

9.99666 

o,7 

0.00334 

.781 

.90507 

.90841 

.99666 

.00334 

.782 

.90551 

.90884 

.99667 

.00333 

.783 

.90595 

.90927 

.99668 

.00332 

.784 

.90638 

.90970 

.99668 

.00332 

2.785 

0.90682 

43,8 

0.91013 

43,1 

9.99669 

o,7 

0.00331 

.786 

.00726 

.91056 

.99670 

.00330 

.787 

.90770 

.91099 

.99670 

.00330 

.788 

.90813 

.91142 

.99671 

.00329 

.789 

.90857 

.91186 

.99672 

.00328 

2.790 

0.90901 

43>8 

0.91229 

43,1 

9.99672 

o,7 

0.00328 

.791 

.90945 

.91272 

.99673 

.00327 

.792 

.90989 

.91315 

.99674 

.00326 

.793 

.91032 

.91358 

.99674 

.00326 

•  794 

.91076 

.91401 

.99675 

.00325 

2-795 

O.9II2O 

43,8 

0.91444 

43,1 

9.99676 

0,6 

0.00324 

.796 

.91164 

.91487 

.99676 

.00324 

.797 

.91207 

.91530 

.99677 

.00323 

.798 

.91251 

.91574 

.99678 

.00322 

.799 

.91295 

.91617 

.99678 

.00322 

2.800 

0.91339 

43,8 

0.91660 

43.1 

9.99679 

0,6 

0.00321 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

w  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


75 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

-Fo' 

log  tanh  u 

«Fo' 

log  coth  u 

2.800 

0.91339 

43,8 

0.91660 

43,1 

9.99679 

0,6 

0.00321 

.801 

.91382 

.91703 

.99679 

.00321 

.802 

.91426 

.91746 

.99680 

.00320 

.803 

.91470 

43,7 

.91789 

.99681 

.00319 

.804 

.91514 

.91832 

.99681 

.00319 

2.805 

0.91557 

43,7 

0.91875 

43,1 

9.99682 

0,6 

0.00318 

.806 

.91601 

.91918 

.99683 

.00317 

.807 

.91645 

.91962 

.99683 

.00317 

.808 

.91689 

.92005 

.99684 

.00316 

.809 

.91732 

.92048 

.99685 

*  .00315 

2.810 

0.91776 

43,7 

0.92091 

43,1 

9.99685 

0,6 

0.00315 

.811 

.91820 

.92134 

.99686 

.00314 

.812 

.91864 

.92177 

.99686 

.00314 

.813 

.91907 

.92220 

.99687 

.00313 

.814 

.91951 

.92263 

.99688 

.00312 

2.815 

0.91995 

43,7 

0.92306 

43,1 

9.99688 

0,6 

O.OO3I2 

.816 

.92039 

.92350 

.99689 

.00311 

.817 

.92082 

.92393 

.90690 

.00310 

.818 

.92126 

.92436 

.99690 

.00310 

.819 

.92170 

.92479 

.99691 

.00309 

2.820 

0.92213 

43,7 

0.92522 

43,1 

9.99691 

0,6 

0.00309 

.821 

.92257 

.92565 

.09692 

.00308 

.822 

.92301 

.92608 

.99693 

.00307 

.823 

.92345 

.92651 

.99693 

.00307 

.824 

.92388 

.92695 

.99694 

.00306 

2.825 

0.92432 

43,7 

0.92738 

43,1 

9.99694 

0,6 

0.00306 

.826 

•92476 

.92781 

.99695 

.00305 

.827 

.92520 

.92824 

.99696 

.00304 

.828 

.92563 

.92867 

.99606 

.00304 

.829 

.92607 

.92910 

.99697 

.00303 

2.830 

0.92651 

43,7 

0.92953 

43,1 

9.99698 

0,6 

0.00302 

.831 

.92695 

.92996 

.99698 

.00302 

.832 

.92738 

.93040 

•99609 

.00301 

.833 

.92782 

.93083 

.99699 

.00301 

.834 

.92826 

.93126 

.99700 

.00300 

2.835 

0.92869 

43,7 

0.93169 

43,1 

9.99701 

0,6 

O.OO2O9 

.836 

.92913 

.93212 

.99701 

.00299 

.837 

.92957 

.93255 

.99702 

.00298 

.838 

•93001 

.93298 

.99702 

.00298 

.839 

.93044 

•93341 

.09703 

.00297 

2.840 

0.93088 

43,7 

0.93385 

43,1 

9.99704 

0,6 

0.00296 

.841 

.93132 

.93428 

.09704 

.00296 

.842 

.93176 

•93471 

.99705 

.00295 

.843 

.93219 

.93514 

•  99705 

.00295 

.844 

.93263 

•93557 

.99706 

.00294 

2.845 

0.93307 

43,7 

0.93600 

43J 

9.99706 

0,6 

0.00204 

.846 

•93350 

.93643 

.99707 

.00293 

.847 

•93394 

.93687 

.99708 

.00202 

.848 

.93438 

.93730 

.09708 

.00292 

.849 

.93482 

.93773 

.99709 

.OO29I 

2.850 

0.93525 

43,7 

0.93816 

43J 

9.09709 

0,6 

0.00291 

u 

log  tan  od  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

-Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLCS 


-r, 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.850 

0.93525 

43,7 

0.93816 

43,1 

9.99709 

0,6 

O.OO29I 

.851 

.93569 

.93859 

.99710 

.00200 

.852 

.93613 

.93902 

•997II 

.00289 

.853 

.93657 

•93945 

.997H 

.00289 

.854 

.93700 

.93989 

.99712 

.00288 

2.855 

0.93744 

43,7 

0.94032 

43,1 

9.99712 

0,6 

0.00288 

.856 

.93788 

.94075 

.99713 

.00287 

.857 

.93831 

.94118 

.99713 

.00287 

.858 

.93875 

.94161 

.99714 

.00286 

.859 

.93919 

.94204 

.99715 

.00285 

2.860 

0.93963 

43,7 

0.94247 

43,1 

9.99715 

0,6 

0.00285 

.861 

.94006 

.94291 

.99716 

.00284 

.862 

.94050 

•94334 

.99716 

.00284 

.863 

.94094 

•94377 

.99717 

.00283 

.864 

.94137 

.94420 

.99717 

.00283 

2.865 

0.94181 

43,7 

0.94463 

43,1 

9.99718 

0,6 

0.00282 

.866 

.94225 

.94506 

.99719 

.00281 

.867 

.94269 

•94549 

.99719 

.00281 

.868 

.94312 

•94593 

.99720 

.00280 

.869 

.94356 

•94636 

43,2 

.99720 

.00280 

2.870 

0.94400 

43,7 

0.94679 

43,2 

9-99721 

0,6 

0.00279 

.871 

.94443 

.94722 

.99721 

.00279 

.872 

.94487 

•94765 

.99722 

.00278 

.873 

•94531 

.94808 

.99722 

.00278 

.874 

•94575 

.94852 

•99723 

.00277 

2.875 

0.94618 

43,7 

0.94895 

43,2 

9.99724 

0,6 

0.00276 

.876 

.94662 

.94938 

.99724 

.00276 

.877 

.94706 

.94981 

•99725 

.00275 

O»-O 

.94749 

.95024 

•99725 

o,5 

•00275 

^879 

•94793 

.95067 

.99726 

.00274 

2.880 

0.94837 

43,7 

0.95110 

43,2 

9.99726 

o,5 

0.00274 

.881 

.94880 

.95154 

.99727 

.00273 

.882 

.94924 

.95197 

.99727 

.00273 

.883 

.94968 

.95240 

.99728 

.00272 

.884 

.95012 

•95283 

.99728 

.00272 

2.885 

0.95055 

43,7 

0.95326 

43,2 

9.99729 

o,5 

0.00271 

.886 

•95099 

.95369 

.99730 

.00270 

.887 

.95143 

.95413 

.99730 

.00270 

.888 

.95186 

.95456 

.99731 

.00269 

.889 

.95230 

•95499 

.99731 

.00269 

2.890 

0.95274 

43,7 

0.95542 

43,2 

9-99732 

o,5 

0.00268 

.891 

.95317 

.95585 

•99732 

.00268 

.892 

.95361 

.95628 

•99733 

.00267 

•893 

.95405 

.95672 

•99733 

.00267 

.894 

•95449 

.95715 

•99734 

.00266 

2.895 

0.95492 

43,7 

0.95758 

43,2 

9.99734 

0,5 

0.00266 

.896 

.95536 

.95801 

•99735 

.00265 

.897 

.95580 

.95844 

•99735 

.00265 

.898 

.95623 

.95887 

.99736 

.00264 

.899 

.95667 

•95931 

•99737 

.00263 

2.900 

0.957H 

43,7 

0.95974 

43,2 

9-99737 

0,5 

0.00263 

u 

log  tan  gd  u 

«FO' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

logcscgdu 

SMITHSONIAN  TABLES 


77 


Logarithms   of   Hyperbolic   Functions. 


,  u 

log  sinh  u 

«Fo' 

log  cosh  u 

«FO' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.900 

0.957H 

43,7 

0.95974 

43,2 

9.99737 

0,5 

0.00263 

.901 

•95754 

.96017 

.99738 

.00262 

.902 

.95798 

.96060 

.99738 

.00262 

.903 

.95842 

.96103 

•99739 

.00261 

.904 

.95885 

.96146 

•99739 

.00261 

2.905 

0.95929 

43,7 

0.96190 

43,2 

9.99740 

o,5 

O.OO2OO 

.906 

.95973 

.96233 

•99740 

.O02OO 

.907 

.96017 

.96276 

.99741 

.00259 

.908 

.96060 

.96319 

.99741 

.00259 

.909 

.96104 

.96362 

.99742 

.00258 

2.910 

0.96148 

43,7 

0.96405 

43,2 

9.99742 

o,5 

0.00258 

.911 

.96191 

.96449 

.99743 

(00257 

.912 

.96235 

.96492 

.99743 

.00257 

.913 

.96279 

.96535 

.99744 

.00256 

.914 

.96322 

.96578 

.99744 

.00256 

2.915 

0.96366 

43,7 

0.96621 

43,2 

9-99745 

o,5 

0.00255 

.916 

.96410 

.96664 

.99745 

.00255 

.917 

.96453 

.96708 

.99746 

.00254 

.918 

.96497 

.96751 

•99746 

.00254 

.919 

.96541 

.96794 

•99747 

.00253 

2.920 

0.96584 

43,7 

0.96837 

43,2 

9-99747 

o,5 

0.00253 

.921 

.96628 

.96880 

.99748 

.00252 

.922 

.96672 

.96923 

.99748 

.00252 

.923 

.96716 

.96967 

•99749 

.00251 

.924 

.96759 

.97010 

.99749 

.00251 

2.925 

0.96803 

43,7 

0.97053 

43,2 

9.99750 

o,5 

0.00250 

.926 

.96847 

.97096 

•99750 

.00250 

.927 

.96890 

•97139 

.99751 

.00249 

.928 

.96934 

.97183 

•99751 

.00249 

.929 

.96978 

.97226 

.99752 

.00248 

2.930 

0.97021 

43,7 

0.97269 

43,2 

9.99752 

o,5 

0.00248 

.931 

.97065 

.97312 

.99753 

.00247 

.932 

.97109 

.97355 

•99753 

.00247 

•  933 

.97152 

.97398 

•99754 

.00246 

•934 

.97196 

.97442 

•99754 

.00246 

2.935 

0.97240 

43,7 

0.97485 

43,2 

9-99755 

o,5 

0.00245 

.936 

.97283 

.97528 

.99755 

.00245 

•  937 

.97327 

•97571 

.99756 

.00244 

.938 

•97371 

.97614 

.99756 

.00244 

•  939 

.97414 

.97658 

•99757 

.00243 

2.940 

0.97458 

43,7 

0.97701 

43,2 

9-99757 

o,5 

0.00243 

.941 

•97502 

•97744 

.99758 

.00242 

.942 

•97545 

.97787 

•99758 

.00242 

•  943 

.97589 

.97830 

.99759 

.00241 

•  944 

.97633 

.97874 

.99759 

.00241 

2.945 

0.97676 

43,7 

0.97917 

43,2 

9.99760 

o,5 

0.00240 

.946 

.97720 

.97960 

.99760 

.00240 

•  947 

.97764 

.98003 

.99761 

. 

.00239 

.948 
.949 

.97807 
.97851 

.98046 
.98089 

.9976i 
.99762 

.00239 
.00238 

2.950 

0.97895 

43,7 

0.98133 

43,2 

9.99762 

o,5 

0.00238 

u 

loo  tan  gd  u 

«F0' 

log  tec  gd  u 

•  F  ' 

log  sin  gd  u 

••  Fo' 

logcscgdu 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F<>' 

log  tanh  u 

«  Fo' 

log  coth  u 

2.950 

0.97895 

43,7 

0.98133 

43,2 

9.99762 

o,5 

0.00238 

.951 

.97938 

.98176 

.99763 

.00237 

.952 

.97982 

.98219 

.99763 

.00237 

•  953 

.98026 

.98262 

.99763 

.00237 

•954 

.98069 

.98305 

.99764 

.00236 

2.955 

0.98II3 

43,7 

0.98349 

43,2 

9-99764 

o,5 

0.00236 

.956 

.98157 

.98392 

.99765 

.00235 

•957 

.98200 

.98435 

.99765 

•00235 

.958 

.98244 

.98478 

.99766 

.00234 

•959 

.98288 

.98521 

.99766 

.00234 

2.960 

0.98331 

43,7 

0.98565 

43,2 

9.99767 

o,5 

0.00233 

.961 

.98375 

.98608 

.00233 

.962 

.98419 

.08651 

.99768 

.00232 

•  963 

.98462 

.98694 

.99768 

.00232 

.964 

.98506 

.98737 

.99769 

.00231 

2.965 

0.98550 

43,7 

0.98781 

43,2 

9.99769 

o,5 

0.00231 

.966 

.98593 

.98824 

.99770 

.00230 

.967 

.98637 

.98867 

.99770 

.00230 

.968 

.98681 

.98910 

•99770 

.00230 

.969 

.98724 

•98953 

.99771 

.00229 

2.970 

0.98768 

43,7 

0.98997 

43,2 

9.99771 

0,5 

0.00229 

.971 

.98812 

.99040 

•99772 

.00228 

.972 

.08855 

.99083 

.99772 

.00228 

•  973 

.98899 

.99126 

.99773 

.00227 

•974 

.98943 

.99169 

•99773 

.00227 

2.975 

0.98986 

43,7 

0.99213 

43,2 

9-99774 

o,5 

0.00226 

.976 

.99030 

.99256 

•99774 

.00226 

•  977 

.99074 

.99299 

•99775 

.00225 

•  978 

.99H7 

•99342 

.99775 

0,4 

.00225 

•  979 

.99161 

.99385 

•99775 

.00225 

2.980 

0.99205 

43,7 

0.99429 

43,2 

9.99776 

0,4 

0.00224 

.981 

.99248 

.99472 

.99776 

.00224 

.982 

.99292 

.99515 

•99777 

.00223 

.983 

.99336 

.99558 

.99777 

.00223 

.984 

•99379 

.99601 

.99778 

.00222 

2.985 

0.99423 

43,7 

0.99645 

43,2 

9.99778 

0,4 

O.OO222 

.986 

.99466 

.99688 

.99779 

.OO22I 

.987 

.99510 

.99731 

•99779 

.OO22I 

.988 

•99554 

•99774 

•99779 

.00221 

.989 

•99597 

.99818 

.99780 

.00220 

2.990 

0.99641 

43,6 

0.99861 

43,2 

9.99780 

0,4 

0.00220 

.991 

.99685 

.99904 

.99781 

.00219 

.992 

.99728 

.99947 

.99781 

.OO2I9 

•  993 

.99772 

.99990 

.99782 

.OO2l8 

.994 

.99816 

1.00034 

.99782 

.00218 

2.995 

0.99859 

43,6 

1.00077 

43,2 

9.99783 

0,4 

0.00217 

.996 

.99903 

.00120 

.99783 

.00217 

•  997 

•99947 

.00163 

.99783 

.00217 

.998 

.99990 

.00206 

.99784 

.00216 

.999 

1.00034 

.00250 

.99784 

.00216 

3.000 

1.00078 

43,6 

1.00293 

43,2 

9.99785 

0,4 

0.00215 

u 

log  tan  gd  u 

«F0' 

log  sec  gd  u 

«  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


79 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

-Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

3.00 

1.00078 

436,5 

1.00293 

432,1 

9.99785 

4,3 

O.OO2I5 

.01 

.00514 

436,4 

.00725 

432,2 

.99789 

4,2 

.00211 

.02 

.00950 

436,4 

.01157 

432,2 

•99793 

4,1 

.OO2O7 

.03 

.01387 

436,3 

.01589 

432,3 

•99797 

4,1 

.00203 

.04 

.01823 

436,3 

.02022 

432,3 

.90801 

4,0 

.00199 

3.05 

1.02259 

436,2 

1.02454 

432,4 

9.90805 

3,9 

0.00195 

.06 

.02696 

43^2 

.02886 

432,4 

•99809 

3,8 

.OOI9I 

.07 

.03132 

436,2 

.03319 

432,4 

.99813 

3,7 

.00187 

.08 

.03568 

436,1 

.03751 

432,5 

.99817 

3,7 

.00183 

.09 

.04004 

436,1 

.04184 

432,5 

.99820 

3,6 

.OOlSo 

3.10 

I  .04440 

436,1 

1.04616 

432,5 

9.99824 

3,5 

0.00176 

.11 

.04876 

436,0 

.05049 

432,6 

.99827 

3,4 

.00173 

.12 

.05312 

436,0 

.05481 

432,6 

•99831 

3,4 

.00169 

•13 

.05748 

436,0 

.059H 

432,6 

•99834 

3,3 

.00l66 

.14 

.06184 

435,9 

.06347 

432,7 

.99837 

3,3 

.OOl63 

3-15 

1.06620 

435,9 

1.06779 

432,7 

9.99841 

3,2 

0.00159 

.16 

.07056 

435,9 

.07212 

432,7 

.99844 

3,1 

.OOI56 

.17 

.07492 

435,8 

.07645 

432,8 

.99847 

3,1 

.00153 

.18 

.07927 

435,8 

.08078 

432,8 

.99850 

3,0 

.00150 

.19 

.08363 

435,8 

.08510 

432,8 

.99853 

2,9 

.00147 

3.20 

1.08799 

435,7 

1.08943 

432,9 

9.99856 

2,9 

O.OOI44 

.21 

.09235 

435,7 

.09376 

432,9 

.99859 

2,8 

.OOI4I 

.22 

.09670 

435,7 

.09809 

432,9 

.99861 

2,8 

.00139 

•23 

.IOIO6 

435,7 

.  10242 

432,9 

.99864 

2,7 

.OOI36 

.24 

.10542 

435,6 

.10675 

433,0 

.99867 

2,7 

.00133 

3-25 

i.  10977 

435,6 

I.  11108 

433,0 

9.99869 

2,6 

O.OOI3I 

.26 

.11413 

435,6 

.11541 

433,0 

.99872 

2,6 

.00128 

.27 

.11849 

435,6 

.11974 

433,0 

.99875 

2,5 

.00125 

.28 

.12284 

435,5 

.  12407 

433,1 

.99877 

2,5 

.00123 

.29 

.  12720 

435,5 

.12840 

433,1 

.99879 

2,4 

.00121 

3-30 

I.I3I5S 

435,5 

I.I3273 

433,1 

9.99882 

2,4 

O.OOIlS 

•  31 

.13591 

435,5 

.13706 

433J 

.99884 

2,3 

.OOIl6 

•  32 

.14026 

435,4 

.14139 

433,2 

.99886 

2,3 

.00114 

•  33 

.14461 

435,4 

•  14573 

433,2 

.99889 

2,2 

.OOIII 

•34 

.14897 

435,4 

.15006 

433,2 

.99891 

2,2 

.OOIO9 

3-35 

i  •  15332 

435-,4 

I.  15439 

433,2 

9.99893 

2,1 

0.00107 

.36 

.15768 

435,3 

.15872 

433,2 

.99895 

2,1 

.00105 

•  37 

.16203 

435,3 

.16306 

433,3 

.99897 

2,1 

.00103 

•38 

.16638 

435,3 

.  16739 

433,3 

.99899 

2,0 

.OOIOI 

•  39 

.  17073 

435,3 

.  17172 

433,3 

•99901 

2,0 

.00099 

3.40 

i  .  17509 

435,3 

1.17605 

433,3 

9.99903 

1,9 

0.00097 

.41 

.17944 

435,2 

.18039 

433,3 

.99905 

1,9 

.00095 

.42 

.  18379 

435,2 

.  18472 

433,4 

.99907 

1,9 

.00093 

•43 

.18814 

435,2 

.18906 

433,4 

.99909 

1,8 

.00091 

.44 

.19250 

435,2 

.19339 

433,4 

.99911 

1,8 

.00089 

3-45 

1.10685 

435,2 

I  .  19772 

433,4 

9.99912 

1,8 

0.00088 

.46 

.20120 

435,2 

.20206 

433,4 

.99914 

i,7 

.00086 

•47 

.20555 

435,1 

.20639 

433,5 

.90916 

i,7 

.00084 

.48 

.20900 

435,1 

.21073 

433,5 

.99918 

1,6 

.00082 

.49 

.21425 

435,1 

.21506 

433,5 

.99919 

1,6 

.00081 

3-50 

1.21860 

435,1 

1.21940 

433,5 

9.99921 

i/) 

0.00079 

u 

loo  tan  od  u 

•  F0' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


80 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

wF0' 

log  tanh  u 

«F0' 

log  coth  u 

3.50 

I.  21860 

435,1 

1.21940 

433,5 

9.99921 

1,6 

O.OOO79 

.51 

.22296 

.22373 

.99922 

.00078 

.52 

.22731 

.22807 

.99924 

1,5 

.00076 

.53 

.23166 

435,0 

.23240 

.99925 

.00075 

.54 

.23601 

.23674 

433,6 

.99927 

.00073 

3.55 

1.24036 

435,0 

1.24107 

433,6 

9.99928 

1,4 

0.00072 

.56 

.24471 

.24541 

•99930 

.00070 

•  57 

.24906 

.24975 

.99931 

.00069 

.58 

.25341 

.25408 

•99933 

1,3 

.00067 

•  59 

.25776 

.25842 

•99934 

.00066 

3.60 

I.262II 

434,9 

1.26275 

433,6 

9-99935 

1,3 

0.00065 

.61 

.26646 

.26709 

433,7 

.99936 

.00064 

.62 

.27080 

.27143 

.99938 

1,2 

.00062 

.63 

.27515 

.27576 

•99939 

.00061 

.64 

.27950 

.28010 

.99940 

.00060 

3.65 

1.28385 

434,9 

1.28444 

433,7 

9.99941 

1,2 

0.00059 

.66 

.28820 

.28878 

.99942 

.00058 

.67 

.29255 

.29311 

•99944 

i,i 

.00056 

.68 

.29690 

434,8 

.29745 

•99945 

.00055 

.69 

.30125 

.30179 

433,8 

.99946 

.00054 

3-70 

1.30559 

434,8 

1.30612 

433,8 

9.99947 

1,1 

0.00053 

.30994 

.31046 

.99948 

1,0 

.00052 

•  72 

.31429 

.31480 

.99949 

.00051 

•  73 

.31864 

.31914 

.99950 

.00050 

•  74 

.32299 

.32348 

•99951 

.00049 

3-75 

1.32733 

434,8 

1.32781 

433,8 

9.99952 

1,0 

0.00048 

•  76 

.33'l68 

.33215 

•99953 

0,9 

.00047 

•  77 

.33603 

.33649 

•99954 

.00046 

.78 

.34038 

434,7 

.34083 

•99955 

.00045 

•  79 

•34472 

.34517 

433,9 

.99956 

.00044 

3.8o 

1.34007 

434,7 

I-3495I 

433,9 

9-99957 

0,9 

0.00043 

.81 

•35342 

.35384 

.99957 

.00043 

.82 

.35777 

.35818 

.99958 

0,8 

.00042 

.83 

.36211 

.36252 

•99959 

.00041 

•84 

.36646 

.36686 

.99960 

.00040 

3.85 

i.37o8i 

434,7 

1.37120 

433,9 

9.99961 

0,8 

0.00039 

.86 

.37515 

.37554 

.99961 

.00039 

.87 

.37950 

.37988 

.99962 

.00038 

.88 

.38385 

.38422 

.99963 

o,7 

.00037 

.89 

.38819 

.38856 

.99964 

.00036 

3.90 

1.39254 

434,7 

1.39290 

433,9 

9.99964 

o,7 

0.00036 

.91 

.39689 

434,6 

.39724 

•99965 

.00035 

.92 

.40123 

.40158 

434,0 

.99966 

.00034 

•93 

.40558 

.40591 

.99966 

.00034 

.94 

.40993 

.41025 

.99967 

.00033 

3-95 

1.41427 

434,6 

I.4I459 

434,0 

9.99968 

0,6 

0.00032 

.96 

.41862 

.41893 

.99968 

.00032 

.97 

.42296 

.42327 

.99969 

.00031 

.98 

.42731 

.42761 

.99970 

.00030 

•  99 

.43166 

.43195 

.99970 

.00030 

4.00 

1.43600 

434,6 

1.43629 

434,0 

9.99971 

0,6 

0.00029 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

«F0' 

log  sin  gd  u 

w  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


81 


Logarithms   of  Hyperbolic  Functions. 


u 

log  sinh  u 

»F0' 

log  cosh  u 

«Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

4.00 

1.43600 

434,6 

1.43629 

434,0 

9-99971 

0,6 

O.OOO29 

.01 

.44035 

.44063 

•99971 

.00029 

.02 

.44409 

•44497 

•99972 

.OO028 

.03 

.44904 

.44931 

•99973 

0,5 

.OO027 

.04 

•45339 

.45365 

•99973 

.OO027 

4-05 

1.45773 

434,6 

1.45799 

434,0 

9-99974 

o,5 

0.00026 

.06 

.46208 

.46233 

•99974 

.00026 

.07 

.46642 

434,5 

.46668 

•99975 

.00025 

.08 

.47077 

.47102 

•99975 

.O0025 

.09 

•475II 

.47536 

434,1 

.99976 

.00024 

4.10 

1.47946 

434,5 

1.47970 

434,1 

9.99976 

o,5 

0.00024 

.11 

.48380 

.48404 

•99977 

.00023 

.12 

.48815 

.48838 

•99977 

.00023 

•13 

.49249 

.49272 

.99978 

0,4 

.00022 

.14 

.49684 

.49706 

.99978 

.OO022 

4-15 

i  .  501  18 

434,5 

1.50140 

434,1 

9.99978 

0,4 

O.OOO22 

.16 

.50553 

•50574 

•99979 

.00021 

•17 

.50987 

.51008 

•99979 

.00021 

.18 

.51422 

.51442 

.99980 

.00020 

.19 

.51856 

.51876 

.99980 

.00020 

4.2O 

1.52291 

434,5 

I.523IO 

434,1 

9.99980 

0,4 

O.OOO2O 

.21 

.52725 

.52745 

.99981 

.OOOI9 

.22 

.53160 

.53179 

.99981 

.OOOI9 

•23 

•53594 

.53613 

.99982 

.00018 

.24 

.54029 

.54047 

.99982 

.00018 

4-25 

1.54463 

434,5 

I.5448I 

434,1 

9.99982 

0,4 

O.OOOlS 

.26 

.54898 

.54915 

.99983 

0,3 

.OOOI7 

.27 

•55332 

.55349 

.99983 

.00017 

.28 

.55767 

.55783 

.99983 

.OOOI7 

.29 

.56201 

.56217 

.99984 

.OOOl6 

4-30 

1.56636 

434,5 

1.56652 

434,1 

9.99984 

0,3 

O.OOOI6 

•31 

.57070 

.57086 

•99984 

.00016 

•32 

.57505 

434,4 

.57520 

.99985 

.00015 

•33 

•57939 

•57954 

.99985 

.OOOI5 

•34 

.58373 

.58388 

.99985 

.00015 

4-35 

1.58808 

434,4 

1.58822 

434,1 

9.99986 

0,3 

O.OOOI4 

.36 

.59242 

.59256 

434,2 

.99986 

.OOOI4 

•  37 

.59677 

.59691 

.99986 

.00014 

•  38 

.60111 

.60125 

.99086 

.00014 

•39 

.60546 

.60559 

.99987 

.00013 

4.40 

1.60080 

434,4 

1.60993 

434,2 

9.99987 

0,3 

O.OOOI3 

.41 

.61414 

.61427 

.99987 

.OOOI3 

.42 

.61849 

.61861 

.99987 

.OOOI3 

•  43 

.62283 

.62296 

.99988 

0,2 

.OOOI2 

.44 

.62718 

.62730 

.99988 

.OOOI2 

4-45 

1.63152 

434A 

1.63164 

434,2 

9.99988 

0,2 

O.OOOI2 

.46 

.63587 

.63598 

•99988 

.OOOI2 

•47 

.64021 

.64032 

.99989 

.00011 

.48 

.64455 

.64467 

.99989 

.00011 

•49 

.64890 

.64901 

.99989 

.0001  1 

4-50 

1.65324 

434A 

1.65335 

434,2 

9.99989 

0,2 

O.OOOII 

u 

loo  tan  ad  u 

-  Fo' 

log  tec  gd  u 

«  Fo' 

logsingdu 

«FO' 

log  csc  gd  u 

SMITHSONIAN  TABLES 


82 


Logarithms   of   Hyperbolic   Functions. 


u 

log  sinh  u 

«  Fo' 

log  cosh  u 

«F0' 

log  tanh  u 

«F</ 

log  coth  u 

4.50 

1.65324 

434,4 

1.65335 

434,2 

9.99989 

0,2 

O.OOOII 

.51 

.65759 

.65769 

.99989 

.00011 

.52 

.66193 

.66203 

•99990 

.00010 

•  53 

.66627 

.66637 

.99990 

.000  10 

•  54 

.67062 

.67072 

.99990 

.00010 

4-55 

1.67496 

434,4 

1.67506 

434,2 

9-99990 

0,2 

O.OOOIO 

.56 

.67931 

.67940 

.99990 

.00010 

•  57 

.68365 

.68374 

.99991 

.00009 

.58 

.68799 

.68808 

.99991 

.00009 

•  59 

.69234 

.69243 

.99991 

.00009 

4.60 

1.69668 

434,4 

1.69677 

434,2 

9.99991 

0,2 

0.00009 

.61 

.70102 

.70111 

.99991 

.00009 

.62 

.70537 

.70545 

•99992 

.00008 

.63 

.70971 

.70979 

•99992 

.00008 

.64 

.71406 

.71414 

.99992 

.00008 

4.65 

1.71840 

434,4 

1.71848 

434,2 

9.99992 

0,2 

0.00008 

.66 

.  72274 

.72282 

.99992 

.00008 

.67 

.72709 

.72716 

•  .99992 

.00008 

.68 

.73143 

.73151 

•99993 

0,1 

.00007 

.69 

.73577 

.73585 

•99993 

.00007 

4.70 

1.74012 

434,4 

I.740I9 

434,2 

9-99993 

0,1 

0.00007 

•  71 

.74446 

•74453 

.99993 

.00007 

.72 

.74881 

.74887 

•99993 

.00007 

•  73 

.75315 

•75322 

•99993 

.00007 

.74 

.75749 

.75756 

•99993 

.00007 

4-75 

1.76184 

434,4 

1.76190 

434,2 

9-99993 

0,1 

0.00007 

.76 

.76618 

.76624 

.99994 

.00006 

•  77 

.77052 

.77059 

.99994 

.00006 

.78 

.77487 

•77493 

.99994 

•  .00006 

•  79 

.77921 

.77927 

•99994 

.00006 

4.80 

1.78355 

434,4 

1.78361 

434,2 

9-99994 

0,1 

0.00006 

.81 

.78790 

.78796 

.99994 

.00006 

.82 

.79224 

.79230 

.99994 

.00006 

.83 

.79658 

434,3 

.79664 

•99994 

.00006 

.84 

.80093 

.80098 

•99995 

.00005 

4.85 

1.80527 

434,3 

1.80532 

434,2 

9-99995 

0,1 

0.00005 

.86 

.80962 

.80967 

•99995 

.00005 

.87 

.81396 

-.81401 

.99995 

.00005 

.88 

.81830 

.81835 

.99995 

.00005 

.89 

.82265 

.82269 

•99995 

.00005 

4.90 

1.82699 

434,3 

1.82704 

434,2 

9-99995 

0,1 

0.00005 

.91 

.83133 

.83138 

.99995 

.00005 

.92 

.83568 

.83572 

.99995 

' 

.00005 

•  93 

.84002 

.84006 

.99995 

.00005 

.94 

.84436 

.84441 

434,3 

.99996 

.00004 

4-95 

1.84871 

434,3 

1.84875 

434,3 

9.99996 

0,1 

0.00004 

.96 

.85305 

.85309 

.99996 

.00004 

•97 

.85739 

.85743 

.99996 

.00004 

.98 

.86174 

.86178 

.99996 

.00004 

•  99 

.86608 

.86612 

•99996 

.00004 

5-00 

1.87042 

434,3 

1.87046 

434,3 

9.99996 

0,1 

0.00004 

u 

log  tan  gd  u 

«  Fo' 

log  sec  gd  u 

»  Fo' 

log  sin  gd  u 

»  Fo' 

logcscgdu 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

„« 

log  cosh  u 

•  IV 

log  tanh  u 

«  Fo' 

log  eoth  u 

5.00 

1.87042 

434,3 

1.87046 

434,3 

9.99996 

0,1 

0.00004 

.01 

.87477 

.87480 

.99996 

.00004 

.02 

.879H 

.87915 

.99996 

.00004 

•03 

.88345 

.88349 

.99996 

.00004 

.04 

.88780 

.88783 

.99996 

.00004 

5-05 

1.89214 

434,3 

1.89217 

434,3 

9.99906 

0,1 

0.00004 

.06 

.89648 

.89652 

.99997 

.00003 

.07 

.90083 

.90086 

.99997 

.00003 

.08 

•00517 

.90520 

•99997 

.00003 

.09 

.00951 

.90955 

.99997 

.00003 

5.  10 

I.9I386 

434,3 

I.9I389 

434,3 

9-99997 

0,1 

0.00003 

.11 

.91820 

.91823 

.99997 

.00003 

.12 

.92254 

.92257 

.90997 

.00003 

•13 

.92689 

.92692 

.99997 

.00003 

.14 

.93123 

.93126 

.99997 

.00003 

5-15 

1.93557 

434,3 

1.93560 

434,3' 

9.99997 

0,1 

0.00003 

.16 

•93992 

•93994 

.99997 

.00003 

.17 

.94426 

.94429 

•99997 

.00003 

.18 

.94860 

.94863 

•99997 

.00003 

.19 

.95294 

.95297 

•99997 

.00003 

5-20 

1.95729 

434,3 

I.9573I 

434,3 

9-99997 

0,1 

0.00003 

.21 

.96163 

.96166 

.99997 

.00003 

.22 

.96597 

.96600 

•99997 

.00003 

•23 

.97032 

.97034 

.99998 

0,0 

.00002 

.24 

.97466 

.97409 

.99998 

.00002 

5.25 

1.97900 

434,3 

1.97903 

434,3 

9.99998 

0,0 

O.OOOO2 

.26 

.98335 

.08337 

.99998 

.00002 

.27 

.98769 

•58771 

•99998 

.00002 

.28 

.99203 

.99206 

.99998 

.00002 

.29 

.99638 

.99640 

.99998 

.00002 

5.30 

2.00072 

434,3 

2.00074 

434,3 

9.99998 

0,0 

O.OOO02 

.31 

.00506 

.00508 

.99998 

.OOOO2 

.32 

.00941 

.00943 

•99998 

.OOOO2 

.33 

•01375 

.01377 

.99998 

.OOOO2 

.34 

.01809 

.01811 

.99998 

.00002 

5.35 

2.02244 

434,3 

2.02246 

434,3 

9.99998 

0,0 

O.OOOO2 

.36 

.02678 

.02680 

.90998 

.OOO02 

.37 

.03112 

.03114 

.99998 

.OOOO2 

•  38 

•03547 

.03548 

.99008 

.OOOO2 

•39 

.03981 

.03983 

.09998 

.OOOO2 

5.40 

2.04415 

434,3 

2.04417 

434,3 

9.99998 

0,0 

O.OOO02 

.41 

.04849 

.04851 

.99998 

.OO002 

.42 

.05284 

.05285 

.99998 

.OOOO2 

•  43 

.05718 

.05720 

.99998 

.O0002 

•  44 

.06152 

.06154 

.99998 

.00002 

5-45 

2.06587 

434,3 

2.06588 

434,3 

9.99998 

0,0 

O.OOOO2 

.46 

.07021 

.07023 

.90998 

.OOOO2 

.47 

•07455 

.07457 

.99998 

.OOOO2 

.48 

.07890 

.07891 

.99998 

.OOOO2 

.49 

.08324 

.08325 

•99999 

.OOOOI 

5-50 

2.08758 

434,3 

2.08760 

434,3 

9.90009 

0,0 

0.00001 

u 

log  tan  gd  u 

-Fo' 

log  sec  gd  u 

•  Fo' 

log  sin  gd  u 

«  Fo' 

log  esc  gd  u 

SMITHSONIAN  TABLES 


Logarithms   of  Hyperbolic   Functions. 


u 

log  sinh  u 

«F0' 

log  cosh  u 

•  Fo' 

log  tanh  u 

«  Fo' 

log  coth  u 

5.50 

2.08758 

434,3 

2.08760 

434,3 

9.99999 

0,0 

O.OOOOI 

.51 

.09193 

.09194 

.99999 

.00001 

•  52 

.09627 

.09628 

.99999 

.00001 

-53 

.10061 

.10063 

•99999 

.00001 

•  54 

.10495 

.  10497 

.99999 

.00001 

5-55 

2.10930 

434,3 

2.10931 

434,3 

9-99999 

0,0 

O.OOOOI 

.56 

.11364 

.11365 

.99999 

.00001 

.57 

.11798 

.11800 

.99999 

.00001 

.58 

.  12233 

.  12234 

.99999 

.00001 

•  59 

.12667 

.12668 

.99999 

.00001 

5.6o 

2.13101 

434,3 

2.13103 

434,3 

9-99999 

0,0 

O.OOOOI 

.61 

.  13536 

.  13537 

•99999 

.00001 

.62 

.  13970 

.  I397I 

•99999 

.00001 

.63 

.14404 

.14405 

•99999 

.00001 

.64 

.  14839 

.  14840 

•99999 

.00001 

5.65 

2.15273 

434,3 

2.15274 

434,3 

9-99999 

0,0 

O.OOOOI 

.66 

.  15707 

.15708 

•99999 

.00001 

.67 

.16141 

.16142 

•99999 

.00001 

.68 

.  16576 

.  16577 

.99999 

.00001 

.69 

.  17010 

.17011 

.99999 

.00001 

5-70 

2.17444 

434,3 

2.17445 

434,3 

9-99999 

0,0 

O.OOOOI 

•  7i 

.  17879 

.17880 

•99999 

.00001 

•  72 

.18313 

.18314 

.99999 

.00001 

•  73 

.  18747 

.  18748 

•99999 

.00001 

•  74 

.  19182 

.  19182 

•99999 

.00001 

5-75 

2.19616 

434,3 

2.19617 

434,3 

9-99999 

0,0 

O.OOOOI 

•  76 

.20050 

.20051 

•99999 

.00001 

•  77 

.  20484 

.20485 

.99999 

.00001 

.78 

.20919 

.20920 

.99999 

.00001 

•  79 

.21353 

.21354 

•99999 

.00001 

5.8o 

2.21787 

434,3 

2.21788 

434,3 

9-99999 

0,0 

O.OOOOI 

.81 

.  22222 

.22222 

•99999 

.00001 

.82 

.22656 

.22657 

•99999 

.00001 

.83 

.23090 

.23091 

•99999 

.00001 

.84 

.23525 

.23525 

•99999 

.00001 

5.85 

2.23959 

434,3 

2.23960 

434,3 

9-99999 

0,0 

O.OOOOI 

.86 

.24394 

•99999 

.00001 

.87 

.24828 

.24828 

•99999 

.00001 

.88 

.25262 

.25262 

•99999 

.00001 

.89 

.25696 

.25697 

•99999 

.00001 

5.90 

2.26130 

434,3 

2.26I3I 

434,3 

9-99999 

0,0 

O.OOOOI 

.91 

.26565 

.26565 

•99999 

.00001 

.92 

.26999 

.27000 

•99999 

.00001 

•  93 

•27433 

.27434 

•99999 

.00001 

.94 

.27868 

.27868 

•99999 

.00001 

5-95 

2.28302 

434,3 

2.28303 

434,3 

9-99999 

0,0 

O.OOOOI 

.96 

.28736 

.28737 

•99999 

.00001 

•97 

.29171 

.29171 

.99999 

.00001 

.98 

.29605 

.29605 

-99999 

.OOOOI 

.99 

.30039 

.30040 

.99999 

.00001 

6.00 

2.30473 

434,3 

2.30474 

434,3 

9-99999 

0,0 

O.OOOOI 

u 

log  tan  gd  u 

<-  Fo' 

log  sec  gd  u 

w  Fo' 

log  sin  gd  u 

«  Fo' 

log  csc  gd  u 

SMITHSONIAN  TABLES 


TABLE  II 


NATURAL  HYPERBOLIC  FUNCTIONS 


87 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«Fo' 

tanh  u 

«  Fo' 

coth  u 

-  Fo' 

o.oooo 

O.OOOOO 

10,0 

I.  00000 

0,0 

O.OOOOO 

10,0 

00 

<x 

.0001 

.OOOIO 

.00000 

.OOOIO 

IOOOO.OO 

1000000,0 

.0002 

.0002O 

.00000 

.00020 

5000.00 

250000,0 

.0003 

.O0030 

.00000 

.00030 

3333.33 

mm,  i 

.0004 

.00040 

.00000 

.00040 

2500.00 

62500,0 

0.0005 

O.OOO5O 

IO,O 

I.OOOOO 

0,0 

0.00050 

10,0 

2000.00 

40000,0 

.OO06 

.00060 

.00000 

.00060 

1666.67 

27777,8 

.OO07 

.O0070 

.00000 

.00070 

1428.57 

20408,2 

.0008 

.OOOSO 

.00000 

.00080 

1250.00 

15625,0 

.0009 

.00090 

.00000 

.00090 

IIII.  II 

12345,7 

O.OOIO 

O.OOIOO 

IO,O 

I.OOOOO 

0,0 

O.OOIOO 

10,0 

1000.00 

10000,0 

.OOII 

.OOIIO 

.00000 

.OOIIO 

909.09 

8264,5 

.0012 

.00120 

.00000 

.00120 

833.33 

6944,4 

.0013 

.00130 

.00000 

.00130 

769.23 

5917,2 

.0014 

.00140 

.00000 

.00140 

714.29 

5102,0 

0.0015 

0.00150 

IO,O 

I.OOOOO 

0,0 

0.00150 

10,0 

666.67 

4444,4 

.0016 

.00160 

.00000 

.00160 

625.00 

3906,2 

.0017 

.00170 

.00000 

.00170 

588.24 

3460,2 

.0018 

.00180 

.00000 

.00180 

555.56 

3086,4 

.0019 

.00190 

.00000 

.00190 

526.32 

2770,1 

O.OO2O 

O.OO2OO 

10,0 

I.OOOOO 

0,0 

0.00200 

10,0 

500.00 

2500,0 

.0021 

.OO2IO 

.00000 

.00210 

476.  19 

2267,6 

.OO22 

.00220 

.00000 

.00220 

454.55 

2066,  1 

.OO23 

.OO23O 

.00000 

.00230 

434.78 

1800,4 

.O024 

.00240 

.00000 

.00240 

416.67 

1736,1 

O.O025 

0.00250 

IOSO 

I.OOOOO 

0,0 

0.00250 

10,0 

400.00 

1600,0 

.0026 

.00260 

.00000 

.00260 

384.62 

1479,3 

.0027 

.O027O 

.00000 

.00270 

370.37 

1371,7 

.0028 

.O028O 

.00000 

.00280 

357.14 

1275,5 

.0029 

.00290 

.00000 

.00290 

344.83 

1189,1 

O.O03O 

0.00300 

10,0 

I.OOOOO 

0,0 

0.00300 

IO,O 

333.33 

IIII,  I 

.0031 

.OO3IO 

.00000 

.00310 

322.58 

1040,6 

.0032 

.O032O 

.00001 

.00320 

312.50 

976,6 

.0033 

.00330 

.00001 

.00330 

303.03 

918,3 

.0034 

.00340 

.00001 

.00340 

294.12 

865,1 

0.0035 

0.00350 

IO,O 

I.OOOOI 

0,0 

0.00350 

10,0 

285.72 

816,3 

.0036 

.00360 

.00001 

.00360 

277.78 

771,6 

.0037 

.00370 

.00001 

.00370 

270.27 

730,5 

.0038 

.00380 

.00001 

.00380 

263.16 

692,5 

.0039 

.00390 

.00001 

.00300 

256.41 

657,5 

0.0040 

O.OO4OO 

10,0 

I.OOOOI 

0,0 

0.00400 

10,0 

250.00 

625,0 

.0041 

.004IO 

.00001 

.00410 

243.90 

594,9 

.0042 

.OO42O 

.00001 

.00420 

238.10 

566,9 

.0043 

.00430 

.00001 

.00430 

232.56 

540,8 

.0044 

.00440 

.00001 

.00440 

227.27 

516,5 

0.0045 

0.00450 

10,0 

I.OOOOI 

0,0 

0.00450 

10,0 

222.22 

493,8 

.0046 

.00460 

.00001 

.00460 

217.39 

472,6 

.0047 

.00470 

.00001 

.00470 

212.77 

452,7 

.0048 
.0049 

.00480 
.00400 

.00001 

.00001 

.00480 

.00490 

208.33 

204.08 

434,0 

416,5 

0.0050 

0.00500 

10,0 

I.OOOOI 

0,1 

0.00500 

IO,O 

200.00 

400,0 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

-  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

-  Fo' 

SMITHSONIAN  TABLCS 


88 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

<-FO' 

cosh  u 

•  Fo' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.0050 

0.00500 

IO,O 

I.OOOOI 

0,1 

0.00500 

IO,O 

200.00 

400,0 

.0051 

.005IO 

.00001 

.00510 

196.08 

384,5 

.0052 

.O0520 

.00001 

.00520 

192.31 

369,8 

.0053 

.00530 

.00001 

.00530 

188.68 

356,0 

.0054 

.00540 

.00001 

.00540 

185.19 

342,9 

0.0055 

0.00550 

IO,O 

I.O0002 

0,1 

0.00550 

IO,O 

181.82 

330,6 

.0056 

.00560 

.00002 

.00560 

178.57 

3i8,9 

.0057 

.00570 

.00002 

.00570 

175.44 

307,8 

.0058 

.00580 

.00002 

.00580 

172.42 

297,3 

.0059 

.00590 

.00002 

.00590 

169.49 

287,3 

0.0060 

0.00600 

IO,O 

I.OOO02 

0,1 

0.00600 

IO,O 

166.67 

277,8 

.0061 

.00610 

.OO002 

.00610 

163.94 

268,7 

.0062 

.00620 

.OOOO2 

.00620 

161.29 

260,1 

.0063 

.00630 

.O0002 

.00630 

158.73 

251,9 

.0064 

.00640 

.OOOO2 

.00640 

156.25 

244,1 

0.0065 

0.00650 

10,0 

I.OOOO2 

0,1 

0.00650 

10,0 

153.85 

236,7 

.0066 

.00660 

.OOO02 

.00660 

151.52 

229,6 

.0067 

.00670 

.00002 

.00670 

149.26 

222,8 

.0068 

.00680 

.OOO02 

.00680 

147.06 

216,3 

.0069 

.00690 

.OOOO2 

.00690 

144.93 

210,0 

0.0070 

0.00700 

10,0 

I.OOOO2 

0,1 

0.00700 

10,0 

142.86 

204,1 

.0071 

.00710 

.00003 

.00710 

140.85 

I08,4 

.0072 

.O072O 

.00003 

.00720 

138.89 

192,9 

.0073 

.00730 

.00003 

.00730 

136.99 

187,6 

.0074 

.00740 

.OOOO3 

'.00740 

135.14 

182,6 

0.0075 

0.00750 

IO,O 

I.OOOO3 

0,1 

0.00750 

IO,O 

133.34 

177,8 

.0076 

.00760 

.OOOO3 

.00760 

131.58 

173,1 

.0077 

.00770 

.00003 

.00770 

129.87 

168,7 

.0078 

.00780 

.00003 

.00780 

128.21 

164,4 

.0079 

.00790 

.OOOO3 

.00790 

126.58 

160,2 

0.0080 

O.OOSOO 

10,0 

I.OOOO3 

01, 

0.00800 

IO,O 

125.00 

156,2 

.0081 

.OoSlO 

.00003 

.00810 

123.46 

152,4 

.0082 

.00820 

.00003 

.00820 

121.95 

148,7 

.0083 

.00830 

.00003 

.00830 

120.48 

145,2 

.0084 

.00840 

.OOOO4 

.00840 

119.05 

141,7 

0.0085 

0.00850 

10,0 

I.OOOO4 

0,1 

0.00850 

IO,O 

117.65 

138,4 

.0086 

.00860 

.OOOO4 

.00860 

116.28 

135,2 

.0087 

.00870 

.00004 

.00870 

114.95 

132,1 

.0088 

.00880 

.00004 

.00880 

113.64 

129,1 

.0089 

.00890 

.00004 

.00890 

112.36 

126,2 

0.0090 

o.ooooo 

10,0 

1.00004 

0,1 

0.00900 

10,0 

III.  II 

123,5 

.0091 

.00910 

.00004 

.00910 

109.89 

120,8 

.0092 

.00920 

.00004 

.00920 

108.70 

118,1 

.0093 

.00930 

.00004 

.00930 

107.53 

115,6 

.0094 

.00940 

.00004 

.00940 

106.39 

113,2 

0.0095 

0.00950 

10,0 

1.00005 

0,1 

0.00950 

10,0 

105.27 

110,8 

.0096 

.00960 

.00005 

.00960 

104.17 

108,5 

.0097 

.00970 

.00005 

.00970 

103.10 

106,3 

.0008 

.00980 

.00005 

.00980 

102.04 

104,1 

.0099 

.00090 

.00005 

.00990 

101.01 

102,0 

O.OIOO 

0.01000 

IO,O 

I.OOOO5 

0,1 

O.OIOOO 

10,0 

IOO.OO 

100,0 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«-  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

»F0' 

SMITHSONIAN  TABLES 


89 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«FO' 

cosh  u 

•  Fo' 

tanh  u 

«   Fo' 

coth  u 

-  Fo' 

O.OIOO 

O.OIOOO 

10,0 

1.00005 

0,1 

O.OIOOO 

IO,O 

100.003 

1000,0 

.OIOI 

.OIOIO 

.00005 

.OIOIO 

99.013 

980,3 

.0102 

.01020 

.00005 

.01020 

98.043 

961,1 

.0103 

.01030 

.00005 

.01030 

97.091 

942,6 

.0104 

.01040 

.00005 

.01040 

'96.157 

924,5 

0.0105 

0.01050 

10,0 

1.00006 

0,1 

0.01050 

IO,O 

95.242 

907,0 

.0106 

.01060 

.00006 

.01060 

94.343 

890,0 

.0107 

.01070 

.00006 

.01070 

93.462 

873,4 

.0108 

.01080 

.00006 

.01080 

92.595 

857,3 

.0109 

.01090 

.00006 

.01090 

91.747 

841,6 

O.OIIO 

O.OIIOO 

10,0 

1.00006 

0,1 

O.OIIOO 

IO,O 

90.913 

826,4 

.OIII 

.OHIO 

.00006 

.01110 

90.094 

811,6 

.OII2 

.OII2O 

.00006 

.OII20 

89.289 

797,2 

.0113 

.01130 

.00006 

.01130 

88.499 

783,1 

.0114 

.01140 

.00006 

.01140 

87.723 

769,4 

0.0115 

0.01150 

IO,O 

1.00007 

0,1 

0.01150 

IO,0 

86.960 

756,1 

.0116 

.01100 

.00007 

.01160 

86.211 

743,1 

.0117 

.01170 

.00007 

.01170 

85.474 

730,5 

.0118 

.01180 

.00007 

.01180 

84.750 

718,2 

.0119 

.01190 

.00007 

.01190 

84.038 

706,1 

O.OI2O 

O.OI2OO 

10,0 

1.00007 

0,1 

O.OI2OO 

10,0 

83.337 

694,4 

.OI2I 

.OI2IO 

.00007 

.OI2IO 

82.649 

683,0 

.0122 

.OI220 

.00007 

.01220 

81.971 

671,8 

.OI23 

.01230 

.00008 

.01230 

81.305 

660,9 

.0124 

.01240 

.00008 

.01240 

80.649 

650,3 

0.0125 

O.OI25O 

IO,O 

1.00008 

0,1 

0.01250 

IO,O 

80.004 

640,0 

.OI26 

.OI26O 

.00008 

.01260 

79.369 

629,8 

.OI27 

.OI270 

.00008 

.01270 

78.744 

620,0 

.0128 

.OI28O 

.00008 

.01280 

78.129 

6  10,3 

.OI29 

.OI20O 

.00008 

.01290 

77.524 

600,9 

O.OI3O 

O.OI3OO 

IO,O 

1.00008 

O,I 

0.01300 

10,0 

76.927 

591,7 

.0131 

.01310 

.00009 

.01310 

76.340 

582,7 

.0132 

.OI32O 

.00009 

.01320 

75.762 

573,9 

•  0133 

.01330 

.00009 

.01330 

75.192 

565,3 

.0134 

.01340 

.00009 

.01340 

74.631 

556,9 

0.0135 

0.01350 

10,0 

1.00009 

0,1 

0.01350 

IO,O 

74.079 

548,7 

.0136 

.01360 

.00009 

.01360 

73.534 

540,6 

.0137 

.01370 

.00009 

.01370 

72.997 

532,8 

.0138 

.01380 

.00010 

.01380 

72.468 

525,1 

.0139 

.01390 

.00010 

.01390 

71.947 

517,5 

O.OI4O 

O.OI4OO 

IO,O 

I.OOOIO 

0,1 

0.01400 

IO,O 

71.433 

510,2 

.0141 

.OI4IO 

.00010 

.01410 

70.927 

503,0 

.OI42 

.OI42O 

.00010 

.01420 

70.427 

495,9 

.0143 

.01430 

.00010 

.01430 

69.935 

489,0 

.0144 

.01440 

.00010 

.01440 

69.449 

482,2 

0.0145 

O.OI45O 

10,0 

I.OOOII 

0,1 

0.01450 

IO,0 

68.970 

475,6 

.0146 

.01460 

.OOOII 

.01460 

68.498 

469,1 

.0147 

.01470 

.OOOII 

.01470 

68.032 

462,7 

.0148 

.01480 

.OOOII 

.01480 

67.573 

456,5 

.0149 

.01400 

.OOOII 

.01490 

67.119 

450,4 

0.0150 

O.OI5OO 

10,0 

I.OOOII 

0,2 

0.01500 

IO,0 

66.672 

444,4 

U 

tan  gd  u 

•  Fo' 

sec  gd  u 

•  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


90 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

u>F0' 

COSh  u 

«Fo' 

tanh  u 

-   Fo' 

coth  u 

«  Fo' 

0.0150 

©.CISCO 

IO,O 

I.OOOII 

0,2 

0.01500 

10,0 

66.672 

444»4 

.0151 

.01510 

.OOOII 

.01510 

66.230 

438,5 

.0152 

.OI52O 

.00012 

.01520 

65.795 

432,8 

.0153 

.01530 

.00012 

.01530 

65.365 

427,2 

.0154 

.01540 

.00012 

.01540 

64.940 

421,6 

0.0155 

0.01550 

IO,0 

I.OOOI2 

0,2 

O.OI55O 

10,0 

.64.521 

416,2 

.0156 

.01560 

.00012 

.01560 

64.108 

410,9 

•0157 

.01570 

.OOOI2 

.01570 

63.699 

405,7 

.0158 

.01580 

.OOOI2 

.01580 

63.296 

400,5 

.0159 

.01590 

.00013 

.01590 

62.898 

395,5 

0.0160 

O.OI60O 

IO,O 

I.OOOI3 

0,2 

0,01000 

10,0 

62.505 

390,6 

.0161 

.Ol6lO 

.OOOI3 

.Ol6lO 

62.117 

385,8 

.0162 

.01620 

.00013 

.01620 

61.734 

381,0 

•0163 

.01630 

.00013 

.01630 

61.355 

376,3 

.0164 

.01640 

.00013 

.01640 

60.981 

37i3 

0.0165 

0.01650 

IO,0 

I.OOOI4 

0,2 

0.01650 

10,0 

60.612 

367,3 

.0166 

.Ol66o 

.00014 

.01660 

60.247 

362,9 

.0167 

.01670 

.OOOI4 

.01670 

59-886 

358,5 

.0168 

.01680 

.OOOI4 

.01680 

59-529 

354,3 

.0169 

.01690 

.00014 

.01690 

59-177 

350,1 

0.0170 

O.OI70O 

10,0 

I.OOOI4 

0,2 

O.OI7OO 

IO,O 

58.829 

346,0 

.0171 

.OI7IO 

.00015 

.01710 

58.485 

342,0 

.0172 

.OI72O 

.00015 

.01720 

58.145 

338,0 

•0173. 

.01730 

.00015 

.01730 

57.809 

334,1 

.0174 

.OI74O 

.00015 

.01740 

57.477 

330,3 

0.0175 

O.OI75O 

10,0 

I.OOOI5 

0,2 

0.01750 

IO,O 

57.149 

326,5 

.0176 

.01760 

.00015 

.01760 

56.824 

322,8 

.0177 

.01770 

.00016 

.01770 

56.503 

319,2 

.0178 

.01780 

.00016 

.01780 

56.186 

315,6 

.0179 

.01790 

.OOOl6 

.01790 

55.872 

312,1 

0.0180 

O.OlSoO 

IO,O 

I.  OOOl6 

0,2 

O.OlSoo 

IO,O 

55  •  562 

308,6 

.0181 

.OlSlO 

.000l6 

.OlSlO 

55.255 

305,2 

.0182 

.Ol82O 

.00017 

.01820 

54.951 

301,9 

.0183 

.01830 

.00017 

.01830 

54-651 

298,6 

.0184 

.01840 

.00017 

.01840 

54-354 

295,3 

0.0185 

O.OI85O 

IO,O 

I.OOOI7 

O,2 

0.01850 

10,0 

54.060 

292,2 

.0186 

.01860 

.00017 

.01860 

53.770 

289,0 

.0187 

.01870 

.OOOI7 

.01870 

53.482 

285,9 

.0188 

.01880 

.OOOlS 

.01880 

53.198 

282,9 

.0189 

.01800 

.00018 

.01890 

52.916 

279,9 

0.0190 

0.01900 

IO,O 

I.OOOlS 

0,2 

0.01900 

10,0 

52.638 

277,0 

.0191 

.OI9IO 

.OOOlS 

.01910 

52.362 

274,1 

.0192 

.OI92O 

.OOOlS 

.01920 

52.090 

271,2 

.0193 

.01930 

.OOOI9 

.01930 

51.820 

268,4 

.0194 

.OI94O 

.00019 

.01940 

5L553 

265,7 

0.0195 

O.OI95O 

IO,0 

I.OOOI9 

0,2 

0.01950 

10,0 

51.289 

263,0 

.0196 

.01960 

.00019 

.01960 

51.027 

260,3 

.0197 

.OI97O 

.00019 

.01970 

50.768 

257,6 

.0198 

.01980 

.OO02O 

.01980 

50.512 

255,0 

.0109 

.01990 

.OOO20 

.01990 

50.258 

252,5 

O.O2OO 

O.O2OOO 

IO,O 

I.OOO2O 

0,2 

O.020OO 

IO,O 

50.007 

250,0 

U 

tan  gd  u 

»  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«   Fo' 

esc  gd  u 

«   Fo' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

o»Fo' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

O.O2OO 

O.O20OO 

IO,O 

I.O0020 

O,2 

O.O20OO 

IO,O 

50.007 

250,0 

.0201 

.02010 

.00020 

.O2OIO 

49.758 

247,5 

.0202 

.O2O2O 

.OOO2O 

.O2O2O 

49.512 

245,o 

.0203 

.0203O 

.00021 

.O2O3O 

49.268 

242,6 

.02O4 

.02040 

.O002I 

.02O40 

49.026 

240,3 

O.O205 

O.O2O50 

IO,O 

I.O002I 

0,2 

0.02O5O 

IO,O 

48.787 

237,9 

.0206 

.02O6O 

.O002I 

.02000 

48.551 

235,6 

.O207 

.02O70 

.00021 

.02070 

48.316 

233,3 

.0208 

.O2O8O 

.00022 

.02080 

48.084 

231,1 

.0209 

.02000 

.00022 

.O2OOO 

47.854 

228,9 

O.O2IO 

O.O2IOO 

IO,O 

I.OOO22 

0,2 

O.O2IOO 

10,0 

47.626 

226,7 

.O2I  I 

.021  10 

.OOO22 

I 

.021  10 

47.400 

224,6 

.O2I2 

.O2I2O 

.OOO22 

.02I2O 

47.177 

222,5 

.0213 

.02I3O 

.00023 

.02130 

46.955 

220,4 

.O2I4 

.O2I4O 

.OOO23 

.02I4O 

46.736 

218,3 

0.0215 

0.02150 

10,0 

I.O0023 

0,2 

0.02150 

IO,O 

46.519 

216,3 

.0216 

.02100 

.00023 

.02100 

46.303 

214,3 

.O2I7 

.02170 

.00024 

.02170 

46.090 

212,3 

.0218 

.02180 

.00024 

.O2l8o 

45.879 

210,4 

.O2I9 

.02190 

.OOO24 

.O2IOX) 

45-669 

208,5 

O.O22O 

O.O22OO 

IO,O 

I.OOO24 

0,2 

O.O22OO 

IO,O 

45.462 

206,6 

.O22I 

.022IO 

.OOO24 

.02210 

45.256 

204,7 

.O222 

.O222O 

.OOO25 

.O222O 

45.052 

202,9 

.O223 

.0223O 

.00025 

.0223O 

44.850 

2OI,I 

.O224 

.O224O 

.00025 

.O224O 

44.650 

199,3 

0.0225 

0.02250 

10,0 

I.OOO25 

0,2 

O.O225O 

10,0 

44.452 

197,5 

.O226 

.O226O 

.OOO26 

.O226O 

44.255 

195,7 

.O227 

.O227O 

.00026 

.02270 

44.060 

194,0 

.0228 

.O228O 

.OOO26 

.02280 

43.867 

192,3 

.O229 

.02290 

.OOO26 

.02290 

43.676 

190,7 

O.O23O 

0.02300 

10,0 

1.00026 

0,2 

O.O23OO 

IO,O 

43.486 

189,0 

.O23I 

.O23IO 

.00027 

.O23IO 

43.298 

187,4 

.O232 

.O232O 

.OOO27 

.0232O 

43.111 

185,8 

.0233 

.02330 

.OOO27 

.02330 

42.926 

184,2 

.0234 

.02340 

.00027 

.02340 

42.743 

182,6 

0.0235 

0.02350 

IO,O 

I.OO028 

0,2 

0.02350 

10,0 

42.561 

181,1 

.0236 

.02360 

.OOO28 

.02360 

42.381 

179,5 

.0237 

.02370 

.OO028 

.02370 

42.202 

178,0 

.0238 

.02380 

.00028 

.02380 

42.025 

176,5 

.0239 

.023yO 

.00029 

.02300 

41.849 

175,0 

O.O24O 

0.02400 

10,0 

I.OOO29 

0,2 

0.02400 

10,0 

41.675 

173,6 

.0241 

.O24IO 

.OOO29 

.O24IO 

41.502 

172,1 

.O242 

.O2420 

.00029 

.02420 

41.330 

170,7 

.0243 

.02430 

.00030 

.02430 

41.160 

169,3 

.0244 

.02440 

.OOO3O 

.02440 

40.992 

167,9 

0.0245 

O.O245O 

10,0 

1.00030 

0,2 

O.O2450 

IO,O 

40.824 

166,6 

.0246 

.02460 

.00030 

.02400 

40.659 

165,2 

.0247 

.02470 

.00031 

.02469 

40.494 

163,9 

.0248 

.02480 

.00031 

.02479 

40.331 

162,6 

.0249 

.02400 

.OOO3I 

.02489 

40.169 

161,3 

0.0250 

O.O25OO 

IO,O 

I.0003I 

0,3 

O.02499 

10,0 

40.008 

160,0 

u 

tin  gd  u 

-  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u         ...  F0' 

csc  gd  u 

-  Fo' 

SMITHSONIAN  TABLE* 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«FO' 

cosh  u 

«F0' 

tanh  u 

«   Fo' 

coin  u 

«  Fo' 

0.0250 

O.O25OO 

IO,O 

I.OOO3I 

0,3 

0.02499 

10,0 

40.008 

160,0 

.0251 

.02510 

.OOO32 

.02509 

39.849 

158,7 

.0252 

.02520 

.OOO32 

.02519 

39.691 

157,4 

.0253 

.02530 

.O0032 

.02529 

39.534 

156,2 

.0254 

.02540 

.OOO32 

•02539 

39.379 

155,0 

0.0255 

O.O255O 

10,0 

1.00033 

0,3 

0.02549 

IO,O 

39.224 

153,8 

.0256 

.02560 

.00033 

.02559 

39.071 

152,6 

.0257 

.02570 

.00033 

.02569 

38.919 

i5i,4 

.0258 

.02580 

.00033 

.02579 

38.768 

.     150,2 

.0259 

.02590 

.00034 

.02589 

38.619 

149,0 

0.0260 

0.02600 

10,0 

1.00034 

0,3 

0.02599 

10,0 

38.470 

147,9 

.0261 

.026lO 

.00034 

.02609 

38.323 

146,8 

.0262 

.O262O 

.00034 

.02619 

38.177 

145,7 

.0263 

.02630 

.00035 

.02629 

38.032 

144,5 

.0264 

.02640 

.00035 

.02639 

37-888 

143,4 

0.0265 

0.02650 

IO,O 

1.00035 

0,3 

0.02649 

IO,O 

37.745 

142,4 

.0266 

.02660 

.00035 

.02659 

37.603 

I4i,3 

.0267 

.02670 

.00036 

.02669 

37.462 

140,2 

.0268 

.02680 

.00036 

.02679 

37.322 

139,2 

.0269 

.02690 

.00036 

.02689 

37.184 

138,2 

0.0270 

O.O27OO 

IO,O 

1.00036 

0,3 

0.02699 

IO,O 

37.046 

137,1 

.0271 

.O27IO 

.00037 

.02709 

36.909 

136,1 

.0272 

.02720 

.00037 

.02719 

36.774 

135,1 

.0273 

.02730 

.00037 

.02729 

36.639 

134,1 

.0274 

.02740 

.00038 

.02739 

36.505 

133,2 

0.0275 

0.02750 

IO,O 

1.00038 

0,3 

0.02749 

10,0 

36.373 

132,2 

.0276 

.02760 

.00038 

.02759 

36.241 

131,2 

.0277 

.02770 

.00038 

.02769 

36.110 

130,3 

.0278 

.02780 

.00039 

.02779 

35.980 

129,4 

.0279 

.02790 

.00039 

.02789 

35.852 

128,4 

0.0280 

O.O28OO 

IO,O 

1.00039 

0,3 

0.02799 

10,0 

35.724 

127,5 

.0281 

.O28lO 

.00039 

.02809 

35.597 

126,6 

.0282 

.O282O 

.00040 

.02819 

35.470 

125,7 

.0283 

.02830 

.00040 

.02829 

35.345 

124,8 

.0284 

.02840 

.00040 

.02839 

35.221 

124,0 

0.0285 

O.O285O 

IO,O 

1.00041 

0,3 

0.02849 

10,0 

35.097 

123,2 

.0286 

.02860 

.00041 

.02859 

34.975 

122,2 

.0287 

.02870 

.00041 

.02869 

34.853 

121,4 

.0288 

.02880 

.00041 

.02879 

34.732 

120,5 

.0289 

.02890 

.00042 

.02889 

34.612 

H9,7 

0.0290 

O.O2OOO 

IO,O 

1.00042 

0,3 

0.02899 

10,0 

34.492 

118,9 

.0291 

.O29IO 

.00042 

.02909 

34.374 

118,1 

.0292 

.0292O 

.00043 

.02919 

34.256 

117,2 

.0293 

.O293O 

.00043 

.02929 

34.139 

116,4 

.0294 

.02940 

.00043 

.02939 

34.023 

115,7 

0.0295 

0.02950 

10,0 

1.00044 

0,3 

0.02949 

10,0 

33.908 

114,9 

.0296 

.02960 

.00044 

.02959 

33.794 

114,1 

.0297 

.O297O 

.00044 

.02969 

33.680 

H3,3 

.0298 

.02980 

.00044 

.02979 

33.567 

112,6 

.0299 

.02990 

.00045 

.02989 

33.455 

111,8 

0.0300 

0.03000 

10,0 

1.00045 

0,3 

0.02999 

IO,O 

33.343 

in,  i 

u 

tan  gd  u 

<-  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


93 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F</ 

cosh  u 

•  Fo' 

tanh  u 

«  Fo' 

coth  u 

*>  Fo' 

0.0300 

0.03000 

10,0 

1.00045 

0,3 

0.02999 

10,0 

33.343 

III,I 

.0301 

.O30IO 

.00045 

.03009 

33.233 

1  10,3 

.0302 

.03020 

.00046 

.03019 

33.123 

109,6 

.0303 

.03030 

.00046 

.03029 

33.013 

108,9 

.0304 

.03040 

.00046 

.03039 

32.905 

108,2 

0.0305 

O.03O5O 

IO,O 

1.00047 

0,3 

0.03049 

10,0 

32.797 

107,5 

.0306 

.03060 

.00047 

.03059 

106,8 

.0307 

.03070 

.00047 

.03069 

32  .  584 

106,1 

.0308 

.03080 

.00047 

.03079 

32.478 

105,4 

.0309 

.03000 

.00048 

.03089 

32.373 

104,7 

0.0310 

0.03IOO 

IO,O 

1.00048 

0,3 

0.03099 

IO,O 

32.268 

104,0 

.0311 

.O3III 

.00048 

.03109 

32.165 

103,4 

.0312 

.O3I2I 

.00049 

.03119 

32.062 

102,7 

.0313 

.03131 

.00049 

.03129 

31.959 

102,0 

.0314 

.03141 

.00049 

.03139 

31.858 

101,4 

0.0315 

0.03I5I 

IO,O 

1.00050 

0,3 

0.03149 

10,0 

31.757 

100,7 

.0316 

.03161 

.00050 

.03159 

31.656 

IOO,I 

.0317 

.03171 

.00050 

.03169 

31.556 

99,5 

.0318 

.03181 

.00051 

.03179 

31.457 

98,9 

.0319 

.03191 

.00051 

.03189 

31.359 

98,2 

0.0320 

0.03201 

10,0 

1.00051 

0,3 

0.03199 

IO,O 

31.261 

97,6 

.0321 

.03211 

.00052 

.03209 

31.163 

97,o 

.0322 

.03221 

.00052 

.03219 

31.067 

96,4 

.0323 

.03231 

.00052 

.03229 

30.971 

95,8 

.0324 

.03241 

.00052 

.03239 

30.875 

95,2 

0.0325 

O.O325I 

IO,O 

1.00053 

0,3 

0.03249 

IO,O 

30.780 

94,6 

.0326 

.03261 

.00053 

.03259 

30.686 

94,1 

.0327 

.03271 

.00053 

.03269 

30.592 

93,5 

.0328 

.03281 

.00054 

.03279 

30.499 

92,9 

.0329 

.03291 

.00054 

.03289 

30.406 

92,4 

0.0330 

0.03301 

IO,O 

1.00054 

0,3 

0.03299 

10,0 

30.314 

9i,8 

.0331 

.03311 

.00055 

.03309 

30.223 

91,2 

.0332 

.03321 

.00055 

.03319 

30.132 

90,7 

.0333 

.03331 

.00055 

.03329 

30.041 

90,1 

•  0334 

.03341 

.00056 

•03339 

29.951 

89,6 

0.0335 

0.03351 

IO,O 

1.00056 

0,3 

0.03349 

IO,O 

29.862 

89,1 

.0336 

.03361 

.00056 

•03359 

29.773 

88,5 

•  0337 

•03371 

.00057 

.03369 

29.685 

88,0 

.0338 

•03381 

.00057 

•03379 

29.597 

87,5 

.0339 

.03391 

.00057 

.03389 

29.510 

87,0 

0.0340 

O.O34OI 

IO,O 

1.00058 

0,3 

0.03399 

IO,O 

29.423 

86,6 

.0341 

.034H 

.00058 

.03409 

29.337 

86,0 

.0342 

.03421 

.00058 

•03419 

29.251 

85,5 

.0343 

•03431 

.00059 

.03429 

29.166 

85,0 

•0344 

.03441 

.00059 

•03439 

29.081 

84,5 

0.0345 

0.03451 

10,0 

1.00060 

0,3 

0.03449 

IO,O 

28.997 

84,0 

.0346 

.03461 

.00060 

.03459 

28.913 

83,5 

•  0347 

.03471 

.00060 

.03469 

28.830 

83,0 

.0348 

.03481 

.00061 

.03479 

28.747 

82.5 

.0349 

.03491 

.00061 

.03489 

28.665 

82,1 

0.0350 

O.O35OI 

10,0 

i.  00061 

0,4 

0.03499 

1  0,0 

28.583 

81,6 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


94 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«Fo' 

cosh  u 

"Fo' 

tanh  u 

«  Fo' 

colh  u 

«  Fo' 

0.0350 

0.03501 

IO,O 

I.  00061 

0,4 

0.03499 

IO,O 

28.583 

81,6 

•0351 

.03511 

.00062 

.03509 

28.502 

81,1 

•0352 

.03521 

.00062 

.03519 

28.421 

80,7 

.0353 

.03531 

.00062 

.03529 

28.340 

80,2 

.0354 

.03541 

.00063 

•03539 

28.260 

79,8 

0.0355 

\J+J*J 

0.03551 

10,0 

1.00063 

0,4 

0.03549 

IO,O 

28.181 

79,3 

.0356 

.03561 

.00063 

.03558 

28.102 

78,9 

.0357 

.03571 

.00064 

.03568 

28.023 

78,4 

.0358 

.03581 

.00064 

.03578 

27.945 

78,o 

.0359 

.03591 

.00064 

.03588 

27.867 

77,6 

0.0360 

0.03601 

10,0 

1.00065 

0,4 

0.03598 

IO,O 

27.790 

77,i 

.0361 

.03611 

.00065 

.03608 

27.713 

76,7 

.0362 

.03621 

.00066 

.03618 

27.636 

76,3 

.0363 

.03631 

.00066 

.03628 

27.560 

75,9 

.0364 

.03641 

.00066 

.03638 

27.485 

75,4 

0.0365 

0.03651 

10,0 

1.00067 

0,4 

0.03648 

10,0 

27.409 

75,0 

.0366 

.03661 

.00067 

.03658 

27.335 

74,6 

.0367 

.03671 

.00067 

.03668 

27.260 

74,2 

.0368 

.03681 

.00068 

.03678 

27.186 

73,8 

.0369 

.03691 

.00068 

.03688 

27.113 

73,4 

0.0370 

0.03701 

10,0 

1.00068 

0,4 

0.03698 

IO,O 

27.039 

73,0 

.0371 

.03711 

.00069 

.03708 

26.067 

72,6 

.0372 

.03721 

.00069 

.03718 

26.894 

72,2 

.0373 

.03731 

.00070 

.03728 

26.822 

7i,8 

•0374 

.03741 

.00070 

.03738 

26.750 

7i,5 

0.0375 

0.03751 

10,0 

1.00070 

0,4 

0.03748 

IO,O 

26.679 

7i,i 

.0376 

.03761 

.00071 

.03758 

26.608 

70,7 

.03/7 

•03771 

.00071 

.03768 

26.538 

70,3 

.0378 

.03781 

.00071 

.03778 

26.468 

70,0 

•  0379 

.03791 

.00072 

.03788 

26.398 

69,6 

0.0380 

0.03801 

IO,O 

1.00072 

0,4 

0.03798 

10,0 

26.328 

69,2 

.0381 

.03811 

.00073 

.03808 

26.259 

68,9 

.0382 

.03821 

.00073 

.03818 

26.191 

68,5 

.0383 

.03831 

.00073 

.03828 

26.122 

68,1 

.0384 

.03841 

.00074 

.03838 

26.054 

67,8 

0.0385 

0.03851 

10,0 

1.00074 

0,4 

0.03848 

10,0 

25.987 

67,4 

.0386 

.03861 

.00075 

.03858 

25.920 

67,1 

.0387 

.03871 

.00075 

.03868 

25.853 

66,7 

.0388 

.03881 

.00075 

.03878 

25.786 

66,4 

.0389 

.03891 

.00076 

.03888 

25.720 

66,1 

0.0300 

O.0390I 

10,0 

1.00076 

0,4 

0.03898 

10,0 

25.654 

65,7 

.0391 

.039H 

.00076 

.03908 

25.588 

65,4 

.0392 

.03921 

.00077 

.03918 

25.523 

64,0 

•  0393 

.03931 

.00077 

.03928 

25.458 

64,7 

•  0394 

.03941 

.00078 

.03938 

25.394 

64,4 

0.0395 

0.03951 

IO,0 

1.00078 

0,4 

0.03948 

10,0 

25.330 

64,1 

.0306 

.03061 

.00078 

.03958 

25.266 

63,7 

.0397 

.03971 

.00079 

.03968 

25.202 

63,4 

.0398 

.03981 

.00079 

.03978 

25  .  139 

63,1 

•  0399 

.03991 

.00080 

.03988 

25.076 

62,8 

0.0400 

O.O4OOI 

IO,0 

1.00080 

0,4 

0.03998 

10,0 

25.013 

62,5 

u     tan  gd  u 

«FO' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

«-  Fo' 

I 

SMITHSONIAN  TABLES 


95 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

COSh  u 

wF0' 

tanh  u 

-  Fo' 

coth  u 

«  Fo' 

0.0400 

O.O4OOI 

10,0 

1.00080 

0,4 

0.03998 

10,0 

25.013 

62,5 

.0401 

.04011 

.00080 

.04008 

24.951 

62,2 

.0402 

.04021 

.00081 

.04018 

24.889 

61,8 

.0403 

.04031 

.OOoSi 

.04028 

24.827 

61,5 

.0404 

.04041 

.00082 

.04038 

24.766 

61,2 

0.0405 

0.04051 

IO,O 

I.OOO82 

0,4 

0.04048 

IO,O 

24.705 

60,8 

.0406 

.04061 

.00082 

.04058 

24.644 

60,6 

.0407 

.04071 

.00083 

.04068 

24.584 

60,3 

.0408 

.04081 

.00083 

.04078 

24.523 

60,0 

.0409 

.04091 

.00084 

.04088 

24.464 

59,7 

0.0410 

O.O4IOI 

IO,O 

1.00084 

0,4 

0.04098 

IO,O 

24.404 

59,5 

.0411 

.04111 

.00084 

.04108 

24.345 

59,2 

.0412 

.04121 

.00085 

.04118 

24.286 

58,9 

.0413 

.04131 

.00085 

.04128 

24.227 

58,7 

.0414 

.04141 

.00086 

.04138 

24.168 

58,3 

0.0415 

0.04151 

IO,O 

1.00086 

0,4 

0.04148 

10,0 

24.IIO 

58,0 

.0416 

.04161 

.00087 

.04158 

24.052 

57,8 

.0417 

.04171 

.00087 

.04168 

23.995 

57,5 

.0418 

.04181 

.00087 

.04178 

23.937 

57,2 

.0419 

.04191 

.00088 

.04188 

23.880 

56,9 

0.0420 

0.04201 

10,0- 

1.00088 

0,4 

0.04198 

IO,O 

23.824 

56,7 

.0421 

.04211 

.00089 

.04208 

23.767 

56,4 

.0422 

.04221 

.00089 

.04217 

23.7H 

56,i 

.0423 

.04231 

.00089 

.04227 

23.655 

55,9 

.0424 

.04241 

.00090 

.04237 

23.599 

55,6 

0.0425 

0.04251 

IO,O 

I.OOOOO 

0,4 

0.04247 

IO,O 

23.544 

55,3 

.0426 

.04261 

.00091 

.04257 

23-488 

55,1 

.0427 

.04271 

.00091 

.04267 

23-433 

54,8 

.0428 

.04281 

.00092 

.04277 

23.379 

54,6 

.0429 

.04291 

.00092 

.04287 

23.324 

54,3 

0.0430 

0.04301 

10,0 

1.00092 

0,4 

0.04297 

10,0 

23.270 

54,0 

.0431 

.043H 

.00093 

.04307 

23.216 

53,8 

.0432 

.04321 

.00093 

.04317 

23-163 

53,6 

.0433 

.04331 

.00094 

.04327 

23.109 

53,3 

.0434 

.04341 

.00094 

•04337 

23.056 

53,1 

0.0435 

0.04351 

IO,O 

1.00095 

0,4 

0.04347 

10,0  . 

23.003 

52,8 

.0436 

.04361 

.00095 

.04357 

22.95O 

52,6 

.0437 

.04371 

.00095 

.04367 

22.898 

52,3 

.0438 

.04381 

.00096 

•04377 

22.846 

52,i 

.0439 

.04391 

.00096 

.04387 

22.794 

5i,9 

0.0440 

0.04401 

IO,0 

1.00097 

0,4 

0.04397 

IO,O 

22.742 

5i,6 

.0441 

.04411 

.00097 

.04407 

22.690 

51,4 

.0442 

.04421 

.00098 

.04417 

22.639 

51,2 

•  0443 

.04431 

.00008 

.04427 

22.588 

50,9 

.0444 

.04441 

.00099 

.04437 

22.537 

50,7 

0.0445 

0.04451 

10,0 

1.00099 

0,4 

0.04447 

IO,O 

22.487 

50,5 

.0446 

.04461 

.00099 

•04457 

22.436 

50,2 

.0447 

.04471 

.00100 

.04467 

22.386 

50,0 

.0448 

.04481 

.00100 

.04477 

22.336 

49,8 

.0449 

.04492 

.OOIOI 

.04487 

22.287 

49,6 

0.0450 

O.O4502 

IO,O 

I.OOIOI 

0,5 

0.04497 

1  0,0 

22.237 

49,3 

u 

tan  gd  u 

-  Fo' 

sec  gd  u 

•  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u     -  Fo' 

SMITHSONIAN  TABLES 


96 


Natural  Hyperbolic  Functions. 


u 

tinh  u 

»F0' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

COth  u 

»  Fo' 

0.0450 

O.O45O2 

10,0 

I.OOIOI 

0,5 

0.04497 

10,0 

22.237 

49,3 

.0451 

.04512 

.00102 

.04507 

22.188 

49,1 

.0452 

.04522 

.00102 

.04517 

22.139 

48,9 

.0453 

.04532 

.00103 

.04527 

22.OOO 

48,7 

.0454 

.04542 

.00103 

.04537 

22.042 

48,5 

0.0455 

0.04552 

10,0 

1.00104 

o,5 

0.04547 

10,0 

21.993 

48,3 

.0456 

.04562 

.00104 

.04557 

21-945 

48,1 

.0457 

.04572 

.00104 

.04567 

21.897 

47,8 

.0458 

.04582 

.00105 

•04577 

21.849 

47,6 

.0459 

.04592 

.00105 

.04587 

21.802 

47,4 

0.0460 

0.04602 

10,0 

1.00106 

o,5 

0.04597 

10,0 

21.754 

47,2 

.0461 

.04612 

.00106 

.04607 

21.707 

47,o 

.0462 

.04622 

.00107 

.04617 

21.660 

46,8 

.0463 

.04632 

.00107 

.04627 

21.614 

46,6 

.0464 

.04642 

.00108 

.04637 

21.567 

46,4 

0.0465 

0.04652 

.  10,0 

1.00108 

o,5 

0.04647 

10,0 

21.521 

46,2 

.0466 

.04662 

.00109 

.04657 

21.475 

46,0 

.0467 

.04672 

.00109 

.04667 

21.429 

45,8 

.0468 

.04682 

.OOIIO 

.04677 

21.383 

45,6 

.0469 

.04692 

.OOIIO 

.04687 

21.338 

45,4 

0.0470 

0.04702 

IO,0 

I.  OOIIO 

o,5 

0.04697 

IO,O 

21.292 

45,2 

.0471 

.04712 

.OOIII 

.04707 

21.247 

45,o 

.0472 

.04722 

.OOIII 

.04716 

21.  2O2 

44,9 

•0473 

.04732 

.OOII2 

.04726 

21.157 

44,7 

.0474 

.04742 

.OOII2 

.04736 

21.113 

44,5 

0.0475 

0.04752 

10,0 

1.00113 

o,5 

0.04746 

IO,O 

21.068 

44,3 

.0476 

.04762 

.00113 

.04756 

2I.O24 

44,1 

.0477 

.04772 

.00114 

.04766 

2O.O80 

43,9 

.0478 

.04782 

.00114 

.04776 

20.936 

43,7 

.0479 

.04792 

.00115 

.04786 

20.893 

43,6 

0.0480 

0.04802 

10,0 

1.00115 

o,5 

0.04796 

IO,O 

20.849 

43,4 

.0481 

.04812 

.00116 

.04806 

20.806 

43,2 

.0482 

.04822 

.00116 

.04816 

20.763 

43,0 

.0483 

.04832 

.00117 

.04826 

20.720 

42,8 

.0484 

.04842 

.00117 

.04836 

20.677 

42,7 

0.0485 

0.04852 

10,0 

I.  00118 

o,5 

0.04846 

10,0 

20.635 

42,5 

.0486 

.04862 

.00118 

.04856 

20.592 

42,3 

.0487 

.04872 

.00119 

.04866 

20.550 

42,1 

.0488 

.04882 

.00119 

.04876 

20.508 

42,0 

.0489 

.04892 

.00120 

.04886 

20.466 

41,8 

0.0490 

0.04902 

10,0 

I.  00120 

o,5 

0.04896 

10,0 

2O.424 

41,6 

.0491 

.04912 

.00121 

.04006 

20.383 

41,4 

.0492 

.04922 

.00121 

.04916 

20.342 

4i,3 

.0493 

.04932 

.00122 

.04926 

20.300 

41,1 

.0494 

.04942 

.00122 

.04936 

20.259 

40,9 

0.0495 

0.04952 

10,0 

I.OOI23 

o,5 

0.04946 

10,0 

2O.2I9 

40,8 

.0496 

.04962 

.00123 

.04956 

2O.I78 

40,6 

.0497 

.04972 

.00124 

.04966 

20.137 

40,5 

.0498 

.04982 

.00124 

.04976 

20.097 

40,3 

.0499 

.04992 

.00125 

.04986 

20.057 

40,1 

0.0500 

O.O5OO2 

IO,O 

I.OOI25 

o,5 

0.04996 

10,0 

20.017 

40,0 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


97 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.0500 

O.O5OO2 

IO,O 

1.00125 

0,5 

0.04996 

IO,O 

20.017 

4O,O 

.0501 

.O50I2 

.00126 

.05006 

19-977 

39,8 

.0502 

.O5O22 

.00126 

.05016 

19-937 

39,6 

.0503 

.05032 

.00127 

.05026 

19.897 

39,5 

.0504 

.05042 

.00127 

.05036 

19.858 

39,3 

0.0505 

0.05052 

IO,O 

1.00128 

0,5 

0.05046 

IO,O 

I9.8I9 

39,2 

.0506 

.05062 

.00128 

.05056 

19.780 

39,0 

.0507 

.05072 

.00129 

.05066 

19.741 

38,9 

.0508 

.05082 

.00129 

.05076 

19.702 

38,7 

.0509 

.05092 

.00130 

.05086 

19.663 

38,6 

0.0510 

0.05102 

IO,O 

1.00130 

0,5 

0.05096 

10,0 

19.625 

38,4 

.0511 

.05112 

.00131 

.05106 

I9o87 

38,3 

.0512 

.05122 

.02131 

.05116 

19.548 

38,1 

.0513 

.05132 

.00132 

.05126 

I9.5IO 

38,0 

.0514 

.05142 

.00132 

.05135 

19.472 

37,8 

0.0515 

O.O5I52 

10,0 

1.00133 

0,5 

0.05145 

10,0 

19.435 

37,7 

.0516 

.05162 

.00133 

.05155 

19-397 

37,5 

.0517 

.05172 

.00134 

.05165 

19.360 

37,4 

.0518 

.05182 

.00134 

.05175 

19.322 

37,2 

.0519 

.05192 

.00135 

.05185 

19.285 

37,1 

0.0520 

0.05202 

IO,O 

1.00135 

0,5 

0.05195 

IO,O 

19.248 

36,9 

.0521 

.05212 

.00136 

.05205 

19.211 

36,8 

.0522 
.0523 

.05222 
.05232 

.00136 

.00137 

.05215 
.05225 

19.174 
19.138 

36,7 
36,5 

.0524 

.05242 

.00137 

.05235 

19.101 

36,4 

0.0525 

0.05252 

10,0 

1.00138 

0,5 

0.05245 

IO,O 

19.065 

36,2 

.0526 

.05262 

.00138 

.05255 

I9.O29 

36,1 

.0527 

.05272 

.00139 

.05265 

18.093 

36,0 

.0528 

.05282 

.00139 

.05275 

18.957 

35,8 

.0529 

.05292 

.00140 

.05285 

I8.92I 

35,7 

0.0530 

0.05302 

IO,O 

1.00140 

0,5 

0.05295 

1  0,0 

18.886 

35,6 

.0531 

.05312 

.00141 

.05305 

18.850 

35,4 

.0532 

.05323 

.00142 

.05315 

18.815 

35,3 

.0533 

.05333 

.00142 

.05325 

18.779 

35,2 

•  0534 

.05343 

.00143 

.05335 

18.744 

350 

0.0535 

0.05353 

IO,O 

I.  00143 

o,5 

0.05345 

10,0 

18.709 

34,9 

.0536 

.05363 

.00144 

•05355 

18.675 

34,8 

.0537 

.05373 

.00144 

.05365 

18.640 

34,6 

.0538 

.05383 

.00145 

.05375 

18.605 

34,5 

•  0539 

.05393 

.00145 

.05385 

18.571 

34,4 

0.0540 

0.05403 

IO,O 

1.00146 

o,5 

0.05395 

IO,O 

18.537 

34,3 

.0541 

.05413 

.00146 

.05405 

I8.5O2 

34,1 

.0542 

.05423 

.00147 

.05415 

18.468 

34.0 

.0543 
.0544 

.05433 
.05443 

.00147 
.00148 

•05425 
.05435 

18.434 
18.400 

33,9 
33,8 

0.0545 

0.05453 

10,0 

1.00149 

o,5 

0.05445 

1  0,0 

18.367 

33,6 

.0546 

.05463 

.00149 

.05455 

18.333 

33,5 

.0547 

.05473 

.00150 

.05465 

I8.3OO 

33,4 

.0548 

.05483 

.00150 

•05475 

18.266 

33,3 

.0549 

.05493 

.00151 

.05484 

18.233 

33,1 

0.0550 

0.05503 

10,0 

1.00151 

0,6 

0.05494 

1  0,0 

18.200 

33,0 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

•  Fo' 

tin  gd  u 

«-  Fu' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

»Fo' 

tanh  u 

•  FO' 

coth  u 

«F0' 

0.0550 

0.05503 

10,0 

1.00151 

0,6 

0.05494 

10,0 

18.200 

33,0 

.0551 

.05513 

.00152 

.05504 

18.167 

32,9 

.0552 

.0552J-. 

.00152 

.05514 

18.134 

32,8 

.0553 

.05533 

.00153 

.05524 

18.102 

32,7 

.0554 

.05543 

.00153 

.05534 

18.069 

32,5 

0.0555 

0.05553 

10,0 

1.00154 

0,6 

0.05544 

10,0 

18.037 

32,4 

•0556 

.05563 

.00155 

.05554 

l8.004 

32,3 

.0557 

.05573 

.00155 

.05564 

17.972 

32,2 

.0558 

.05583 

.00156 

.05574 

17.940 

32,1 

.0559 

.05593 

.00156 

.05584 

17.908 

32,0 

0.0560 

0.05603 

IO,O 

I.  00157 

0,6 

2.05594 

10,0 

17.876 

31,9 

.0561 

.05613 

.00157 

.05604 

17.844 

3i,7 

.0562 

.05623 

.00158 

.05614 

I7.8I2 

31,6 

•  0563 

•05633 

.00159 

.05624 

I7.78I 

31,5 

.0564 

.05643 

.00159 

.05634 

17.749 

31,4 

0.0565 

0.05653 

10,0 

I.  00160 

0,6 

0.05644 

IO,O 

17.718 

31,3 

.0566 

.05663 

.00160 

•05654 

17.687 

3i,2 

.0567 

.05673 

.00161 

.05664 

17.656 

3i,i 

.0568 

.05683 

.00161 

.05674 

17.625 

3i,o 

.0569 

.05693 

.00162 

.05684 

17.594 

30,9 

0.0570 

0.05703 

10,0 

1.00162 

0,6 

0.05604 

IO,O 

17.563 

30,7 

•  0571 

.05713 

.00163 

.05704 

17.532 

30,6 

.0572 

.05723 

.00164 

•05714 

17.502 

30,5 

.0573 

•05733 

.00164 

.05724 

17.471 

30,4 

•  0574 

.05743 

.00165 

.05734 

17.441 

30,3 

0.0575 

0.05753 

10,0 

1.00165 

0,6 

0.05744 

10,0 

17.410 

30,2 

.0576 

.05763 

.00166 

.05754 

17.380 

30,1 

.0577 

.05773 

.00167 

.05764 

17.350 

30,0 

.0578 

.05783 

.00167 

.05774 

17.320 

29,9 

.0579 

.05793 

.00168 

.05784 

17.290 

.   29,8 

0.0580 

0.05803 

10,0 

1.00168 

0,6 

0.05794 

10,0 

I7.26l 

29,7 

.0581 

.05813 

.00169 

.05803 

17.231 

29,6 

.0582 

.05823 

.00169 

.05813 

17.202 

29,5 

.0583 

.05833 

.00170 

.05823 

17.172 

29,4 

.0584 

.05843 

.00171 

•  05833 

17.143 

29,3 

0.0585 

0.05853 

10,0 

1.00171 

0,6 

0.05843 

10,0 

17.114 

29,2 

.0586 

.05863 

.00172 

.05853 

17.084 

29,1 

.0587 

.05873 

.00172 

.05863 

17.055 

29,0 

.0588 

.05883 

.00173 

.05873 

17.026 

28,9 

.0589 

.05893 

.00174 

.05883 

16.998 

28,8 

0.0500 

0.05903 

IO,0 

I.  00174 

0,6 

0.05893 

IO,0 

16.069 

28,7 

.0591 

.05913 

.00175 

•05003 

16.940 

28,6 

.0592 

.05923 

.00175 

.05913 

16.912 

28,5 

.0593 

•05933 

.00176 

.05923 

16.883 

28,4 

.0594 

•05943 

.00176 

.05933 

16.855 

28,3 

0.0595 

0.05954 

IO,O 

1.00177 

0,6 

0.05943 

IO,O 

16.827 

28,2 

.0596 

.05964 

.00178 

•05953 

16.798 

28,1 

.0597 

.05974 

.00178 

.05063 

16.770 

28,0 

.0598 

.05984 

.00179 

.05973 

16.742 

27,9 

.0599 

.05994 

.00179 

•05083 

16.714 

27,8 

0.0600 

0.06004 

10,0 

1.00180 

0,6 

0.05093 

10,0 

16.687 

27,7 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES. 


99 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

cosh  u 

-Fo' 

tanh  u 

•  Fo' 

coth  u 

»Fo' 

0.0600 

0.06004 

IO,O 

I.OOlSo 

0,6 

0.05993 

IO,O 

16.687 

27,7 

.0601 

.06014 

.OOlSl 

.06003 

16.659 

27,7 

.0602 

.06024 

.OOlSl 

.06013 

16.631 

27,6 

.0603 

.06034 

.00182 

.06023 

16.604 

27,5 

.0604 

.00044 

.00182 

.06033 

16.576 

27,4 

0.0605 

0.06054 

IO,O 

1.00183 

0,6 

0.06043 

IO,O 

16.549 

27,3 

.0606 

.06064 

.00184 

.06053 

16.522 

27,2 

.0607 

.06074 

.00184 

.06063 

16.495 

27,1 

.0608 

.06084 

.00185 

.06073 

16.468 

27.0 

.0609 

.06094 

.00185 

.06082 

16.441 

26,9 

0.0610 

0.06104 

IO,O 

I.OOI86 

0,6 

0.06092 

IO,O 

16.414 

26,8 

.0611 

.06114 

.00187 

.06102 

16.387 

26,8 

.0612 

.06124 

.00187 

.06112 

16.360 

26,7 

.0613 

.06134 

.00188 

.06122 

16.334 

26,6 

.0614 

.06144 

.00189 

.06132 

16.307 

26,5 

0.0615 

0.06154 

IO,O 

1.00189 

0,6 

0.06142 

10,0 

16.281 

26,4 

.0616 

.06164 

.OOIOO 

.06152 

16.254 

26,3 

.0617 

.06174 

.00100 

.06162 

16.228 

26,2 

.0618 

.06184 

.00191 

.06172 

16.202 

26,1 

.0619 

.06194 

.00192 

.06182 

16.176 

26,1 

0.0620 

0.06204 

10,0 

I.OOI92 

0,6 

0.06192 

10,0 

16.150 

26,0 

.0621 

.06214 

.00193 

.06202 

16.124 

25,9 

.0622 

.06224 

.00194 

.06212 

16.098 

25,8 

.0623 

.06234 

.00194 

.06222 

16.072 

25,7 

.0624 

.06244 

.00195 

.06232 

16.046 

25,6 

0.0625 

0.06254 

IO,O 

I.OOI95 

0,6 

0.06242 

IO,O 

16.021 

25,6 

.0626 

.06264 

.00196 

.06252 

15.995 

25,5 

.0627 

.06274 

.00197 

.06262 

15.970 

25,4  I 

.0628 

.06284 

.00197 

.06272 

15.944 

25,3 

.0629 

.06294 

.00198 

.06282 

15.919 

25,2 

0.0630 

0.06304 

10,0 

I.OOI99 

0,6 

0.06292 

IO,O 

15.894 

25,2 

.0631 

.06314 

.00199 

.06302 

15.869 

25,1 

.0632 

.06324 

.OO2OO 

.06312 

15.844 

25,0 

.0633 

.06334 

.OO2OO 

.06322 

15.819 

24,9 

.0634 

.06344 

.OO2OI 

.06332 

15.794 

24,8 

0.0635 

0.06354 

IO,0 

I.OO2O2 

0,6 

0.06342 

10,0 

15.769 

24,8 

.0636 

.06364 

.00202 

.06351 

15.744 

24,7 

.0637 

.06374 

.OO2O3 

.06361 

15.720 

24,6 

.0638 

.06384 

.OO2O4 

.06371 

15.695 

24,5 

.0639 

.06394 

.00204 

.06381 

15.671 

24,5 

0.0640 

0.06404 

10,0 

I.OO205 

0,6 

0.06391 

10,0 

15.646 

24,4 

.0641 

.06414 

.OO2O6 

.06401 

15.622 

24,3 

.0642 

.06424 

.00206 

.06411 

15.598 

24,2 

.0643 

.06434 

.OO2O7 

.06421 

15.574 

24,2 

.0644 

.06444 

.OO2O7 

.06431 

15.549 

24,1 

0.0645 

0.06454 

10,0 

I.OO2O8 

0,6 

0.06441 

IO,O 

15.525 

24,0 

.0646 

.06464 

.00209 

.06451 

15.501 

23,9 

.0647 

.06475 

.00209 

.06461 

15.478 

23,9 

.0648 

.06485 

.00210 

.06471 

15.454 

23,8 

.0649 

.06495 

.00211 

.06481 

15.430 

23,7 

0.0650 

0.06505 

10,0 

I.OO2II 

o,7 

0.06491 

IO,O 

15.406 

23,6 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

-  Fo' 

csc  gd  u 

«  Fo' 

SMITHSONIAN  TABLCS 


IOO 


Natural  Hyperbolic  Function^ 


u 

sinh  u 

-Fo' 

cosh  u 

«F0' 

tanh  i- 

«  Fo'" 

coiK  tf  '. 

*F0' 

0.0650 

0.06505 

IO,O 

I.002II 

o,7 

0.06491 

10,0 

15.406 

23,6 

.0651 

.05515 

.00212 

.06501 

15.383 

23,6 

.0652 

.06525 

.00213 

.06511 

15-359 

23,5 

.0653 

.06535 

.00213 

.06521 

15.336 

23,4 

.0654 

.06545 

.OO2I4 

.06531 

15-312 

23,3 

0.0655 

0.06555 

IO,O 

I.OO2I5 

o,7 

0.06541 

10,0 

15.289 

23,3 

.0656 

.06565 

.OO2I5 

.06551 

15.266 

23,2 

.0657 

.06575 

.OO2l6 

.06561 

15.243 

23,1 

.0658 

.06585 

.00217 

.06571 

15.219 

23,1 

.0659 

.06595 

.OO2I7 

.06580 

15.196 

23,0 

0.0660 

O.O66O5 

IO,O 

I.OO2I8 

o,7 

0.06590 

IO,O 

15.174 

22,9 

.0661 

.06615 

.O02I9 

.06600 

15.151 

22,9 

.0662 

.06625 

.00219 

.06610 

15.128 

22,8 

.0663 

.06635 

.OO220 

.06620 

15.105 

22,7 

.0664 

.06645 

.OO22I 

.06630 

15.082 

22,6 

0.0665 

0.06655 

IO,O 

I.OO22I 

o,7 

0.06640 

IO,O 

15.060 

22,6 

.0666 

.06665 

.00222 

.06650 

15.037 

22,5 

.0667 

.06675 

.00223 

.06660 

15.015 

22,4 

.0668 

.06685 

.00223 

.06670 

14.992 

22,4 

.0669 

.06695 

.00224 

.06680 

14.970 

22,3 

0.0670 

0.06705 

IO,O 

1.00225 

o,7 

0.06690 

IO,O 

14.948 

22,2 

.0671 

.06715 

.00225 

.06700 

14.925 

22,2 

.0672 

.06725 

.OO226 

.06710 

14.903 

22,1 

.0673 

.06735 

.OO227 

.06720 

14.881 

22,O 

.0674 

.06745 

.00227 

.06730 

14.859 

22,O 

0.0675 

0.06755 

IO,O 

1.00228 

o,7 

0.06740 

10,0 

14-837 

21,9 

.0676 

.06765 

.OO229 

.06750 

14-815 

21,8 

.0677 

.06775 

.O0229 

.06760 

14-794 

21,8 

.0678 

.06785 

.00230 

.06770 

14.772 

21,7 

.xtf79 

.06795 

.00231 

.06780 

14.750 

21,7 

0.0680 

0.06805 

10,0 

I.OO23I 

o,7 

0.06790 

IO,O 

14.729 

'   21,6 

.0681 

.06815 

.00232 

.06799 

14.707 

21,5 

.0682 

.06825 

.00233 

.06809 

14.685 

21,5 

.0683 

.06835 

.00233 

.06819 

14.664 

21,4 

.0684 

.06845 

.00234 

.06829 

14.643 

21,3 

0.0685 

0.06855 

10,0 

1.00235 

o,7 

0.06839 

IO,O 

14.621 

21,3 

.0686 

.06865 

.00235 

.06849 

14.600 

21,2 

.0687 

.06875 

.00236 

.06859 

14.579 

21,2 

.0688 

.06885 

.00237 

.06869 

14.558 

21,1 

.0689 

.06895 

.00237 

.06879 

H-537 

21,0 

0.0690 

0.06005 

IO,O 

1.00238 

o,7 

0.06889 

IO,O 

I4.5I6 

21,0 

.0691 

.06916 

.00239 

.06899 

14-495 

20,9 

.0692 

.06926 

.00240 

.06909 

14.474 

20,8 

.0693 

.06936 

.00240 

.06919 

14-453 

20,8 

.0694 

.06946 

.00241 

.06929 

14.432 

20,7 

0.0695 

0.06956 

IO,O 

1.00242 

o,7 

0.06939 

IO,O 

14.412 

20,7 

.0696 

.06966 

.00242 

.06949 

14.391 

20,6 

.0697 

.06976 

.00243 

.06959 

14.370 

20,6 

.0698 

.06986 

.00244 

.06969 

14.350 

20,5 

.0699 

.06996 

.00244 

.06979 

14.329 

20,4 

0.0700 

0.07006 

10,0 

1.00245 

0,7 

0.06989 

IO,O 

14.309 

20,4 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


101 


'•Natural  Hyperbolic  Functions. 


u 

.*mhu    .«F0' 

cosh  iv 

«Fo* 

tanh  u 

«  Fo' 

coth  u 

«*  Fo' 

0.0700 

0.07006 

10,0 

1.00245 

0,7 

0.06989 

IO,O 

14.309 

20,4 

.0701 

.07016 

.00246 

.06999 

14.289 

20,3 

.0702 

.07026 

.00247 

.07008 

14.268 

20,3 

.0703 

.07036 

.00247 

4 

.07018 

14.248 

20,2 

.0704 

.07046 

.00248 

.07028 

14.228 

2O,  I 

0.0705 

0.07056 

10,0 

1.00249 

o,7 

0.07038 

10,0 

14.208 

20,1 

.0706 

.07066 

.00249 

.0/048 

14.188 

20,0 

.0707 

.07076 

.00250 

.07058 

14.168 

20,0 

.0708 

.07086 

.00251 

.07068 

14.148 

19,9 

.0709 

.07006 

.00251 

.07078 

9,9 

14.128 

19,9 

0.0710 

0.07106 

IO,0 

1.00252 

o,7 

0.07088 

9,9 

14.108 

19,8 

.0711 

.07116 

.00253 

.07098 

14.088 

19,7 

.0712 

.07126 

.00254 

.07108 

14.069 

19,7 

.0713 

.07136 

.00254 

.07118 

14.049 

19,6 

.0714 

.07146 

.00255 

.07128 

14.029 

19,6 

0.0715 

0.07156 

IO,O 

1.00256 

o,7 

0.07138 

9,9 

14.010 

19,5 

.0716 

.07166 

.00256 

.07148 

13.990 

19,5 

-  .0717 

.07176 

.00257 

.07158 

13.971 

19,4 

.0718 

.07186 

.00258 

.07168 

13.952 

19,4 

.0719 

.07196 

.00259 

.07178 

13.932 

19,3 

0.0720 

0.07206 

10,0 

1.00259 

o,7 

0.07188 

9,9 

13.913 

19,3 

.0721 

.07216 

.00200 

.07108 

13.894 

19,2 

.0722 

.07226 

.00261 

.07207 

13.874 

19,2 

.0723 

.07236 

.00261 

.07217 

13.855 

19,1 

.0724 

.07246 

.00262 

.07227 

13.836 

19,0 

0.0725 

0.07256 

IO,O 

1.00263 

o,7 

0.07237 

9,9 

13.817 

I9,o 

.0726 

.07266 

.00264 

.07247 

13.798 

18,9 

.0727 

.07276 

.00264 

.07257 

13.779 

18,9 

.0728 

.07286 

.00265 

.07267 

I3.76I 

18,8 

.0729 

.07296 

.00266 

.07277 

13.742 

1-8,8 

0.0730 

0.07306 

10,0 

1.00267 

o,7 

0.07287 

9,9 

13.723 

18,7 

.0731 

.07317 

.00267 

.07297 

13.704 

18,7 

.0732 

.07327 

.00268 

.07307 

13.686 

18,6 

.0733 

•07337 

.00269 

.07317 

13.667 

18,6 

.0734 

.07347 

.00269 

.07327 

13.648 

18,5 

0.0735 

0.07357 

IO,O 

1.00270 

o,7 

0.07337 

9,9 

13.630 

18,5 

.0736 

.07367 

.00271 

.07347 

I3.6il 

1*4 

.0737 

.07377 

.00272 

.07357 

13.593 

18,4 

.0738 

.07387 

.00272 

.07367 

13-575 

18,3 

•  0739 

.07397 

.00273 

•07377 

13.556 

18,3 

0.0740 

0.07407 

10,0 

1.00274 

o,7 

0.07387 

9,9 

13.538 

18,2 

.0741 

.07417 

.00275 

.07306 

13.520 

18,2 

.0742 

.07427 

.00275 

.07406 

13.502 

18,1 

•0743 

.07437 

.00276 

.07416 

13.484 

18,1 

.0744 

.07447 

.00277 

.07426 

13.466 

18,0 

0.0745 

0.07457 

10^0 

1.00278 

o,7 

0.07436 

9,9 

13.448 

1  8,0 

.0746 

.07467 

.00278 

.07446 

13.430 

17,9 

.0747 

•07477 

.00279 

.07456 

13.412 

17.«>  ! 

.0748 

.07487 

.00280 

.07466 

13-394 

I?J 

.0/49 

.07497 

.00281 

.07476 

13.376 

17,8 

0.0750 

0.07507 

10,0 

1.00281 

0,8 

0.07486 

9,9 

13.358 

17,7 

u     tan  ad  u   *»  f  ,' 

sec  gd  u 

-Fo' 

•in  0.1  u 

-  Fo' 

esc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


102 


Natural  Hyperbolic  Functions. 


u 

•inhu 

«F0' 

COSh  u 

«F0' 

tanh  u 

-  Fo' 

coth  u 

«  Fo' 

0.0750 

0.07507 

10,0 

I.OO28I 

0,8 

0.07486 

9,9 

13.358 

17,7 

.0751 

.07517 

.OO282 

.07496 

13.341 

17,7 

.0752 

.07527 

.00283 

.07506 

13.323 

17,7 

.0753 

.07537 

.00284 

.07516 

13.305 

17,6 

.0754 

•07547 

.00284 

.07526 

13.288 

17,6 

0.0755 

0.07557 

IO,O 

I.OO285 

0,8 

0.07536 

9,9 

13.270 

17,5 

*  *^*^ 

.0756 

.07567 

.00286 

.07546 

13.253 

17,5 

.0757 

.07577 

.00287 

.07556 

13.235 

17,4 

.0758 

.07587 

.00287 

.07566 

13.218 

17,4 

.0759 

.07597 

.00288 

.07575 

13.201 

17,3 

0.0760 

0.07607 

IO,0 

1.00289 

0,8 

0.07585 

9,9 

13.183 

17,3 

.0761 

.07617 

.OO290 

.07595 

13.166 

17,2 

.0762 

.07627 

.OO29O 

.07605 

13.149 

17,2 

.0763 

.07637 

.OO29I 

.07615 

13.132 

I7,i 

.0764 

.07647 

.OO292 

.07625 

13.114 

I7,i 

0.0765 

0.07657 

IO,O 

1.00293 

0,8 

0.07635 

9,9 

13.097 

I7J 

.0766 

.07667 

.00294 

.07645 

13.080 

17,0 

.0767 

.07678 

.00294 

.07655 

13.063 

I7,o 

.0768 

.07688 

.00295 

.07665 

13-046 

16,9 

.0769 

.07698 

.00296 

.07675 

13.030 

16,9 

0.0770 

0.07708 

IO,O 

1.00297 

0,8 

0.07685 

9,9 

13.013 

16,8 

.0771 

.07718 

.00297 

.07695 

12.996 

16,8- 

.0772 

.07728 

.00298 

.07705 

12.979 

16,7 

•  0773 

.07738 

.00299 

.07715 

12.962 

16,7 

.0774 

.07748 

.00300 

.07725 

12.946 

16,7 

0.0775 

0.07758 

IO,O 

1.00300 

0,8 

0.07735 

9,9 

12.929 

16,6 

.0776 

.07768 

.00301 

.07744 

12.912 

16,6 

.0777 

.07778 

.00302 

.07754 

12.896 

16,5 

.0778 

.07788 

.00303 

.07764 

12.879 

16,5 

.0779 

.07798 

.00304 

.07774 

12.863 

16,5 

0.0780 

0.07808 

10,0 

1.00304 

0,8 

0.07784 

9,9 

12.847 

16,4 

.0781 

.07818 

.00305 

.07794 

12.830 

16,4 

.0782 

.07828 

.00306 

.07804 

12.814 

16,3 

.0783 

.07838 

.00307 

.07814 

12.797 

16,3 

.0784 

.07848 

.00307 

.07824 

12.781 

16,2 

0.0785 

0.07858 

IO,O 

1.00308 

0,8 

0.07834 

9,9 

12.765 

16,2 

.0786 

.07868 

.00309 

.07844 

12.749 

16,2 

.0787 

.07878 

.00310 

.07854 

12.733 

16,1 

.0788 

.07888 

.00311 

.07864 

12.717 

16,1 

.0789 

.07898 

.00311 

.07874 

12.701 

16,0 

0.0790 

0.07908 

IO,O 

1.00312 

0,8 

0.07884 

•  9,9 

12.685 

16,0 

.0791 

.07918 

.00313 

.07894 

12.669 

15,9 

.0792 

.07928 

.00314 

.07903 

12.653 

15,9 

.0793 

.07938 

.00315 

.0791*3 

12.637 

15,9 

.0794 

.07948 

.00315 

.07923 

12.621 

15,8 

0.0795 

0.07958 

IO,O 

1.00316 

0,8 

0.07933 

9,9 

12.605 

15,8 

.0796 

.07968 

.00317 

•07943 

12.589 

15,7 

.0797 

.07978 

.00318 

.07953 

12-574 

15,7 

.0798 

.07988 

.00319 

.07963 

12.558 

15,7 

.0799 

.07999 

.00319 

.07973 

12.542 

15,6 

0.0800 

0.08009 

10,0 

1.00320 

0,8 

0.07983 

9,9 

12.527 

15,6 

u 

tan  gd  u 

w  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


103 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

cosh  u 

•  Fo' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.0800 

0.08009 

IO,O 

1.00320 

0,8 

0.07983 

9,9 

12.527 

15,6 

.0801 

.08019 

.00321 

.07993 

12.511 

15,6 

.0802 

.08029 

.00322 

.08003 

12.496 

15,5 

.0803 

.08039 

.00323 

.08013 

12.480 

15,5 

.0804 

.08049 

.00323 

.08023 

12.465 

15,4 

0.0805 

O.O8O59 

IO,O 

1.00324 

0,8 

0.08033 

9,9 

12.449 

15,4 

.0806 

.08069 

.00325 

.08043 

12.434 

15,4 

.0807 

.08079 

.00326 

.08053 

12.418 

15,3 

.0808 

.08089 

.00327 

.08062 

12.403 

15,3 

.0809 

.08099 

.00327 

.08072 

12.388 

15,2 

0.0810 

O.o8l09 

10,0 

1.00328 

0,8 

0.08082 

9,9 

12.373 

15,2 

.0811 

.08119 

.00329 

.08092 

12.357 

15,2 

.0812 

.08129 

.00330 

.08102 

12.342 

I5,i 

.0813 

.08139 

.00331 

.08112 

12.327 

I5,i 

.0814 

.O8l49 

.00331 

.08122 

12.312 

I5,i 

0.0815 

O.o8l59 

IO,O 

1.00332 

0,8 

0.08132 

9,9 

12.297 

15,0 

.0816 

.08169 

.00333 

.08142 

12.282 

I5,o 

.0817 

.08179 

.00334 

.08152 

12.267 

14,9 

.0818 

.08189 

.00335 

.08162 

12.252 

14,9 

.0819 

.08199 

.00336 

.08172 

12.237 

14,9 

0.0820 

0.08209 

10,0 

1.00336 

0,8 

0.08182 

9,9 

12.222 

14,8 

•  .0821 

.08219 

.00337 

.08192 

12.208 

14,8 

.0822 

.08229 

.00338 

.08202 

12.193 

14,8 

.0823 

.08239 

.00339 

.08211 

12.178 

14,7 

.0824 

.08249 

.00340 

.08221 

I2.I63 

14,7 

0.0825 

0.08259 

IO,O 

1.00341 

0,8 

0.08231 

9,9 

12.149 

14,7 

.0826 

.08269 

.00341 

.08241 

12.134 

14,6 

.0827 

.08279 

.00342 

.08251 

12.119 

14,6 

.0828 

.08289 

.00343 

.08261 

12.105 

14,6 

.0829 

.08299 

.00344 

.08271 

12.000 

14,5 

0.0830 

0.08310 

IO,O 

1.00345 

0,8 

0.08281 

9,9 

I2.O76 

14,5 

.0831 

.08320 

•00345 

.08291 

12.061 

14,4 

.0832 

.08330 

.00346 

.08301 

12.047 

14,4 

.0833 

.08340 

.00347 

.08311 

12.033 

U,4 

.0834 

.08350 

.00348 

.08321 

12.018 

14,3 

0.0835 

0.08360 

IO,O 

1.00349 

0,8 

0.08331 

9,9 

12.004 

14,3 

.0836 

.08370 

.00350 

.08341 

11.990 

14,3 

.0837 

.08380 

.00350 

.08351 

11-975 

14,2 

.0838 

.08390 

.00351 

.08360 

11.961 

14,2 

.0839 

.08400 

.00352 

.08370 

11.947 

14,2 

0.0840 

0.08410 

1  0,0 

1.00353 

0,8 

0.08380 

9,9 

H.933 

14  J 

.0841 

.08420 

•00354 

.08390 

11.919 

14,1 

.0842 

.08430 

.00355 

.08400 

11.905 

14.1 

.0843 

.08440 

.00356 

.08410 

11.890 

14,0 

.0844 

.08450 

.00356 

.08420 

11.876 

M,o 

0.0845 

0.08460 

10,0 

1.00357 

0,8 

0.08430 

9,9 

11.862 

14,0 

.0846 

.08470 

.00358 

.08440 

11.849 

13,9 

.0847 

.08480 

•00359 

.08450 

11.835 

13,9 

.0848 

.08400 

.00360 

.08460 

11.821 

13,9 

.0849 

.08500 

.00361 

0,9 

.08470 

11.807 

13,8 

0.0850 

O.O85IO 

IO,O 

1.00361 

0,9 

0.08480 

9,9 

".793 

13,8 

u 

tan  gd  U 

•Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

-  Fo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


104 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«Fu' 

tanh  u 

«-  Fo' 

coth  u 

«  Fo' 

0.0850 

O.OSSIO 

10,0 

I.OO36l 

0,9 

0.08480 

9,9 

11-793 

13,8 

.0851 

.08520 

.00362 

.08490 

11.779 

13,8 

.0852 

.08530 

.00363 

.08499 

11.765 

13,7 

.0853 

.08540 

.00364 

.08509 

11.752 

13,7 

.0854 

.08550 

.00365 

.08519 

n.738 

13,7 

0.0855 

0.08560 

IO,O 

I.OO366 

0,9 

0.08529 

9,9 

11.724 

13,6 

.0856 

.08570 

.00367 

.08539 

11.711 

13,6 

.0857 

.08580 

.00367 

.08549 

11.697 

13,6 

.0858 

.08591 

.00368 

.08559 

11.684 

13,6 

.0859 

.08601 

.00369 

.08569 

11.670 

13,5 

0.0860 

o.  08611 

IO,O 

1.00370 

0,9 

0.08579 

9,9 

11.657 

13,5 

.0861 

.08621 

.00371 

.08589 

11.643 

13,5 

.0862 

.08631 

.00372 

.08599 

11.630 

13,4 

.0863 

.08641 

.00373 

.08609 

11.616 

13,4 

.0864 

.08651 

.00373 

.08619 

11.603 

13,4 

0.0865 

0.08661 

IO,O 

1.00374 

0,9 

0.08628 

9,9 

11.590 

13,3 

.0866 

.08671 

. 

.00375 

.08638 

11.576 

13,3 

.0867 

.O868l 

.00376 

.08648 

11.563 

13,3 

.0868 

.08691 

.00377 

.08658 

11.550 

13,2 

.0869 

.08701 

.00378 

.08668 

n.536 

13,2 

0.0870 

0.08711 

IO,O 

1.00379 

o,9 

0.08678 

9,9 

11.523 

13,2 

.0871 

.08721 

.00380 

.08688 

11.510 

I3,i 

.0872 

.08/31 

.00380 

.08608 

11.497 

I3,i 

.0873 

.08741 

.00381 

.08708 

11.484 

13,1 

.0874 

.08751 

.00382 

.08718 

11.471 

13,1 

0.0875 

O.o876l 

10,0 

1.00383 

0,9 

0.08728 

9,9 

11.458 

I3,o 

.0876 

.08771 

.00384 

.08738 

11-445 

I3,o 

.0877 

.08781 

.00385 

.08748 

11.432 

13,0 

.0878 

.08791 

.00386 

.08758 

11.419 

12,9 

.0879 

.0880I 

.00387 

.08767 

11.406 

12,9 

0.0880 

0.08811 

10,0 

1.00387 

0,9 

0.08777 

9,9 

n.393 

12,9 

.0881 

.08821 

.00388 

.08787 

11.380 

12,8 

.0882 

.08831 

.00389 

.08797 

11.367 

12,8 

.0883 

.08841 

.00390 

.08807 

H-354 

12,8 

.0884 

.08852 

.00391 

.08817 

11.342 

12,8 

0.0885 

0.08862 

10,0 

1.00392 

0,9 

0.08827 

9,9 

11-329 

12,7 

.0886 

.08872 

.00393 

.08837 

11.316 

12,7 

.0887 

.08882 

.00394 

.08847 

11.304 

12,7 

.0888 

.08892 

.00395 

.08857 

11.291 

12,6 

.0889 

.08902 

.00395 

.08867 

11.278 

12,6 

0.0890 

0.08912 

10,0 

1.00396 

0,9 

0.08877 

0,9 

11.266 

12,6 

.0891 

.08922 

.00397 

.08886 

H.253 

12,6 

.0892 

.08932 

.00398 

.08896 

i  i  .  240 

12,5 

.0893 

.08942 

.00309 

.08906 

11.228 

12,5 

.0894 

.08952 

.00400 

.08916 

11.215 

12,5 

0.0895 

0.08962 

IO,O 

1.00401 

0,9 

0.08926 

9,9 

11.203 

12,5 

.0896 

.08972 

.00402 

.08936 

11.191 

12,4 

.0897 

.08982 

.00403 

.08946 

11.178 

12,4 

.0898 

.08992 

.00403 

.08956 

11.166 

12,4 

.0899 

.09002 

.00404 

.08966 

ii.  153 

12,3 

0.0900 

0.00012 

10,0 

1.00405 

0,9 

0.08976 

9,9 

11.141 

12,3 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

cosh  u 

«FO' 

tanh  u 

«  Fo' 

coth  u 

<•>  Fo' 

0.0900 

0.09012 

IO,O 

1.00405 

0,9 

0.08976 

9,9 

11.141 

12,3 

.0901 

.09022 

.00406 

.08986 

11.129 

12,3 

.0902 

.09032 

.00407 

.08996 

II.II7 

12,3 

.0903 

.09042 

.00408 

.09006 

I  I  .  104 

12,2 

.0904 

.09052 

.00409 

.09015 

11.092 

12,2 

0.0905 

0.09062 

IO,O 

1.00410 

0,9 

0.09025 

9,9 

11.080 

12,2 

.0906 

.09072 

.00411 

.09035 

11.068 

12,1 

.0907 

.09082 

.00412 

.09045 

11.056 

12,1 

.0008 

.00092 

.00413 

.09055 

11.043 

12,1 

.0909 

.09103 

.00413 

.09065 

11.031 

12,1 

0.0910 

0.09113 

10,0 

1.00414 

0,9 

0.00075 

9,9 

11.019 

12,0 

.0911 

.09123 

.00415 

.09085 

11.007 

1  2,O 

.0912 

.09133 

.00416 

.09095 

10.995 

1  2,O 

.0913 

.09143 

.00417 

.09105 

10.983 

1  2,O 

.0914 

.09153 

.00418 

.09115 

10.971 

11,9 

0.0915 

0.09163 

IO,O 

1.00419 

o,9 

O.O9I25 

9,9 

10.959 

11,9 

.0916 

.09173 

.00420 

.09134 

10.948 

11,9 

.0917 

.09183 

.00421 

.09144 

10.936 

11,9 

.0918 

.09193 

.00422 

.09154 

10.924 

n,8 

.0919 

.09203 

.00423 

.09164 

10.912 

n,8 

0.0920 

0.09213 

10,0 

1.00423 

0,9 

0.09174 

9,9 

10.900 

11,8 

.0921 

.09223 

.00424 

.09184 

10.888 

11,8 

.0922 

.09233 

.00425 

.09194 

10.877 

",7 

.0923 

.09243 

.00426 

.O9204 

10.865 

n,7 

.0924 

.09253 

.00427 

.09214 

10.853 

n,7 

0.0925 

0.09263 

IO,O 

1.00428 

0,9 

O.09224 

9,9 

10.842 

n,7 

.0926 

.09273 

.00429 

.09234 

10.830 

11,6 

.0927 

.09283 

.00430 

.09244 

10.818 

n,6 

.0928 

.09293 

.00431 

.09253 

10.807 

n,6 

.0929 

.09303 

.00432 

.09263 

10.795 

11,6 

0.0930 

0.09313 

IO,O 

1.00433 

0,9 

0.09273 

9,9 

10.784 

n,5 

.0931 

.09323 

.00434 

.09283 

10.772 

n,5 

.0932 

.09333 

.00435 

.09293 

10.761 

ii,5 

.0933 

.09344 

.00436 

.09303 

10.749 

n,5 

.0934 

.09354 

.00436 

.09313 

10.738 

H,4  i 

0.0935 

0.09364 

10,0 

1.00437 

o,9 

0.09323 

9,9 

10.726 

11,4 

.0936 

.09374 

.00438 

.09333 

10.715 

11,4 

•0937 

.09384 

.00439 

•  09343 

10.704 

11,4 

.0938 

.09394 

.00440 

•09353 

10.692 

n,3 

.0939 

.09404 

.00441 

.09362 

10.681 

ii,3 

0.0940 

0.094U 

IO,O 

1.00442 

0,9 

0.09372 

9,9 

10.670 

ii,3 

.0941 

.09424 

.00443 

.09382 

10.658 

H,3 

.0942 

.09434 

.00444 

.09392 

10.647 

11,2 

•  0943 

.09444 

.00445 

.00402 

10.636 

11,2 

.0944 

•09454 

.00446 

.09412 

10.625 

11,2 

0.0945 

0.09464 

IO,O 

1.00447 

0,9 

0.09422 

9,9 

10.613 

II,-' 

.0946 

.09474 

.00448 

.09432 

10.602 

II,  I 

.0947 

.09484 

.00449 

.09442 

10.591 

II,  I 

.0948 

.09494 

.00450 

0,9 

•09452 

10.580 

II,  I 

.0949 

.09504 

.00451 

1,0 

.09462 

10.569 

II,  I 

0.0950 

0.09514 

IO,O 

1.00452 

1,0 

0.00472 

9,9 

10.558 

11,0 

u 

tin  gd  u 

-Fo' 

sec  gd  u 

-  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.0950 

0.09514 

10,0 

1.00452 

1,0 

0.09472 

9,9 

10.558 

11,0 

.0951 

.09524 

.00453 

.09481 

10.547 

11,0 

.0952 

•09534 

.00453 

.09491 

10.536 

11,0 

.0953 

.09544 

.00454 

.09501 

10.525 

11,0 

•  0954 

.09554 

.00455 

.095H 

10.514 

11,0 

0.0955 

0.09565 

10,0 

1.00456 

1,0 

0.09521 

9,9 

10.503 

10,9 

.0956 

.09575 

.00457 

.09531 

10.492 

10,9 

.0957 

.09585 

.00458 

.09541 

10.481 

10,9 

.0958 

.09595 

.00459 

.09551 

10.470 

10,9 

.0959 

.09605 

.00460 

.09561 

10.459 

10,8 

0.0960 

0.09615 

10,0 

1.00461 

1,0 

0.09571 

9,9 

10.449 

10,8 

.0961 

.09625 

.00462 

.09581 

10.438 

10,8 

.0962 

.09635 

.00463 

.09590 

10.427 

10,8 

.0963 

.09645 

.00464 

.09600 

10.416 

10,7 

.0964 

.09655 

.00465 

.09610 

10.406 

10,7 

0.0965 

0.09665 

10,0 

1.00466 

I,O 

0.09620 

9,9 

10.395 

10,7 

.0966 

.09675 

.00467 

.09630 

10.384 

10,7 

.0967 

.09685 

.00468 

.09640 

10.373 

10,7 

.0968 

.09695 

.00469 

.09650 

10.363 

10,6 

.0969 

.09705 

.00470 

.09660 

10.352 

10,6 

0.0970 

0.097IS 

IO,O 

1.00471 

1,0 

0.09670 

9,9 

10.342 

10,6 

.0971 

.09725 

.00472 

.09680 

10.331 

10,6 

.0972 

.09735 

.00473 

.09689 

10.320 

10,6 

•0973 

•09745 

.00474 

.09699 

10.310 

io,5 

.0974 

.09755 

.00475 

.09709 

10.299 

10,5 

0.0975 

0.09765 

IO,O 

1.00476 

1,0 

0.09719 

9,9 

10.289 

10,5 

.0976 

.09776 

.00477 

.09729 

10.278 

10,5 

.0977 

.09786 

.00478 

.09739 

10.268 

10,4 

.0978 

.09796 

.00479 

.09749 

10.258 

10,4 

.0979 

.09806 

.00480 

.09759 

10.247 

10,4 

0.0980 

0.09816 

IO,O 

1.00481 

1,0 

0.09769 

9,9 

10.237 

10,4 

.0981 

.09826 

.00482 

.09779 

10.226 

10,4 

.0982 

.09836 

.00483 

.09788 

10.216 

10,3 

.0983 

.09846 

.00484 

.09798 

10.206 

10,3 

.0984 

.09856 

.00485 

.09808 

10.195 

10,3 

0.0985 

0.09866 

IO,O 

1.00486 

1,0 

0.09818 

9,9 

10.185 

10,3 

.0986 

.09876 

.00486 

.09828 

10.  175 

10,3 

.0987 

.09886 

.00487 

.09838 

10.165 

10,2 

.0988 

.09896 

.00488 

.09848 

10.154 

10,2 

.0989 

.09906 

.00489 

.09858 

10.144 

10,2 

0.0900 

0.00916 

IO,O 

1.00490 

1,0 

0.09868 

9,9 

10.134 

10,2 

.0991 

.09926 

.00491 

.09878 

10.124 

10,1 

.0992 

.09936 

.00492 

.09888 

10.114 

10,1 

.0993 

.09946 

.00493 

.09897 

10.  104 

10,1 

.0994 

.09956 

.00494 

.09907 

10.093 

10,1 

0.0995 

0.09966 

IO,O 

1.00495 

1,0 

0.09917 

9,9 

10.083 

10,1 

.0996 

.00976 

.00496 

.09927 

10.073 

10,0 

.0997 

.09987 

.00497 

.09937 

10.063 

10,0 

.0098 

.09997 

.00498 

.09947 

10.053 

10,0 

.0999 

.10007 

.00499 

.09957 

10.043 

10,0 

O.IOOO 

0.10017 

10,1 

1.00500 

1,0 

0.00967 

9,9 

10.033 

10,0 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«F0' 

sin  gd  u 

<•>  Fo' 

esc  gd  u 

O,FO' 

SMITHSONIAN  TABLES 


107 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

»Fo' 

cosh  u 

O.FO' 

tanh  u 

«  Fo' 

coth  u 

»  Fo' 

0;IOO 

O.IOOI7 

100,5 

1.00500 

10,0 

0,09967 

99,0 

10.0333 

996,7 

.101 

.10117 

100,5 

.00510 

10,1 

.10066 

99,0 

9.9346 

977,o 

.IO2 

.IO2l8 

100,5 

.00521 

10,2 

.  IOI65 

99,0 

.8379 

957,9 

.103 

.10318 

100,5 

.00531 

10,3 

.10264 

98,9 

•7430 

939,3 

.104 

.10419 

100,5 

.00541 

10,4 

.10363 

98,9 

.6500 

921,2 

0.105 

0.10519 

100,6 

1.00552 

10,5 

o.  10462 

98,9 

9.5588 

903,7 

.106 

.10620 

100,6 

.00562 

10,6 

.10560 

98,9 

.4693 

886,7 

.107 

.IO72O 

100,6 

.00573 

10,7 

.10659 

98,9 

.3814 

870,1 

.108 

.10821 

1  00,6 

.00584 

10,8 

.10758 

98,8 

.2952 

854,0 

.109 

.10922 

100,6 

.00595 

10,9 

.10857 

98,8 

.2106 

838,4 

O.IIO 

O.IIO22 

100,6 

1.00606 

11,0 

o.  10956 

98,8 

9-  1275 

823,1 

.in 

.11123 

100,6 

.00617 

n,  i 

.11055 

98,8 

.0460 

808,3 

.112 

.  I  1223 

100,6 

.00628 

11,2 

.HI53 

98,8 

8.9659 

793,9 

.113 

.11324 

100,6 

.00639 

n,3 

.11252 

98,7 

.8872 

779,8 

.114 

.11425 

100,7 

.00651 

n,4 

.11351 

98,7 

.8099 

766,1 

O.II5 

O.II525 

100,7 

1.00662 

n,5 

0.11450 

98,7 

8.7340 

752,8 

.116 

.11626 

100,7 

.00674 

11,6 

.11548 

98,7 

.6593 

739,8 

.117 

.11727 

100,7 

.00685 

n,7 

.11647 

98,6 

.5860 

727,2 

.118 

.11827 

100,7 

.00697 

11,8 

.11746 

98,6 

.5139 

714,9 

.119 

.11928 

100,7 

.00709 

11,9 

.11844 

98,6 

•  4430 

702,8 

0.120 

0.12029 

100,7 

1.00721 

1  2,0 

0.11943 

98,6 

8-3733 

691,1 

.121 

.12130 

100,7 

.00733 

12,1 

.12041 

98,6 

.3048 

679,7 

.122 

.  12230 

100,7 

.00745 

12,2 

.12140 

98,5 

.2373 

668,5 

.123 

.12331 

100,8 

.00757 

12,3 

.  12238 

98,5 

.1710 

657,7 

.124 

.12432 

100,8 

.00770 

12,4 

•12337 

98,5 

.1058 

647,0 

O.I25 

o.  12533 

100,8 

1.00782 

12,5 

0.12435 

98,5 

8.0416 

636,7 

.126 

.  12633 

100,8 

.00795 

12,6 

.  12534 

98,4 

7.9785 

626,6 

.127 

•  12734 

100,8 

.00808 

12,7 

.12632 

98,4 

.9163 

616,7 

.128 

.12835 

1  00,8 

.00820 

12,8 

.12731 

98,4 

.8551 

607,0 

.129 

.12936 

100,8 

.00833 

12,9 

.12829 

98,4 

•  7949 

597,6 

0.130 

0.13037 

100,8 

1.00846 

13,0 

o.  12927 

98,3 

7.7356 

588,4 

.131 

.13138 

100,9 

.00859 

13,1 

.  13026 

98,3 

.6772 

579,4 

.132 

.13238 

100,9 

.00872 

13,2 

.13124 

98,3 

•  6197 

570,6 

•133 

.  U339 

100,9 

.00886 

13,3 

.  13222 

98,3 

.5631 

562,0 

•134 

.13440 

100,9 

.00899 

13,4 

.13320 

98,2 

.5073 

553,6 

0.135 

o.  13541 

100,9 

1.00913 

13,5 

0.13419 

98,2 

7.4524 

545,4 

.136 

.13642 

100,9 

.00926 

13,6 

.13517 

98,2 

.3982 

537,3 

.137 

.  13743 

100,9 

.00940 

13,7 

.13615 

98,1 

.3449 

529,5 

.138 

.13844 

IOI,O 

.00954 

13,8 

•13713 

98,1 

.2923 

521,8 

•139 

.  13945 

IOI,0 

.00968 

13,9 

.13811 

98,1 

.2405 

514,3 

O.I4O 

0.14046 

IOI,O 

1.00982 

14,0 

0.13909 

98,1 

7.1895 

506,9 

.141 

.  14147 

101,0 

.00096 

14,1 

.14007 

98,0 

.1391 

499,7 

.142 

.  14248 

IOI,O 

.01010 

14,2 

.  14105 

98,0 

.0895 

492,6 

•143 

.  14349 

101,0 

.01024 

14,3 

.  14203 

98,0 

.0406 

485,7 

.144 

.14450 

101,0 

.01039 

14,4 

.14301 

98,0 

6.9924 

478,9 

0.145 

0.14551 

IOI, 

1.01053 

14,6 

0.  14399 

97,9 

6.9448 

472,3 

.146 

.  14652 

101, 

.01068 

14,7 

.  14497 

97,9 

.8979 

465,8 

.147 

.  14753 

IOI, 

.01082 

14,8 

•14595 

97,9 

.8517 

459,5 

.148 

.14854 

IOI, 

.01097 

14,9 

.14693 

97,8 

.8060 

453,2 

.149 

-  14955 

IOI, 

.01112 

i5,o 

.  I479I 

97,8 

.7610 

447,1 

0.150 

0.15056 

101,1 

1.01127 

I5,i 

0.14889 

97,8 

6.7166 

441,1 

U 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

•in  gd  u 

«  Fo' 

esc  gd  u 

•  FV 

SMITHSONIAN  TABLES 


108 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

c-Fo' 

tanh  u 

*Fo' 

coth  u 

C  Fo' 

0.150 

0.15056 

101,1 

I.  01127 

I5,i 

0.14889 

97,8 

6.7166 

441,1 

.151 

.15157 

IOI,I 

.01142 

I&2 

.14986 

97,8 

.6728 

435,3 

.152 

.  15259 

101,2 

.01157 

15,3 

.15084 

97,7 

.6295 

429,5 

.153 

.15360 

101,2 

.01173 

15,4 

.15182 

97,7 

.5869 

423,9 

.154 

.15461 

101,2 

.01188 

15,5 

•  15279 

97,7 

.5448 

418,3 

0.155 

0.15562 

101,2 

I.  01204 

15,6 

0.15377 

97,6 

6.5032 

412,9 

.156 

.15663 

101,2 

.01219 

15,7 

.15475 

97,6 

.4622 

407,6 

.157 

•  15765 

101,2 

.01235 

15,8 

.  15572 

97,6 

.4217 

402,4 

.158 

.15866 

101,3 

.01251 

15,9 

.  15670 

97,5 

.3817 

397,3 

.159 

.  15967 

101,3 

.01267 

16,0 

.  15767 

97,5 

.3422 

392,2 

0.160 

O.l6o68 

101,3 

1.01283 

16,1 

0.15865 

97,5 

6.3032 

387,3 

.161 

.  16170 

101,3 

.01299 

16,2 

.15962 

97,5 

.2648 

382,5 

.162 

.  16271 

101,3 

.01315 

16,3 

.16060 

97,4 

.2267 

377,7 

.163 

.  16372 

101,3 

.01331 

16,4 

.16157 

97,4 

.1892 

.164 

•  16474 

101,3 

.01348 

16,5 

.  16254 

97,4 

.1521 

368,5 

0.165 

0.16575 

101,4 

1.01364 

16,6 

0.16352 

97,3 

6.H55 

364,0 

.166 

.16676 

101,4 

.01381 

16,7 

.16449 

97,3 

.0793 

359,6 

.167 

.16778 

101,4 

.01398 

16,8 

.  16546 

97,3 

.0436 

355,2 

.168 

.16879 

101,4 

.01415 

16,9 

.16644 

97,2 

.0083 

35i,o 

.169 

.16981 

101,4 

.01431 

17,0 

.16741 

97,2 

5-9734 

346,8 

0.170 

o.  17082 

101,4 

1.01448 

I7,i 

o.  16838 

97,2 

5.9389 

342,7 

.171 

.17183 

ioi,5 

.01466 

17^2 

.16935 

97,i 

.9048 

338,7 

.172 

.17285 

ioi,5 

.01483 

17,3 

.  17032 

97,1 

.8712 

334,7 

.173 

.17386 

101,5 

.01500 

17,4 

.17129 

97,1 

.8379 

330,8 

.174 

.17488 

101,5 

.01518 

17,5 

.17226 

97,o 

.8050 

327,0 

0.175 

0.17589 

ioi,5 

I.  01535 

17,6 

o.  17324 

97,0 

5.7725 

323,2 

.176 

.17691 

101,6 

.01553 

17,7 

.  17420 

97,o 

.7404 

319,5 

.177 

.17793 

101,6 

.01571 

17,8 

.17517 

96,9 

.7086 

315,9 

.178 

.17894 

101,6 

.01588 

17,9 

.17614 

96,9 

.6772 

312,3 

.179 

.17996 

101,6 

.01606 

18,0 

.17711 

96,9 

.6461 

308,8 

0.180 

0.18097 

101,6 

1.01624 

18,1 

0.17808 

96.8 

5.6154 

305,3 

.181 

.18199 

101,6 

.01643 

18,2 

.  17905 

96,8 

.5851 

301,9 

.182 

.  18301 

101,7 

.01661 

18,3 

.18002 

96,8 

•  5550 

298,6 

.183 

.  18402 

101,7 

.01679 

18,4 

.18098 

96,7 

.5253 

295,3 

.184 

.18504 

101,7 

.01698 

18,5 

.  18195 

96,7 

.4060 

292,1 

0.185 

0.18606 

101,7 

1.01716 

18,6 

o.  18292 

96,7 

5.4669 

288,9 

.186 

.  18707 

101,7 

.01735 

18,7 

.18388 

96,6 

.4382 

285,8 

.187 

.18809 

101,8 

.01754 

18,8 

.18485 

96,6 

.4098 

282,7 

.188 

.18911 

101,8 

.01772 

18,9 

.  18582 

96,5 

.3817 

279,6 

.189 

.19013 

101,8 

.01791 

19,0 

.18678 

96,5 

.3539 

276,6 

0.190 

0.19115 

101,8 

I.  01810 

19,1 

0.18775 

96,5 

5.3263 

273,7 

.191 

.19216 

101,8 

.01830 

19,2 

.18871 

96,4 

.2991 

270,8 

.192 

.19318 

101,8 

.01849 

19,3 

.18967 

96,4 

.2722 

268,0 

•  193 

.  19420 

101,9 

.01868 

19,4 

.19064 

96,4 

.2455 

265,2 

.194 

.  19522 

101,9 

.01888 

19,5 

.19160 

96,3 

.2191 

262,4 

0.195 

0.19624 

101,9 

1.01907 

19,6 

0.19257 

96,3 

5.1930 

259,7 

.196 

.  19726 

101,9 

.01927 

19,7 

.19353 

96,3 

.1672 

257,0 

.197 

.19828 

101,9 

.01947 

19,8 

.19449 

96,2 

.1416 

254,4 

.198 

.19930 

102,0 

.01967 

19,9 

.  19545 

96,2 

.1163 

251,8 

-.199 

.20032 

102,0 

.01987 

20,0 

.19641 

96,1 

.0913 

249,2 

0.200 

0.20134 

IO2,O 

1.02007 

20,1 

0.19738 

06,1 

5.0665 

246,7 

U 

tan  gd  u 

«F0' 

sec  gd  u 

a.  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

<-  Fo' 

SMITHSONIAN  TABLES 


109 


Natural  Hyperbolic  Functions. 


u 

sinhu 

<-Fo' 

cosh  u 

»FO' 

tanh  u 

U»FO' 

coth  u 

«  Fo' 

O.20O 

0.20134 

IO2.O 

1.02007 

20,1 

0.19738 

96,1 

5.0665 

246,7 

.2OI 

.20236 

IO2,O 

.02027 

20,2 

.19834 

96,1 

.0419 

244,2 

.202 

.20338 

IO2,0 

.02047 

20,3 

.19930 

96,0 

.0176 

241,8 

.203 

.20440 

IO2,I 

.02068 

20,4 

.20026 

96,0 

4.9936 

239,4 

.204 

.20542 

IO2,I 

.02088 

20,5 

.20122 

96,0 

•  9698 

237,0 

O.205 

0.20644 

IO2,I 

1.02109 

20,6 

O.2O2I8 

95,9 

4.9462 

234,6 

.206 

.20746 

102,1 

.02129 

20,7 

.20313 

95,9 

.9228 

232,3 

.207 

.20848 

102,2 

.02150 

20,8 

.20409 

95,8 

.8997 

230,1 

.208 

.20950 

102,2 

.02171 

2I,O 

.20505 

95,8 

.8768 

227,8 

.209 

.21052 

IO2,2 

.02192 

21,1 

.20601 

95,8 

.8542 

225,6 

O.2IO 

0.21155 

IO2,2 

1.02213 

21,2 

0.20697 

95,7 

4.8317 

223,5 

.211 

.21257 

IO2,2 

.02234 

21,3 

.20792 

95,7 

.8095 

221,3 

.212 

.21359 

102,3 

.02256 

21,4 

.20888 

95,6 

.7874 

219,2 

.213 

.21461 

102,3 

.02277 

21,5 

.20984 

95,6 

.7656 

217,1 

.214 

.21564 

102,3 

.02299 

21,6 

.21079 

95,6 

.7440 

215,1 

0.215 

0.21666 

102,3 

1.02320 

21,7 

0.21175 

95,5 

4.7226 

213,0 

.2l6 

.21768 

102,3 

.02342 

21,8 

.21270 

95,5 

.7014 

211,0 

.217 

.21871 

102,4 

.02364 

21,9 

.21366 

95,4 

.6804 

209,1 

.218 

.21973 

102,4 

.02386 

22,0 

.21461 

95,4 

.6596 

2O7.I 

.219 

.22075 

102,4 

.02408 

22,1 

.21556 

95,4 

.6390 

205,2 

O.22O 

0.22178 

102,4 

1.02430 

22,2 

0.21652 

95,3 

4.6186 

203,3 

.221 

.22280 

102,5 

.02452 

22,3 

.21747 

95,3 

.5983 

201,4 

.222 

.22383 

102,5 

.02474 

22,4 

.21842 

95,2 

.5/83 

199,6 

.223 

.22485 

102,5 

.02497 

22,5 

.21938 

95,2 

.5584 

197,8 

.224 

.22588 

102,5 

.02519 

22,6 

.22033 

95,1 

.5387 

196,0 

O.225 

0.22690 

102,5 

1.02542 

22,7 

0.22128 

95,1 

4.5192 

194,2 

.226 

.22793 

102,6 

.02565 

22,8 

.22223 

95,1 

.4999 

192,5 

.227 

.22895 

102,6 

.02588 

22,9 

.22318 

95,o 

.4807 

190,8 

.228 

.22998 

102,6 

.02610 

23,0 

.22413 

95,o 

.4617 

189,1 

.229 

.23101 

102,6 

.02634 

23,1 

.22508 

94,9 

.4429 

187,4 

O.23O 

0.23203 

102,7 

1.02657 

23,2 

0.22603 

94.0 

4.4242 

i85,7 

.231 

.23306 

102,7 

.02680 

23,3 

.22698 

94,8 

.4057 

184,1 

.232 

.23409 

102,7 

.02703 

23,4 

.22793 

94,8 

.3874 

182,5 

•233 

.23511 

102,7 

.02727 

23,5 

.22887 

94,8 

.3692 

180,9 

•  234 

.23614 

102,8 

.02750 

23,6 

.22982 

94,7 

•  3512 

179,3 

0.235 

0.23717 

102,8 

I  .02774 

23,7 

0.23077 

94,7 

4.3334 

177,8 

.236 

.23820 

102,8 

.02798 

23,8 

.23171 

94,6 

.3157 

176,2 

.237 

.23922 

102,8 

.02822 

23,9 

.23266 

94,6 

.2981 

174,7 

.238 

.24025 

102,8 

.02846 

24,0 

.23361 

94,5 

.2807 

173,2 

•  239 

.24128 

102,9 

.02870 

24,1 

.23455 

94,5 

•  2635 

171,8 

0.240 

0.24231 

102,9 

1.02894 

24,2 

0.23550 

94,5 

4.2464 

170,3 

.241 

.24334 

102,9 

.02918 

24,3 

.23644 

94,4 

.2294 

168,9 

.242 

.24437 

102,9 

.02043 

24,4 

.23738 

94,4 

.2126 

l6>,5 

.243 

.24540 

103,0 

.02967 

24,5 

.23833 

94,3 

.1959 

166,1 

.244 

.24643 

103,0 

.02992 

24,6 

.23927 

94,3 

.1794 

164,7 

0.245 

0.24746 

103,0 

1.03016 

24,7 

0.24021 

94,2 

4.1630 

163,3 

.246 

.24849 

103,0 

.03041 

24,8 

.24115 

94,2 

.1467 

162,0 

.247 

.24952 

103,1 

.03066 

25,0 

.24210 

94,1 

.1306 

160,6 

.248 

.25055 

103,1 

.03091 

25,1 

.24304 

94,1 

.1146 

159,3 

.249 

.25158 

103,1 

.03116 

25,2 

•24398 

94,0 

.0987 

158,0 

0.250 

0.25261 

103,1 

1.03141 

25,3 

0.24402 

94,0 

4.0830 

156,7 

u     tan  gd  u 

«F0' 

sec  od  u 

«  Fo' 

sin  od  u 

«  Fo' 

esc  gd  u 

a,  Fo' 

SMITHSONIAN  TABLES 


110 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

wF0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.250 

O.2526I 

103,1 

1.03141 

25,3 

0.24492 

94,0 

4.0830 

156,7 

.251 

.25364 

103,2 

.03167 

25,4 

.24586 

94,0 

.0674 

155,4 

.252 

.25468 

103,2 

.03192 

25,5 

.24680 

93,9 

.0519 

154,2 

.253 

.25571 

103,2 

.03218 

25,6 

•24774 

93,9 

.0365 

152,9 

.254 

.25674 

103,2 

.03243 

25,7 

.24867 

93,8 

.O2I3 

151,7 

0.255 

0.25777 

103,3 

1.03269 

25,8 

0.24961 

93,8 

4.0062 

150,5 

.256 

.25881 

103,3 

.03295 

25,9 

.25055 

93,7 

3.9912 

149,3 

.257 

.25984 

103,3 

.03321 

26,0 

.25149 

93,7 

.9763 

148.1 

.258 

.26087 

103,3 

.03347 

26,1 

.25242 

93,6 

.9616 

146,9 

.259 

.26191 

103,4 

.03373 

26,2 

.25336 

93,6 

•9470 

145,8 

0.260 

0.26294 

103,4 

1.03399 

26,3 

0.25430 

93,5 

3.9324 

144,6 

.261 

.26397 

103,4 

.03425 

26,4 

.25523 

93,5 

.9180 

143,5 

.262 

.26501 

103,5 

.03452 

26,5 

.25617 

93,4 

.9037 

142,4 

.263 

.26604 

103,5 

.03478 

26,6 

.25710 

93,4 

.8895 

141,3 

.264 

.26708 

103,5 

.03505 

26,7 

.25803 

93,3 

.8755 

140,2 

0.265 

0.26811 

103,5 

1.03532 

26,8 

0.25897 

93,3 

3.8615 

139,1 

.266 

.26915 

103,6 

.03559 

26,9 

.25990 

93,2 

.8476 

138,0 

.267 

.27018 

103,6 

.03586 

27,0 

.26083 

93,2 

.8339 

137,0 

.268 

.27122 

103,6 

.03613 

27,1 

.26176 

93,1 

.8203 

135,9 

.269 

.27226 

103,6 

.03640 

27,2 

.26269 

93,1 

.8067 

134,9 

0.270 

0.27329 

103,7 

1.03667 

27,3 

0.26362 

93,1 

3-7933 

133,9 

.271 

.27433 

103,7 

.03695 

27,4 

.26456 

93,0 

•  7799 

132,9 

.272 

.27537 

103,7 

.03722 

27,5 

.26548 

93,0 

.7667 

I3L9 

.273 

.27640 

103,7 

.03750 

27,6 

.26641 

92,9 

.7536 

130,9 

.274 

.27744 

103,8 

.03777 

27,7 

.26734 

92,9 

.7405 

129,9 

0.275 

0.27848 

103,8 

1.03805 

27,8 

0.26827 

92,8 

3.7276 

128,9 

.276 

.27952 

103,8 

.03833 

28,0 

.26920 

92,8 

.7147 

128,0 

-  .277 

.28056 

103,9 

.03861 

28,1 

.27013 

92,7 

.7020 

127,0 

.278 

.28159 

103,9 

.03889 

28,2 

.27105 

92,7 

.6893 

126,1 

.279 

.28263 

103,9 

•03917 

28,3 

.27198 

92,6 

.6768 

125,2 

0.280 

0.28367 

J03,9 

1.03946 

28,4 

0.27291 

92,6 

3-6643 

124,3 

.281 

.28471 

104,0 

•03974 

28,5 

.27383 

92,5 

.6519 

123,4 

.282 

.28575 

104,0 

.04003 

28,6 

.27476 

92,5 

.6396 

122,5 

.283 

.28679 

104,0 

.04031 

28,7 

.27568 

92,4 

.6274 

121,6 

.284 

.28783 

104,1 

.04060 

28,8 

.27660 

92,4 

.6153 

120,7 

0.285 

0.28887 

104,1 

1.04089 

28,9 

0.27753 

92,3 

3-6033 

119,8 

.286 

.28991 

104,1 

.04118 

29,0 

.27845 

92,2 

.5913 

119,0 

.287 

.29006 

104,1 

.04147 

29,1 

.27937 

92,2 

•  5795 

118,1 

.288 

.29200 

104,2 

.04176 

29,2 

.28029 

92,1 

.5677 

H7,3 

.289 

.29304 

104,2 

.04205 

29,3 

.28121 

92,i 

.5560 

116,5 

O.2OO 

0.29408 

104,2 

1.04235 

29,4 

0.28213 

92,0 

3.5444 

115,6 

.291 

.29512 

104,3 

.04264 

29,5 

.28305 

92,0 

.5329 

114,8 

.292 

.29617 

104,3 

.04294 

29,6 

.28397 

9i,9 

.5214 

114,0 

.293 

.29721 

104,3 

.04323 

29,7 

.28489 

9i,9 

.5101 

113,2 

.294 

.29825 

104,4 

.04353 

29,8 

.28581 

9i,8 

.4988 

112,4 

0.295 

0.29930 

104,4 

1.04383 

29,9 

0.28673 

91,8 

3.4876 

111,6 

.296 

.30034 

104,4 

.04413 

30,0 

.28765 

9i,7 

.4765 

110,9 

.297 

.30139 

104,4 

.04443 

30,1 

.28856 

9i,7 

.4654 

no,  i 

.298 

.30243 

104,5 

•04473 

30,2 

.28948 

91,6 

•4545 

109,3 

.299 

.30348 

104,5 

.04503 

30,3 

.29040 

91,6 

.4436 

108,6 

0.300 

0.30452 

104,5 

1.04534 

30,5 

0.29131 

9i,5 

3.4327 

107,8 

u     tan  gd  u 

*>  Fo' 

sec  gd  u 

«-  Fo' 

sin  gd  u 

w  Fo' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


III 


Natural  Hyperbolic  Functions. 


u 

tinh  u 

-FV 

cosh  u 

wF0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.300 

0.30452 

1045 

1.04534 

30,5 

0.29131 

91,5 

3.4327 

107,8 

.301 

•30557 

104,6 

.04564 

30,6 

.29223 

91,5 

.4220 

107,1 

.302 

.30661 

104,6 

.04595 

30,7 

.293M 

91,4 

.4113 

106,4 

.303 

.30766 

104,6 

.04626 

30,8 

.29406 

91,4 

.4007 

105,6 

.304 

.30870 

104,7 

.04656 

30,9 

.29497 

91,3 

•  3902 

104,9 

0.305 

0.30975 

104,7 

1.04687 

3i,o 

0.29588 

91,2 

3.3797 

104,2 

.306 

.31080 

104,7 

.04718 

3i,i 

.29679 

91,2 

.3693 

103,5 

.307 

.3H85 

104,7 

.04750 

31,2 

.29771 

91,1 

.3590 

102,8 

.308 

.31289 

104,8 

.04781 

3i,3 

.29862 

91,1 

.3488 

102,1 

.309 

.31394 

104,8 

.04812 

3i,4 

•29953 

91,0 

.3386 

101,5 

0.310 

0.31499 

104,8 

1.04844 

3i,5 

0.30044 

91,0 

3.3285 

100,8 

.311 

.31004 

104,9 

.04875 

3i,6 

.30135 

90,9 

.3184 

100,1 

.312 

.31709 

104,9 

.04007 

3i,7 

.30226 

90,9 

.3085 

99,5 

.313 

.3l8l4 

104,9 

.04939 

3i,8 

.30316 

90,8 

.2985 

98,8 

.314 

.31919 

105,0 

.04970 

3i,9 

.30407 

90,8 

.2887 

98,2 

0.315 

0.32024 

105,0 

I  .05002 

32,0 

0.30408 

90,7 

3.2789 

97,5 

.316 

.32129 

105,0 

.05034 

32,1 

.30589 

90,6 

.2692 

96,9 

.317 

.32234 

105,1 

.05067 

32,2 

.30679 

90,6 

.2595 

96,2 

.318 

.32339 

105,1 

.05009 

32,3 

.30770 

90,5 

.2499 

95,6 

.319 

.32444 

105,1 

.05131 

32,4 

.30860 

90,5 

.2404 

95,o 

0.320 

0.32549 

105,2 

1.05164 

32,5 

0.30951 

90,4 

3-2309 

94,4 

.321 

.32654 

105,2 

.05196 

32,7 

.31041 

90,4 

.2215 

93,8 

.322 

.32759 

105,2 

.05229 

32,8 

.3H3I 

90,3 

.2122 

93,2 

.323 

.32865 

105,3 

.05262 

32,9 

.31222 

90,3 

.2O29 

92,6 

.324 

.32970 

105,3 

.05295 

33,0 

.31312 

90,2 

•  1937 

92,0 

0.325 

0.33075 

105,3 

1.05328 

33,1 

0.31402 

90,1 

3-1845 

91,4 

.326 

.33181 

105,4 

.05361 

33,2 

.31492 

90,1 

.1754 

90,8 

.327 

.33286 

105,4 

•05394 

33,3 

.31582 

90,0 

.1663 

90,3 

.328 

.33391 

105,4 

.05428 

33,4 

.31672 

90,0 

.1573 

89,7 

.329 

•33497 

105,5 

.05461 

33,5 

.31762 

89,9 

.1484 

89,1 

0.330 

0.33602 

105,5 

1.05495 

33,6 

0.31852 

89,9 

3.1395 

88,6 

.331 

.33708 

105,5 

.05528 

33,7 

.31942 

89,8 

.1307 

88,0 

.332 

.33813 

105,6 

.05562 

33,8 

.32032 

89,7 

.1219 

87,5 

•  333 

.33919 

105,6 

.05506 

33,9 

.32121 

89,7 

.1132 

86,9 

•334 

.34024 

105,6 

.05630 

34,0 

.32211 

89,6 

.1045 

86,4 

'0.335 

0.34130 

105,7 

1.05664 

34,1 

0.32301 

89,6 

3.0959 

85,8 

.336 

.34236 

105,7 

.05608 

34,2 

.32300 

89,5 

.0874 

85.3 

•  337 

•34342 

105,7 

•05732 

34,3 

.32480 

89,5 

.0789 

84,8 

.338 

•34447 

105,8 

.05767 

34,4 

.32569 

89,4 

.0704 

84,3 

•339 

•34553 

105,8 

.05801 

34,6 

.32658 

89,3 

.0620 

83,8 

0.340 

0.34659 

105,8 

1.05836 

34,7 

0.32748 

89,3 

3.0536 

83,2 

•  341 

.34765 

105,9 

.05871 

34,8 

.32837 

89,2 

•0453 

82,7 

.342 

.34871 

105,9 

.05905 

34,9 

.32926 

89,2 

.0371 

82,2 

•  343 

•34977 

105,9 

.05940 

35,0 

.33015 

89,1 

.0289 

8i,7 

•  344 

.35082 

106,0 

•05975 

35,i 

.33104 

89,0 

.0207 

81,2 

0.345 

0.35188 

106,0 

i.  06011 

35,2 

0.33193 

89,0 

3.0126 

80,8 

.346 

.35295 

1  06,0 

.06046 

35,3 

.33282 

88,9 

.0046 

80,3 

•  347 

•35401 

106,1 

.06081 

35,4 

•33371 

88,9 

2.9966 

79,8 

.348 

.35507 

106,1 

.06117 

35,5 

-334<60 

88,8 

.9886 

79,3 

•  349 

•35613 

106,2 

.06152 

35,6 

•33549 

88,7 

.9807 

7«,8 

0.350 

0.35719 

106,2 

i.  06188 

35,7 

0.33638 

88,7 

2.9729 

78,4 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

»  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


112 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  tt 

«Fo' 

tanh  u 

«  Fo'  ' 

coth  u 

-Fo' 

0.350 

0.35719 

106,2 

I.  06188 

35,7 

0.33638 

88,7 

2.9729 

78,4 

.351 

.35825 

106,2 

.06224 

35,8 

.33726 

88,6 

.9651 

77,9 

.352 

•35931 

106,3 

.06259 

35,9 

.33815 

88,6 

.9573 

77,5 

•  353 

.36038 

106,3 

.06295 

36,0 

•33903 

88,5 

.9496 

77,o 

•  354 

.36144 

106,3 

.06332 

36,1 

•33992 

88,4 

•9419 

76,5 

0.355 

0.36250 

106,4 

1.06368 

36,3 

0.34080 

88,4 

2.9343 

76,1 

.356 

.36357 

106,4 

.06404 

36,4 

.34169 

88,3 

.9267 

75,7 

•  357 

•36463 

106,4 

.06440 

36,5 

.34257 

88,3 

.9191 

75,2 

•  358 

.36570 

106,5 

.06477 

36,6 

•34345 

88,2 

.9116 

74,8 

•359 

.36676 

106,5 

.06514 

36,7 

•34433 

88,1 

.9042 

74,3 

0.360 

0.36783 

106,6 

1.06550 

36,8 

0.34521 

88,1 

2.8968 

73,9 

.361 

.36889 

106,6 

.06587 

36,9 

.34609 

88,0 

.8894 

73,5 

.362 

.36996 

106,6 

.06624 

37,o 

.34697 

88,0 

.8821 

73,i 

•  363 

•37102 

106,7 

.06661 

37,1 

.34785 

87,9 

.8748 

72,6 

.364 

.37209 

106,7 

.06698 

37,2 

.34873 

87,8 

.8675 

72,2 

0.365 

0.37316 

106,7 

1.06736 

37,3 

0.34961 

87,8 

2.8603 

71,8 

.366 

.37423 

106,8 

.06773 

37,4 

.35049 

87,7 

.8532 

71,4 

.367 

.37529 

106,8 

.06810 

37,5 

.35136 

87,7 

.8460 

71,0 

.368 

.37636 

106,8 

.06848 

37,6 

.35224 

87,6 

.8390 

70,6 

.369 

•37743 

106,9 

.06886 

37,7 

.35312 

87,5 

.8319 

70,2 

0.370 

0.37850 

106,9 

1.06923 

37,9 

0.35399 

87,5 

2.8249 

69,8 

•  371 

.37957 

107,0 

.06061 

38,0 

.35487 

87,4 

.8180 

69,4 

•372 

.38064 

107,0 

.06999 

38,i 

•35574 

87,3 

.8110 

69,0 

•  373 

.38171 

107,0 

.07037 

38,2 

.35661 

87,3 

.8042 

68,6 

.374 

.38278 

107,1 

.07076 

38,3 

•35749 

87,2 

•  7973 

68,2 

0.375 

0.38385 

107,1 

1.07114 

38,4 

0.35836 

87,2 

2.7905 

67,9 

.376 

.38492 

107,2 

.07152 

38,5 

.35923 

87,1 

.7837 

67,5 

•  377 

.38599 

107,2 

.07191 

38,6 

.36010 

87,0 

•  7770 

67,1 

•  378 

•38707 

107,2 

.07230 

38,7 

.36097 

87,0 

.7703 

66,7 

•  379 

.38814 

107,3 

.07268 

38,8 

.36184 

86,9 

.7637 

66,4 

0.380 

0.38921 

107,3 

1.07307 

3&9 

0.36271 

86,8 

2.7570 

66,0 

.381 

.39028 

107,3 

.07346 

39,0 

.36358 

86,8 

•  7505 

65,7 

.382 

.39136 

107,4 

.07385 

39,i 

.36444 

86,7 

•  7439 

65,3 

.383 

.39243 

107,4 

.  .07425 

39,2 

•36531 

86,7 

.7374 

64,9 

.384 

•39351 

107,5 

.07464 

39,4 

.36618 

86,6 

.7309 

64,6 

0.385 

0.39458 

107,5 

1.07503 

39,3 

0.36704 

86,5 

2.7245 

64,2 

.386 

.39566 

107,5 

.07543 

39,6 

.36791 

86,5 

.7181 

63,9 

.387 

.39673 

107,6 

.07582 

39,7 

.36877 

86,4 

.7117 

63,5 

.388 

.3978i 

107,6 

.07622 

39,8 

.36063 

86,3 

•  7054 

63,2 

.389 

.39889 

107,7 

.07662 

39,9 

.37050 

86,3 

.6991 

62,8 

0.390 

0.39996 

107,7 

1.07702 

40,0 

0.37136 

86,2 

2.6928 

62,5 

•  391 

.40104 

107,7 

.07742 

40,1 

.37222 

86,1 

.6866 

62,2 

•392 

.40212 

107,8 

.07782 

40,2 

.37308 

86,1 

.6804 

61,8 

•  393 

.40319 

107,8 

.07822 

40,3 

86,0 

.6742 

6i,5 

•  394 

.40427 

107,9 

.07863 

40,4 

.3748o 

86,0 

.6681 

61,2 

0.395 

0.40535 

107,9 

1.07903 

40,5 

0.37566 

85,9 

2.6620 

60,9 

.396 

.40643 

107,9 

.07944 

40,6 

.37652 

85,8 

.6559 

60,5 

•  397 

.40751 

108,0 

.07984 

40,8 

.37738 

85,8 

.6499 

60,2 

.398 

.40859 

108,0 

.08025 

40,9 

.37824 

85,7 

.6438 

59,9 

.399 

.40967 

108,1 

.08066 

41,0 

.37909 

85,6 

.6379 

59,6 

0.400 

0.41075 

108,1 

1.08107 

41,1 

0.37995 

85,6 

2.6319 

59,3 

u 

tan  gd  u 

»F0' 

sec  gd  u 

w  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES. 


Natural  Hyperbolic  Functions. 


a 

sinh  u 

«F0' 

cosh  u 

coFo' 

tanh  u 

«  Fo' 

coth  u 

-  F0' 

0.400 

0.41075 

108,1 

1.08107 

41,1 

0.37995 

85,6 

2.6319 

59,3 

.401 

.41183 

108,1 

.08148 

41,2 

.38080 

85,5 

.6260 

59,0 

.402 

.41292 

108,2 

.08190 

41,3 

.38166 

85,4 

.6201 

58,7 

•  403 

.41400 

108,2 

.08231 

41,4 

.38251 

85,4 

.6i43 

58,3 

.404 

.41508 

108,3 

.08272 

41,5 

.38337 

85,3 

.6085 

58,0 

0.405 

0.41616 

108,3 

1.08314 

41,6 

0.38422 

85,2 

2.6027 

57,7 

.406 

.41725 

108,4 

.08356 

41,7 

•38507 

85,2 

•  5969 

57,4 

.407 

.41833 

108,4 

.08397 

41,8 

.38592 

85,1 

.5912 

57,i 

.408 

.41941 

108,4 

.08439 

4i,9 

.38677 

85,0 

.5855 

56,8 

.409 

.42050 

108,5 

.08481 

42,0 

.38762 

85,0 

.5798 

56,6 

0.410 

0.42158 

108,5 

1.08523 

42,2 

0.38847 

84,9 

2.5742 

56,3 

.411 

.42267 

108,6 

.08566 

42,3 

.38932 

84,8 

.5686 

56,0 

.412 

.42376 

108,6 

.08608 

42,4 

.39017 

84,8 

.5630 

55,7 

•413 

.42484 

108,7 

.08650 

42,5 

.39102 

84,7 

•5574 

55,4 

.414 

.42593 

108,7 

.08693 

42,6 

.39186 

84,6 

.5519 

55,i 

0.415 

0.42702 

108,7 

1.08736 

42,7 

0.39271 

84,6 

2.5464 

54,8 

.416 

.42810 

108,8 

.08778 

42,8 

.39356 

84,5 

.5409 

54,6 

.417 

.42919 

108,8 

.08821 

42,9 

.39440 

84,4 

•  5355 

54,3 

.418 

.43028 

108,9 

.08864 

43,0 

.39524 

84,4 

.5301 

54,0 

.419 

.43137 

108,9 

.08907 

43,1 

.39609 

84,3 

.5247 

53,7 

0.420 

0.43246 

109,0 

1.08950 

43,2 

0.39693 

84,2 

2.5193 

53,5 

.421 

.43355 

109,0 

.08994 

43,4 

•39777 

84,2 

.5140 

53,2 

.422 

.43464 

109,0 

.09037 

43,5 

.39861 

84,1 

.5087 

52,9 

.423 

•43573 

109,1 

.09081 

43,6 

•39945 

84,0    .5034 

52,7 

.424 

.43682 

109,1 

.09124 

43,7 

.40029 

84,0 

.4982 

52,4 

0.425 

0.43791 

109,2 

1.09168 

43,8 

0.40113 

83,9 

2.4929 

52,2 

.426 

-43900 

109,2 

.09212 

43,9 

.40197 

83,8 

.4877 

5i,9 

.427 

.44009 

109,3 

.09256 

44,0 

.40281 

83,8 

.4826 

5i,6 

.428 

.44119 

109,3 

.09300 

44,1 

.40365 

83,7 

•  4774 

5i,4 

.429 

.44228 

109,3 

•09344 

44,2 

.40449 

83,6 

.4723 

5i,i 

0.430 

0.44337 

109,4 

1.09388 

44,3 

0.40532 

83,6 

2.4672 

50,9 

•  431 

.44447 

109,4 

.09433 

44,4 

.40616 

83,5 

.4621 

50,6 

•432 

.44556 

109,5 

.09477 

44,6 

.40609 

83,4 

.4571 

50,4 

•  433 

.44666 

109,5 

.09522 

44,7 

.40783 

83,4 

•  4520 

50,1 

•434 

•44775 

109,6 

.09567 

44,8 

.40866 

83,3 

•  4470 

49,9 

0.435 

0.44885 

109,6 

1.09611 

44,9 

0.40949 

83,2 

2.4421 

49,6 

.436 

•44995 

109,7 

.09656 

45,o 

.41032 

83,2 

.4371 

49,4 

•  437 

.45104 

109,7 

.09701 

45,1 

.41115 

83,1 

•4322 

49,2 

.438 

•45214 

109,7 

.09747 

45,2 

.41199 

83,0 

.4273 

48,9 

•439 

•45324 

109,8 

.09792 

45,3 

.41282 

83,0 

.4224 

48,7 

0.440 

0.45434 

109,8 

1.09837 

45,4 

0.41364 

82,9 

2.4175 

48,4 

.441 

•45543 

109,9 

.09883 

45,5 

.41447 

82,8 

.4127 

48,2 

.442 

.45653 

109,9 

.09928 

45,7 

.41530 

82,8 

.4079 

48,0 

•443 

.45763 

IIO,O 

.09974 

45,8 

.41613 

82,7 

.4031 

47,7 

.444 

.45873 

110,0 

.J0020 

45,9 

.41695 

82,6 

.3983 

47,5 

0.445 

0.45083 

no,  i 

I.  IO066 

46,0 

0.41778 

82,5 

2.3936 

47,3 

•  .446 

.46093 

no,  i 

.IOII2 

46,1 

.41861 

82,5 

.3889 

47,1 

•447 

.46204 

IIO,2 

.  IOI58 

46,2 

•41943 

82,4 

.3842 

46,8 

.448 

.46314 

IIO,2 

.I02O4 

46,3 

.42025 

82,3 

•  3795 

46,6 

•  449 

.46424 

110,3 

.10251 

46,4 

.42108 

82,3 

•  3749 

46,4 

0.450 

0.46534 

110,3 

I.I0297 

46,5 

0.42190 

82,2 

2.3702 

46,2 

u 

tan  gd  u 

«  Fo' 

tec  gd  u 

-  Fo' 

•in  od  u 

-Fo' 

esc  gd  u 

-Fo' 

SMITHSONIAN  TABLC3 


114 


Natural  Hyperbolic  Functions. 


• 

sinh  u 

«F0' 

cosh  u 

<oFo' 

tanh  u 

«  Fo' 

coth  u 

-Fo' 

0.450 

0.46534 

H0,3 

I  .  10297 

46,5 

0.42190 

82,2 

2.3702 

46,2 

.451 

.46645 

no,3 

.10344 

46,6 

.42272 

82,1 

.3656 

46,0 

.452 

.46755 

110,4 

.  10300 

46,8 

.42354 

82,1 

.3610 

45,7 

•  453 

.46865 

110,4 

.  10437 

46,9 

.42436 

82,0 

.3565 

45,5 

•  454 

.46976 

no,5 

.  10484 

47,0 

.42518 

81,9 

•3519 

45,3 

0.455 

0.47086 

110,5 

i.  10531s 

47,1 

0.42600 

8i,9 

2.3474 

45,1 

•  456 

.47197 

110,6 

.  10578 

47,2 

.42682 

81,8 

•  3429 

44,9 

-457 

.47307 

110,6 

.10625 

47,3 

.42764 

8i,7 

.3384 

44,7 

.458 

.47418 

110,7 

.10673 

47,4 

.42845 

81,6 

•  3340 

44,5 

•459 

.47529 

110,7 

.  10720 

47,5 

.42927 

81,6 

•  3295 

44,3 

0.460 

0.47640 

110,8 

i  .  10768 

47,6 

0.43008 

8i,5 

2.3251 

44,1 

.461 

•47750 

110,8 

.10816 

47,8 

.43000 

81,4 

•  3207 

43,9 

.462 

.47861 

110,9 

.10863 

47,9 

.43171 

81,4 

.3164 

43,7 

•  463 

.47972 

110,9 

.10911 

48,0 

•43253 

&i,3 

.3120 

43,5 

.464 

.48083 

III,O 

.10959 

48,1 

•43334 

81,2 

•  3077 

43,3 

0.465 

0.48194 

III,O 

i.  11007 

48,2 

0.43415 

81,2 

2.3033 

43,1 

.466 

.48305 

in,  i 

.  i  1056 

48,3 

.43496 

81,1 

.2991 

42,9 

.467 

.48416 

iii.i 

.  i  i  104 

48,4 

•43577 

8  1,0 

.2948 

42,7 

.468 

.48527 

111,2 

.IH53 

48,5 

.43658 

80,9 

.2905 

42,5 

.469 

.48638 

111,2 

.11201 

48,6 

•43739 

80,9 

.2863 

42,3 

0.470 

0.48750 

111,2 

1.11250 

48,7 

0.43820 

80,8 

2.2821 

42,1 

.471 

.48861 

in,3 

.  11299 

48,9 

.43901 

80,7 

.2779 

4i,9 

.472 

.48972 

in,3 

.11348 

49,0 

.43981 

80,7 

.2737 

41,7 

.473 

.49084 

111,4 

.11397 

49,1 

.44062 

80,6 

.2695 

41,5 

•474 

.49195 

111,4 

.11446 

49,2 

.44M3 

80,5 

.2654 

41,3 

0.475 

0.49306 

ni,5 

I.  I  1495 

49,3 

0.44223 

80,4 

2.2613 

41,1 

.476 

.49418 

in,5 

.11544 

49,4 

.44303 

80,4 

.2572 

40,9 

•  477 

•49530 

111,6 

.11594 

49,5 

.44384 

80,3 

.2531 

40,8 

.478 

.40641 

ni,6 

.11643 

49,6 

•44464 

80,2 

.2490 

40,6 

•  479 

•49753 

111,7 

.11693 

49,8 

•44544 

80,2 

.2450 

40,4 

0.480 

0.49865 

ni,7 

1.11743 

49,9 

0.44624 

80,  i 

2.2409 

40,2 

.481 

.49976 

111,8 

.11793 

5o,o 

.44704 

80,0 

.2369 

40,0 

.482 

.50088 

111,8 

.11843 

5o,i 

.44784 

79,9 

.2329 

39,9 

.483 

.  50200 

111,9 

.11893 

50,2 

.44864 

79,9 

.2289 

39,7 

.484 

.50312 

111,9 

.11943 

50,3 

•44944 

79,8 

.2250 

39,5 

0.485 

0.50424 

1  1  2,0 

I.II994 

50,4 

0.45024 

79,7 

2.2210 

39,3 

.486 

.50536 

II2,O 

.12044 

50,5 

•45104 

79,7 

.2171 

39,2 

.487 

.50648 

112,1 

.12095 

50,6 

.45183 

79,6 

.2132 

39,0 

.488 

.50760 

112,1 

.12145 

50,8 

•45263 

79,5 

.2093 

38,8 

.489 

.50872 

112,2 

.12196 

50,9 

.45342 

79,4 

.2054 

38,6 

0.400 

0.50084 

112,2 

i  .  12247 

5i,o 

0.45422 

79,4 

2.  2Ol6 

38,5 

.491 

•51097 

112,3 

.12298 

5i,i 

•45501 

79,3 

.1978 

38,3 

.492 

.51209 

112,3 

.  12349 

51,2 

.45580 

79,2 

•1939 

38,1 

•493 

.51321 

112,4 

.  12401 

5i,3 

.45659 

79,2 

.I9OI 

38,0 

•  494 

.51434 

112,5 

.  12452 

5i,4 

•45739 

79,1 

.1863 

37,8 

0.495 

0.51546 

112,5 

1.12503 

5i,5 

0.45818 

79,0 

2.1826 

37,6 

.495 

.51659 

112,6 

.  12555 

5i,7 

.45897 

78,9 

.1788 

37,5 

•  497 

.51771 

112,6 

.12607 

5i,8 

•45975 

78,9 

.17,51 

37,3 

.498 

.51884 

112,7 

.  12659 

5i,9 

.46054 

78,8 

.1714 

37,1 

.499 

.51997 

112,7 

.12711 

52,0 

.46133 

78,7 

.1676 

37,0 

0.500 

0.52110 

112,8 

1.12763 

52,1 

0.46212 

78,6 

2.1640 

36,8 

tan  gd  u 

u,  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

csc  gd  u 

*>  Fo' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


a 

sinh  u 

*>F0' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

coth  u 

-  Fo' 

0.500 

0.52IIO 

112,8 

1.12763 

52,1 

0.46212 

78,6 

2.1640 

36,8 

.501 

.  52222 

112,8 

.12815 

52,2 

.46290 

78,6 

.1603 

36,7 

.502 

.52335 

112,9 

.12867 

52,3 

.46369 

78,5 

.1566 

36,5 

\J  J*J 

.503 

.52448 

112,9 

.12919 

52,4 

.46447 

78,4 

.1530 

36,4 

•  504 

.52561 

113,0 

.12972 

52,6 

.46526 

78,4 

•  1493 

^ 

36,2 

0.505 

0.52674 

H3,0 

1  .  13025 

52,7 

0.46604 

78,3 

2.1457 

3^,O 

.506 

.52787 

113,1 

•  13077 

52,8 

.46682 

78,2 

.1421 

35,9 

•  507 

.52900 

H3,I 

.13130 

52,9 

.46760 

78,1 

.1386 

35,7 

«-'••'*/ 

.508 

.53013 

113,2 

.13183 

53,o 

.46839 

78,1 

.1350 

35,6 

.509 

.53127 

113,2 

.13236 

53,1 

.46917 

78,0 

.1314 

35,4 

0.510 

0.53240 

H3,3 

I  .  13289 

53,2 

0.46995 

77,9 

2.1279 

35,3 

.511 

•53353 

H3,3 

•  13343 

53,4 

.47072 

77,9 

.1244 

35,i 

.512 

.53466 

H3,4 

.13396 

53,5 

.47150 

77,8 

.1209 

35,o 

•  513 

.53580 

H3,4 

.  13450 

53,6 

.47228 

77,7 

.1174 

34,8 

.5H 

.53693 

113,5 

•  13503 

53,7 

.47306 

77,6 

•1139 

34,7 

0.515 

0.53807 

H3,6 

I.I3557 

53,8 

0.47383 

77,5 

2.  1105 

34,5 

.516 

•53920 

H3,6 

.13611 

53,9 

.47461 

77,5 

.I07O 

34,4 

•  Si? 

.54034 

H3,7 

.13665 

54,0 

.47538 

77,4 

.1036 

34,3 

.518 

.54U8 

H3,7 

.13719 

54,1 

.47615 

77,3 

.1002 

34,1 

.519 

.54262 

H3,8 

•13773 

54,3 

.47693 

77,3 

.0968 

34,0 

0.520 

0-54375 

H3,8 

1.13827 

54,4 

0.47770 

77,2 

2.0934 

33,8 

.521 

.54489 

H3,9 

.13882 

54,5 

.47847 

77,i 

.0000 

33,7 

.522 

.54603 

H3,9 

.13936 

54,6 

.47924 

77,o 

.0866 

33,5 

•  523 
.524 

.54717 
.54831 

114,0 
114,0 

.13991 
.  14046 

54,7 
54,8 

.48001 
.48078 

77,o 
76,9 

.0833 

.0799 

33,4 
33,3 

0.525 

0.54945 

114,1 

I.I4IOI 

54,9 

0.48155 

76,8 

2.0766 

33,1 

.526 

.55059 

114,2 

.14156 

55,1 

.48232 

76,7 

.0733 

33,0 

•  527 

.55173 

114,2 

.14211 

55,2 

.48308 

76,7 

.0700 

32,9 

.528 

.55288 

H4,3 

.14266 

55,3 

•48385 

76,6 

.0668 

32,7 

.529 

•  55402 

H4,3 

.14321 

55,4 

.48462 

76,5 

.0635 

32,6 

0.530 

0.55516 

114,4 

I  •  14377 

55,5 

0.48538 

76,4 

2.0602 

32,4 

•  531 

.55631 

114,4 

.14432 

55,6 

•48615 

76,4 

.0570 

32,3 

•  532 

.55745 

H4,5 

.14488 

55,7 

.48691 

76,3 

.0538 

32,2 

•  533 

.55860 

H4,5 

•14544 

55,9 

•48767 

76,2 

.0506 

32,0 

•  534 

.55974 

114,6 

.14600 

56,0 

.48843 

76,i 

.0474 

3i,9 

0-535 

0.56089 

"4,7 

I  .  14656 

56,1 

0.48919 

76,i 

2.0442 

3i,8 

.536 

.  56204 

H4,7 

.14712 

56,2 

.48995 

76,0 

.0410 

3i,7 

•  537 

.56318 

114,8 

.14768 

56,3 

.49071 

75,9 

.0378 

3i,5 

.538 

.  56433 

114,8 

.14825 

56,4 

.49147 

75,8 

.0347 

3i,4 

•  539 

.56548 

114,9 

.14881 

56,5 

.49223 

75,8 

.0316 

3i,3 

0.540 

0.56663 

114,9 

I  .  14938 

56,7 

0.49299 

75,7 

2.0284 

3iJ 

•  541 

.56778 

H5,o 

.14994 

56,8 

•49374 

75,6 

.0253 

3i,o 

.542 

.56893 

U5,i 

.15051 

56,9 

•49450 

75,5 

.0222 

30,9 

•  543 

.57008 

H5,i 

.15108 

57,o 

.49526 

75,5 

.OI92 

30,8 

•  544 

.57123 

115,2 

.15165 

57,1 

.49601 

75,4 

.Ol6l 

30,6 

0.545 

0.57238 

H5,2 

I.I5223 

57,2 

0.49676 

75,3 

2.OI3O 

30,5 

.546 

•57354 

H5,3 

.15280 

57,4 

.49752 

75,2 

.OIOO 

30,4 

•547 

.57469 

H5,3 

.15337 

57,5 

.49827 

75,2 

.007O 

30,3 

•  548 

.57584 

H5,4 

.15395 

57,6 

.49902 

75,i 

.0039 

30,2 

•549 

•57700 

H5,5 

.15452 

57,7 

.49977 

75,0 

.0009 

30,0 

0.550 

0.57815 

H5,5 

I.I55IO 

57,8 

0.50052 

749 

1.9979 

29,9 

1 

tan  gd  u 

«  Fo' 

sec  gd  u 

-  Fo' 

sin  gd  u 

«  Fo' 

esc  od  u 

-Fo' 

SMITHSONIAN  TABLES 


116 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.550 

0.57815 

H5,5 

I.I55IO 

57,8 

0.50052 

74,9 

1.9979 

29,9 

.551 

.57931 

115,6 

.15568 

57,9 

.50127 

74,9 

.9949 

29,8 

.552 

.58046 

115,6 

.15626 

58,0 

.  50202 

74,8 

.9920 

29,7 

•  553 

.58162 

H5,7 

.15684 

58,2 

.50277 

74,7 

.9890 

29,6 

•  554 

.58278 

H5,7 

.15742 

58,3 

.50351 

74,6 

.9860 

29,4 

0.555 

0.58393 

H5,8 

1.15801 

58,4 

0.50426 

74,6 

1.9831 

29,3 

.556 

.58509 

H5,9 

.15859 

58,5 

.50500 

74,5 

.9802 

29,2 

•  557 

.58625 

H5,9 

.15918 

58,6 

.50575 

74,4 

.9773 

29,1 

•  558 

.58741 

116,0 

.15976 

58,7 

.50649 

74,3 

•9744 

29,0 

•  559 

.58857 

116,0 

.16035 

58,9 

.50724 

74,3 

.9715 

28,9 

0.560 

0.58973 

116,1 

1.16094 

59,o 

0.50798 

74,2 

1.9686 

28,8 

.561 

.59089 

116,2 

.16153 

59,i 

.50872 

74,1 

.9657 

28,6 

.562 

.59205 

116,2 

.id?  12 

59,2 

.50946 

74,0 

.9629 

28,5 

.563 

•59322 

116,3 

.  16272 

59,3 

.51020 

74,o 

.9600 

28,4 

.564 

.59438 

"6,3 

.16331 

59,4 

.51094 

73,9 

.9572 

28,3 

0.565 

0.59554 

116,4 

i  .  16390 

59,6 

0.51168 

73,8 

1.9544 

28,2 

.566 

.59671 

116,5 

.  16450 

59,7 

.51242 

73,7 

.9515 

28,1 

.567 

.59787 

116,5 

.16510 

59,8 

.51315 

73,7 

.9487 

28,0 

.568 

.59904 

116,6 

.  16570 

59,9 

.51389 

73,6 

.9459 

27,9 

.569 

.60020 

116,6 

.16630 

00,0 

.51462 

73,5 

.9432 

27,8 

0.570 

0.60137 

116,7 

1.16690 

60,1 

0.51536 

73,4 

1.9404 

27,7 

.571 

.60254 

116,7 

.  16750 

60,3 

.51609 

73,4 

.9376 

27,5 

•  572 

.60371 

116,8 

.16810 

60,4 

.51683 

73,3 

.9349 

27,4 

.573 

.60487 

116,9 

.16871 

60,5 

.51756 

73,2 

•9321 

27,3 

•  574 

.60604 

116,9 

.16931 

60,6 

.51829 

73,1 

.9294 

27,2 

0.575 

0.60721 

117,0 

1.16992 

60,7 

0.51902 

73,i 

1.9267 

27,1 

.576. 

.60838 

117,1 

.  17053 

60,8 

.51975 

73,0 

.9240 

27,0 

•  577 

•60955 

117,1 

.17113 

61,0 

.52048 

72,9 

.9213 

26,9 

.578 

.61073 

117,2 

.17174 

61,1 

.52121 

72,8 

.9186 

26,8 

.579 

.61190 

117,2 

.17236 

61,2 

.52194 

72,8 

.9159 

26,7 

0.580 

0.61307 

H7,3 

I  .  17297 

61,3 

0.52267 

72,7 

I.9I33 

26,6 

.581 

.61424 

ii7,4 

.17358 

61,4 

.52339 

72,6 

.9106 

26,5 

.582 

.61542 

H7,4 

.17420 

6i,5 

.52412 

72,5 

.9080 

26,4 

.583 

.61659 

H7,5 

.17481 

6i,7 

.52484 

72,5 

•  9053 

26,3 

.584 

.61777 

117,5 

.17543 

61,8 

.52557 

72,4 

.9027 

26,2 

0.585 

0.61894 

117,6 

1.17605. 

61,9 

0.52629 

72,3 

1.9001 

26,1 

.586 

.62012 

H7,7 

.17667 

62,0 

.52701 

72,2 

.8975 

26,0 

.587 

.62130 

117,7 

.  17729 

62,1 

.52773 

72,2 

.8949 

25,9 

.588 

.62247 

117,8 

.17791 

62,2 

.52846 

72,1 

.8923 

25,8 

.589 

.62365 

H7,9 

.17853 

62,4 

.52918 

72,o 

.8897 

25,7 

0.590 

0.62483 

H7,9 

i  .  17916 

62,5 

0.52990 

7i,9 

1.8872 

25,6 

•  591 

.62601 

118,0 

.  17978 

62,6 

.53061 

7i,8 

.8846 

25,5 

.592. 

-"  .  62719  „ 

118,0 

.18041 

62,7 

.53133 

7i,8 

.8821 

25,4 

•  593 

.62837 

118,1 

.  18104 

62,8 

.  53205 

7i,7 

.8795 

25,3 

•  594 

.62955 

118,2 

.  18167 

63,0 

.53277 

7i,6 

.8770 

25,2 

0.595 

0.63073 

118,2 

i  .  18230 

63,1 

0.53348 

7i,5 

1.8745 

25,1 

.596 

.63192 

"8,3 

.  18293 

63,2 

•53420 

7i,5 

.8720 

25,0 

.597 

.63310 

118,4 

.18356 

63,3 

•53491 

7i,4 

.8695 

24,9 

.598 

.63428 

"8,4 

.  18419 

63,4 

.53562 

7i,3 

.8670 

24,9 

•  599 

.63547 

"8,5 

.18483 

63,5 

.53634 

71,2 

.8645 

24,8 

0.600 

0.63665 

"8,5 

i  .  18547 

63,7 

0.53705 

71,2 

1.8620 

247 

u 

tan  gd  u 

*>  Fo' 

sec  gd  u 

«F0' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«  Fo' 

SMITHS  >NIAN  TABLES 


117 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

"Fo' 

tanh  u 

«  Fo' 

coth  u 

*  Fo' 

0.600 

0.63665 

"8,5 

1.18547 

63,7 

0.53705 

71,2 

1.8620 

24,7 

.601 

•63784 

118,6 

.18610 

63,8 

.53776 

7IJ 

.8596 

24,6 

.002 

.63903 

118,7 

.18674 

63,9 

.53847 

71,0 

.8571 

24,5 

.603 

.64021 

"8,7 

.18738 

64,0 

.53918 

70,9 

.8547 

24,4 

.604 

.64140 

11818 

.18802 

64,1 

.53989 

70,9 

.8522 

24,^ 

0.605 

0.64259 

"8,9 

1.18866 

64,3 

0.54060 

70,8 

1.8498 

24,2 

.606 

,64378 

"8,9 

.18931 

64,4 

.54131 

70,7 

.8474 

24,1 

.607 

.64497 

119,0 

.18995 

04,5 

.54201 

70,6 

.8450 

24,0 

.608 

.64616 

119,1 

.19060 

64,6 

.54272 

70,5 

.8426 

24,0 

.609 

.64735 

119,1 

.  19124 

64,7 

•54342 

70,5 

.8402 

23,9 

0.610 

0.64854 

"9,2 

I  .  19189 

64,9 

0.54413 

70,4 

1.8378 

23,8 

.611 

.64973 

"9,3 

.  19254 

65,O 

.54483 

70,3 

.8354 

23,7 

.612 

.65093 

"9,3 

.19319 

65,i 

.54553 

70,2 

.8331 

23,6 

.613 

.65212 

"9,4 

.  19384 

65,2 

.54624 

70,2 

.8307 

23,5 

.614 

.65331 

119,4 

.19449 

65,3 

.54694 

7o,i 

.8284 

23,4 

0.615 

0.65451 

"9,5 

1.19515 

65,5 

0.54764 

70,0 

1.8260 

23,3 

.616 

.65570 

"9,6 

.19580 

65,6 

.54834 

69,9 

.8237 

23,3 

.617 

.65690 

119,6 

.19646 

65,7 

.54904 

69,9 

.8214 

23,2 

.618 

.65810 

"9,7 

.  19712 

65,8 

.54973 

69,8 

.8191 

23,1 

.619 

.65929 

"9,8 

.  19778 

65,9 

.55043 

69,7 

.8168 

23,0 

0.620 

0.66049 

"9,8 

1.19844 

66,0 

0.55"3 

69,6 

I.8I45 

22,9 

.621 

.66169 

119,9 

.19910 

66,2 

.55182 

69,5 

.8122 

22,8 

.622 

.66289 

120,0 

.19976 

66,3 

.55252 

69,5 

.8099 

22,8 

.623 

.66409 

120,0 

.20042 

66,4 

•55321 

69,4 

.8076 

22,7 

.624 

.66529 

I2O,I 

.20109 

66,5 

.55391 

69,3 

.8054 

22,6 

0.625 

0.66649 

1  2O,2 

1.20175 

66,6 

0.55400 

69,2 

1.8031 

22,5 

.626 

.66769 

120,2 

.20242 

66,8 

.55529 

69,2 

.8009 

22,4 

.627 

.66890 

120,3 

.20309 

66,9 

.55598 

69,1 

.7986 

22,4 

.628 

.67010 

120,4 

.20376 

67,0 

.55667 

69,0 

.7964 

22,3 

.629 

.67130 

120,4 

.20443 

67,1 

•  55736" 

68,9 

.7942 

22,2 

0.630 

0.67251 

120,5 

1.20510 

67,3 

0.55805 

68,9 

I.79I9 

22,1 

.631 

.67371 

I2O,6 

.20577 

67,4 

.55874 

68,8 

.7897 

22,0 

.632 

.67492 

1  2O,6 

.20645 

67,5 

.55943 

68,7 

.7875 

22,0 

.633 

.67613 

120,7 

.20712 

67,6 

.56011 

68,6 

.7853 

21,9 

•634 

.67734 

120,8 

.20780 

67,7 

.56080 

68,6 

.7832 

21,8 

0.635 

0.67854 

120,8 

1.20848 

67,9 

0.56149 

68,5 

1.7810 

21,7 

.636 

.67975 

120,9 

.20916 

68,0 

.56217 

68,4 

.7788 

21,6 

.637 

.68096 

I2I,O 

.20084 

68,1 

.56285 

68,3 

.7767 

21,6 

.638 

.68217 

121,1 

.21052 

68,2 

.56354 

68,2 

•  7745 

21,5 

•  639 

.68338 

121,1 

.2II2O 

68,3 

.56422 

68,2 

.7724 

21,4 

0.640 

0.68459 

121,2 

I.2II89 

68,5 

0.56490 

68,1 

1.7702 

21,3 

.641 

.68581 

121,3 

.21257 

68,6 

.56558 

68,0 

.7681 

21,3 

.642 

.68702 

121,3 

.21326 

68,7 

.56626 

67,9 

.7660 

21,2 

.643 

.68823 

121,4 

.21395 

68,8 

.56694 

67,9 

.7639 

21,1 

.644 

.68945 

121,5 

.21463 

68,9 

.56762 

67,8 

.7618 

21,0 

0.645 

0.69066 

121,5 

I.2I532 

69,1 

0.56829 

67,7 

1-7597 

21,0 

.646 

.69188 

121,6 

.21602 

69,2 

.56897 

67,6 

.7576 

2O,9 

.647 

.69309 

121,7 

.21671 

69,3 

.56965 

67,6 

•  7555 

20,8 

.648 

.69431 

121,7 

.21740 

69,4 

.57032 

67,5 

•  7534 

20,7 

•649 

.69553 

121,8 

.2l8lO 

09,6 

.57100 

67,4 

.7513 

20,7 

0.650 

0.69675 

121,9 

I.2I879 

69,7 

0.57167 

67,3 

1.7493 

2O.6 

u 

tan  od  u 

«  F</ 

sec  gd  u 

-Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


118 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

O.FO' 

cosh  u 

<oF0' 

tanh  u 

«  Fo' 

coth  u 

«F0' 

0.650 

0.69675 

121,9 

1.21879 

69,7 

0.57167 

67,3 

1.7493 

20,6 

.651 

.69797 

121,9 

.21949 

69,8 

.57234 

67,2 

.7472 

20,5 

.652 

.69919 

1  22,0 

.22019 

69,9 

•57301 

67,2 

.7452 

20,5 

.653 

.70041 

122,1 

.22089 

7o,o 

.57369 

67,1 

•  7431 

20,4 

.654 

.70163 

122,2 

.22159 

70,2 

.57436 

67,0 

.74H 

20,3 

0.655 

0.70285 

122,2 

1.22229 

70,3 

0.57503 

66,9 

I.739I 

20,2 

.656 

.70407 

122,3 

.22300 

70,4 

•57570 

66,9 

•  7370 

2O,2 

.657 

.70530 

122,4 

.22370 

70,5 

.57636 

66,8 

.7350 

20,1 

.658 

.70652 

122,4 

.22441 

70,7 

•57703 

66,7 

.7330 

20,O 

.659 

•70775 

122,5 

.22511 

70,8 

•57770 

66,6 

.7310 

2O,0 

0.660 

0.70897 

122,6 

1.22582 

70,9 

0.57836 

66,5 

1.7290 

19,9 

.661 

.7I02O 

122,7 

.22653 

71,0 

•57903 

66,5 

.7270 

19,8 

.662 

.71142 

122,7 

.22724 

7i,i 

.57969 

66,4 

.7251 

19,8 

.663 

.71265 

122,8 

.22795 

71,3 

.58036 

66,3 

.7231 

19,7 

.664 

.71388 

122,9 

.22867 

71,4 

.  58102 

66,2 

.7211 

19,6 

0.665 

0.7I5H 

122,9 

1.22938 

71,5 

0.58168 

66,2 

I.7I92 

19,6 

.666 

.71634 

123,0 

.23010 

7i,6 

.58234 

66,1 

.7172 

19,5 

.667 

.71757 

123,1 

.23081 

7i,8 

.58300 

66,0 

•7153 

19,4 

.668 

.71880 

123,2 

.23153 

7i,9 

.58366 

65,9 

.7133 

19,4 

.669 

.72003 

123,2 

.23225 

72,0 

.58432 

65,9 

.7114 

19,3 

0.670 

0.72126 

123,3 

1.23297 

72,1 

0.58498 

65,8 

1.7095 

19,2 

.671 

.72250 

123,4 

.23369 

72,2 

•58564 

65,7 

.7075 

19,2 

.672 

.72373 

123,4 

.23442 

72,4 

.58629 

65,6 

.7056 

19,1 

.673 

.72497 

123,5 

.23514 

72,5 

.58695 

65,5 

.7037 

19,0 

.674 

.72620 

123,6 

.23587 

72,6 

.58760 

65,5 

.7018 

19,0 

0.675 

0.72744 

123,7 

1.23659 

72,7 

0.58826 

65,4 

1.6999 

18,9 

.676 

.72868 

123,7 

.23732 

72,9 

.58891 

65,3 

.6980 

18,8 

.677 

.72091 

123,8 

.23805 

73,o 

.58957 

65,2 

.6962 

18,8 

.678 

.73H5 

123,9 

.23878 

73,i 

.59022 

65,2 

.6943 

18,7 

.679 

.73239 

124,0 

.23951 

73,2 

.59087 

65,1 

.6924 

18,6 

0.680- 

-0.73363 

124,0 

1.24025 

73,4 

0.59152 

65,0 

1.6906 

18,6 

.681 

.73487 

124,1 

.24098 

73,5 

•59217 

64,9 

.6887 

18,5 

.682 

.73611 

124,2 

.24172 

73,6 

.59282 

64,9 

.6869 

18,5 

.683 

.73735 

124,2 

.24245 

73,7 

•59347 

64,8 

.6850 

18,4 

.684 

.73860 

124,3 

.24319 

73,9 

•594II 

64,7 

.6832 

18,3 

0.685 

0.73984 

124,4 

1.24393 

74,0 

0.59476 

64,6 

1.6813 

18,3 

.686 

.74109 

124,5 

.24467 

74,1 

•59541 

64,5 

.6795 

18,2 

.687 

.74233 

124,5 

.24541 

74,2 

.59605 

64,5 

.6777 

18,1 

.688 

•74358 

124,6 

.24616 

74,4 

.59670 

64,4 

.6759 

18,1 

.689 

.74482 

124,7 

.24690 

74,5 

•59734 

64,3 

.6741 

18,0 

0.690 

0.74607 

124,8 

1.24765 

74,6 

0.59798 

64,2 

1.6723 

18,0 

.691 

•74732 

124,8 

.24839 

74,7 

.59862 

64,2 

.6705 

17,9 

.692 

.74857 

124,9 

.24914 

74,9 

•50927 

64,1 

.6687 

17,8 

.693 

.74982 

125,0 

.24989 

75,o 

.59991 

64,0 

.6669 

17,8 

.694 

.75107 

125,1 

.25064 

75,i 

.60055 

63,9 

.6652 

17,7 

0.695 

0.75232 

125,1 

I.25I39 

75,2 

o.  60118 

63,9 

1.6634 

17,7 

.696 

.75357 

125,2 

.25214 

75,4 

.60182 

63,8 

.6616 

17,6 

.697 

.75482 

125,3 

.25290 

75,5 

.60246 

63,7 

.6599 

17,6 

.698 

.75607 

125,4 

.25365 

75,6 

.60310 

63,6 

.6581 

17,5 

.699 

•75733 

125,4 

.25441 

75,7 

.60373 

63,6 

.6564 

17,4 

0.700 

0.75858 

125,5 

I.255I7 

75,9 

0.60437 

63,5 

1.6546 

17,4 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«  Fo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


IIQ 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«FO' 

cosh  u 

«F0' 

tanh  u 

«  Fo' 

coth  u 

«  Fo' 

0.700 

0.75858 

125,5 

I.255I7 

75,9 

0.60437 

63,5 

1.6546 

17,4 

.701 

.75984 

125,6 

•25593 

76,0 

.60500 

63,4 

.6529 

17,3 

.702 

.76110 

125,7 

.25669 

76,1 

.60564 

63,3 

.6512 

17,3 

.703 

.76235 

125,7 

.25745 

76,2 

.60627 

63,2 

.6494 

17,2 

.704 

.76361 

125,8 

.25821 

76,4 

.60690 

63,2 

.6477 

17,1 

0.705 

0.76487 

125,9 

1.25898 

76,5 

0.60753 

63,1 

1.6460 

17,1 

.706 

.76613 

126,0 

.25974 

76,6 

.60816 

63,0 

•  6443 

17,0 

.707 

.76739 

126,1 

.26051 

76,7 

.60879 

62,9 

.6426 

17,0 

.708 

.76865 

126,1 

.26128 

76,9 

.60942 

62,9 

.6409 

16,9 

.709 

.76991 

126,2 

.26205 

77,o 

.61005 

62,8 

.6392 

16,9 

0.710 

0.77H7 

126,3 

1.26282 

77,1 

0.61068 

62,7 

1.6375 

16,8 

.711 

.77244 

126,4 

.26359 

77,2 

.61130 

62,6 

.6358 

16,8 

.712 

.77370 

126,4 

.26436 

77,4 

.61193 

62,6 

.6342 

16,7 

.713 

•77497 

126,5 

.26514 

77,5 

.61255 

62,5 

16,7 

.714 

.77623 

126,6 

.26591 

77,6 

.61318 

62,4 

.6308 

16,6 

0.715 

0.77750 

126,7 

1.26669 

77,7 

0.61380 

62,3 

1.6292 

16,5 

.716 

.77876 

126,7 

.26747 

77,9 

.61443 

62,2 

.6275 

16,5 

.717 

.78003 

126,8 

.26825 

78,0 

.61505 

62,2 

.6259 

16,4 

.718 

.78130 

126,9 

.26903 

78,i 

.61567 

62,1 

.6242 

16,4- 

.719 

.78257 

127,0 

.26981 

78,3 

.61629 

62,O 

.6226 

16,3 

0.720 

0.78384 

127,1 

1.27059 

78,4 

0.61691 

61,9 

1.6210 

16,3 

.721 

.785H 

127,1 

.27138 

78,5 

.61753 

61,9 

.6194 

16,2 

.722 

.78538 

127,2 

.27216 

78,6 

.61815 

61,8 

.6177 

16,2 

.723 

.78766 

127,3 

.27295 

78,8 

.61876 

61,7 

.6161 

16,1 

.724 

.78893 

127,4 

.27374 

78,9 

.61938 

61,6 

.6145 

16,1 

0.725 

0.7902O 

127,5 

1.27453 

79,o 

0.62000 

61,6 

1.6129 

16,0 

.726 

.79M8 

127,5 

.27532 

79,i 

.62061 

61,5 

.6113 

16,0 

.727 

.79275 

127,6 

.27611 

79,3 

.62123 

61,4 

.6097 

15,9 

.728 

.79403 

127,7 

.27690 

79,4 

.62184 

61,3 

.6081 

15,9 

.729 

•79531 

127,8 

.27770 

79,5 

.62245 

61,3 

.6065 

15,8 

0.730 

0.79659 

127,8 

1.27849 

79,7 

0.62307 

61,2 

1.6050 

15,8 

.731 

.79786 

127,9 

.27929 

79,8 

.62368 

61,1 

.6034 

15,7 

.732 

.79914 

128,0 

.28009 

79,9 

.62429 

61,0 

.6018 

15,7 

.733 

.80042 

128,1 

.28089 

80,0 

.62490 

61,0 

.6003 

15,6 

•  734 

.80171 

128,2 

.28169 

80,2 

.62551 

60,9 

•  5087 

15,6 

0.735 

0.80299 

128,2 

1.28249 

80,3 

0.62611 

60,8 

1.5972 

15,5 

.736 

.80427 

128,3 

.28330 

80,4 

.62672 

60,7 

.5956 

15,5 

•  737 

.80555 

128,4 

.28410 

80,6 

.62733 

60,6 

.5941 

15,4 

.738 

.80684 

128,5 

.28491 

80,7 

.62794 

60,6 

.5925 

15,4 

.739 

.80812 

128,6 

.28572 

80,8 

.62854 

60,5 

.5910 

15,3 

0.740 

0.80941 

128,7 

1.28652 

80,9 

0.62915 

60,4 

1.5895 

15,3 

.741 

.81070 

128,7 

.28733 

81,1 

.62975 

60,3 

.5879 

15,2 

.742 

.81109 

128,8 

.28815 

81,2 

.63035 

60,3 

•  5864 

15,2 

•  743 

.81327 

128,9 

.28896 

81,3 

.63095 

60,2 

.5849 

•  744 

.81456 

129,0 

.28977 

81,5 

.63156 

60,  i 

.5834 

I5J 

0.745 

0.81585 

129,1 

1.29059 

81,6 

0.63216 

60,0 

I.58I9 

15,0 

.746 

.81714 

129,1 

.29140 

81,7 

.63276 

60,0 

0804 

I5,o 

•  747 

.81844 

129,2 

.29222 

81,8 

.63336 

59,9 

.5780 

14,9 

.748 

.81973 

129,3 

.29304 

82,0 

.63395 

59,8 

•  5774 

14,9 

•  749 

.82102 

129,4 

.29386 

82,1 

.63455 

59,7 

.5759 

14,8 

0.750 

0.82232 

129,5 

1.29468 

82.2 

0.63515 

59,7 

1.5744 

14,8 

u 

tan  gd  u 

.F.< 

sec  gd  u 

-Fo' 

•in  gd  u 

<-  Fo' 

esc  gd  u 

-  Fo' 

SMITHSONIAN  TABLES 


120 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

»Fo' 

tanh  u 

«FO' 

coth  u 

«  Fo' 

0.750 

0.82232 

129,5 

1.29468 

82,2 

0.63515 

59,7 

1-5744 

14,8 

.751 

.82361 

129,6 

.29551 

82,4 

.63575 

59,6 

•  5730 

14,7 

.752 

.82491 

129,6 

.29633 

82,5 

.63634 

59,5 

.5715 

14,7 

.753 

.82620 

129,7 

.29716 

82,6 

.63694 

59,4 

.5700 

14,6 

•  754 

.82750 

129,8 

.29798 

82,8 

•63753 

59,4 

.5686 

14,6 

0.755 

0.82880 

129,9 

1.29881 

82,9 

0.63812 

59,3 

1.5671 

14,6 

.756 

.83010 

130,0 

.29964 

83,0 

.63871 

59,2 

.5656 

14,5 

•  757 

.83140 

130,0 

.30047 

83,1 

.63931 

59,i 

.5642 

14,5 

•  758 

.83270 

130,1 

.30130 

83,3 

.63990 

59,1 

.5628 

14,4 

•  759 

.83400 

130,2 

.30214 

83,4 

.64049 

59,0 

•  5613 

14,4 

0.760 

0.83530 

130,3 

1.30297 

83,5 

0.64108 

58,9 

1.5599 

14,3 

.761 

.83661 

130,4 

.30381 

83,7 

.64167 

58,8 

.5584 

14,3 

.762 

.83791 

130,5 

.30464 

83,8 

.64225 

58,8 

.5570 

14,2 

.7^3 

.83922 

130,5 

.30548 

83,9 

.64284 

58,7 

.5556 

14,2 

.764 

.  84052 

130,6 

.30632 

84,1 

.64343 

58,6 

•  5542 

14,2 

0.765 

0.84183 

130,7 

1.30716 

84,2 

0.64401 

58,5 

1.5528 

14,1 

.766 

.84314 

130,8 

.30801 

84,3 

.64460 

58,4 

.5514 

14,1 

.767 

.84445 

130,9 

.30885 

84,4 

.64518 

58,4 

.5500 

14,0 

.768 

.84576 

131,0 

.30970 

84,6 

.64576 

58,3 

.5486 

14,0 

.769 

.84707 

131,1 

.31054 

84,7 

.64635 

58,2 

•  5472 

13,9 

0.770 

0.84838 

131,1 

I.3H39 

84,8 

0.64693 

58,i 

1.5458 

13,9 

.771 

.84969 

131,2 

.31224 

85,0 

.64751 

58,i 

.5444 

13,9 

.772 

.85100 

I3i,3 

.31309 

85,1 

.64809 

58,0 

.5430 

13,8 

•  773 

.85231 

131,4 

.31394 

85,2 

.64867 

57,9 

.5416 

13,8 

•  774 

.85363 

131,5 

.31479 

85,4 

.64925 

57,8 

.5402 

13,7 

0.775 

0.85494 

131,6 

I.3I565 

85,5 

0.64983 

57,8 

1.5389 

13,7 

.776 

.85626 

I3i,7 

.31650 

85,6 

.65040 

57,7 

•  5375 

13,6 

•  777 

.85758 

I3i,7 

.31736 

85,8 

.65098 

57,6 

.536i 

13,6 

.778 

.85889 

131,8 

.31822 

85,9 

.65156 

57,5 

.5348 

13,6 

•  779 

.86021 

131,9 

.31908 

86,0 

.65213 

57,5 

•  5334 

13,5 

0.780 

0.86153 

132,0 

1.31994 

86,2 

0.65271 

57,4 

I.532I 

13,5 

.781 

.86285 

132,1 

.32080 

86,3 

.65328 

57,3 

.5307 

13,4 

.782 

.86417 

132,2 

.32166 

86,4 

.65385 

57,2 

.5294 

13,4 

.783 

.86550 

132,3 

.32253 

86,5 

.65443 

57,2 

.5281 

13,3 

.784 

.86682 

132,3 

.32340 

86,7 

.65500 

57,1 

.5267 

13,3 

0.785 

0.86814 

132,4 

1.32426 

86,8 

0.65557 

57,0 

1.5254 

13,3 

.786 

.86947 

132,5 

.32513 

86,9 

.65614 

56,9 

.5241 

13,2 

-787- 

.87079 

132,6 

.32600 

87,1 

.65671 

56,9 

.5228 

13,2 

.788 

.§7212 

132,7 

.32687 

87,2 

.65727 

56,8 

.5214 

I3,i 

.789 

.87345 

132,8 

.32775 

87,3 

.65784 

56,7 

.5201 

I3,i 

0.790 

0.87478 

132,9 

1.32862 

87,5 

0.65841 

56,6 

1.5188 

I3J 

.791 

.87610 

132,9 

.32950 

87,6 

.65898 

56,6 

.5175 

13,0 

•  792 

.87743 

I33,o 

.33037 

87,7 

•65954 

56,5 

.5162 

13,0 

•  793 

.87877 

I33,i 

.33125 

87,9 

.66011 

56,4 

.5149 

12,9 

•  794 

.88010 

133,2 

.33213 

88,0 

.66067 

56,4 

•  5136 

12,9 

0.795 

0.88143 

133,3 

I.3330I 

88,1 

0.66123 

56,3 

1.5123 

12,9 

.796 

.88276 

133,4 

.33389 

88,3 

.66179 

56,2 

.5110 

12,8 

.797 

.88410 

133,5 

.33478 

88,4 

.66236 

56,i 

.5098 

12,8 

.798 

.88543 

133,6 

.33566 

88,5 

.66292 

56,i 

.5085 

12,8 

•  799 

.88677 

133,7 

.33655 

88,7 

.66348 

56,o 

.5072 

12,7 

0.800 

0.88811 

133,7 

1-33743 

88,8 

0.66404 

55,9 

1.5059 

12,7 

u 

tan  gd  u 

«  Fo' 

sec  gd  u 

«  Fo' 

sin  gd  u 

«-  Fo' 

esc  gd  u 

»F0' 

SMITHSONIAN  TABLES 


121 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

»F0' 

cosh  u 

coFo' 

tanh  u 

W  Fo' 

coth  u 

«  Fo' 

0.800 

0.888II 

133,7 

1-33743 

88,8 

0.66404 

55,9 

1.5059 

12,7 

.801 

.88944 

133,8 

.33832 

88,9 

.66460 

55,8 

•5047 

12,6 

.802 

.80078 

133,9 

•33921 

89,1 

.66515 

55,8 

•5034 

12,6 

.803 

.89212 

134,0 

.34011 

89,2 

.66571 

55,7 

.5022 

12,6 

.804 

.89346 

134,1 

.34100 

89,3 

.66627 

55,6 

.5009 

12,5 

0.805 

0.89480 

134,2 

1.34189 

89,5 

0.66682 

55,5 

1.4996 

12,5 

.806 

.89615 

134,3 

.34279 

89,6 

.66738 

55,5 

.4984 

12,5 

.807 

.89749 

134,4 

•34368 

89,7 

.56793 

55,4 

•  4972 

12,4 

.808 

.89883 

134,5 

•34458 

89,9 

.60849 

55,3 

•  4959 

12,4 

.809 

.90018 

1345 

.34548 

90,o 

.66904 

55,2 

•4947 

12,3 

0.810 

0.90152 

134,6 

1.34638 

00,2 

0.66959 

55,2 

1.4935 

12,3 

.811 

.90287 

134,7 

.34729 

90,3 

.67014 

55,i 

.4922 

12,3 

.812 

.90422 

134,8 

.34819 

90,4 

.67069 

55,o 

.4910 

12,2 

.813 

.90557 

134,9 

.34909 

90,6 

.67124 

54,9 

.4898 

12,2 

.814 

.90692 

135,0 

.35000 

90,7 

.67179 

54,9 

.4886 

12,2 

0.815 
.816 

0.90827 
.90962 

I35,i 
135,2 

I.3509I 
.35182 

90,8 
91,0 

0.67234 
.67289 

54,8 

54,7 

1.4873 
.4861 

12,1 
12,1 

.817 

.91097 

135,3 

.35273 

91,1 

.67343 

54,6 

.4849 

12,0 

.818 

.91232 

135,4 

.35364 

91,2 

.67398 

54,6 

.4837 

I2,O 

.819 

.91368 

135,5 

•35455 

91,4 

•67453 

54,5 

.4825 

12,0 

0.820 

0.91503 

135,5 

1.35547 

9i,5 

0.67507 

54,4 

1.4813 

11,9 

.821 

.91639 

135,6 

.35638 

91,6 

.67561 

54,4 

.4801 

11,9 

.822 

•91775 

135,7 

•35730 

9i,8 

.67616 

54,3 

.4789 

11,9 

.823 

.91910 

135,8 

.35822 

91,9 

.67670 

54,2 

•  4778 

11,8 

.824 

.92046 

135,9 

.35914 

92,0 

.67724 

54,1 

.4766 

11,8 

0.825 

0.92182 

136,0 

1.36006 

92,2 

0.67778 

54,1 

1.4754 

11,8 

.826 

.92318 

136,1 

.36098 

92,3 

.67832 

54,0 

•  4742 

n,7 

.827 

•92454 

136,2 

•36190 

92,5 

.67886 

53,9 

•4731 

u,7 

.828 

.92591 

136,3 

.36283 

92,6 

.67940 

53,8 

.4719 

n,7 

.829 

.92727 

136,4 

.36376 

92,7 

.67994 

53,8 

•  4707 

n,6 

0.830 

0.92863 

136,5 

1.36468 

92,9 

0.68048 

53,7 

1.4696 

11,6 

.831 

.93000 

136,6 

.36561 

93,o 

.68101 

53,6 

.4684 

11,6 

.832 

.93137 

136,7 

.36654 

93,i 

.68155 

53,5 

.4672 

n,5 

.833 

.93273 

136,7 

.36748 

93,3 

.68208 

53,5 

.4661 

n,5 

.834 

•93410 

136,8 

.36841 

93,4 

.68262 

534 

.4649 

n,5 

0.835 

0.93547 

136,9 

1.36934 

93,5 

0.68315 

53,3 

1.4638 

11,4 

.836 

.93684 

i37,o 

•370*8 

93,7 

.68368 

53,3 

.4627 

11,4 

.837 

.93821 

i37,i 

•37122 

93,8 

.68422 

53,2 

.4615 

11,4 

.838 

.93958 

137,2 

.37216 

94,o 

.68475 

53,i 

.4604 

ii,3 

.839 

•94095 

137,3 

•37310 

94,1 

.68528 

53,0 

•4593 

ii,3 

0.840 

0.94233 

137,4 

1.37404 

94,2 

0.68581 

53,0 

i.458i 

ii,3 

.841 

•94370 

137,5   .37498 

94,4 

.68634 

52,9 

•  45/0 

11,2 

.842 

.94508 

137,6   .37593 

94,5 

.68687 

52,8 

•  4559 

11,2 

.843 

.94645 

137,7  !  .37687 

94,6 

.68739 

52,7 

.4548 

11,2 

.844 

.94783 

137,8 

.37782 

94,8 

.68792 

52,7 

•  4537 

11,1 

0.845 

O.9492I 

137,9 

1.37877 

94,9 

0.68845 

52,6 

1.4525 

11,1 

.846 

•95059 

138,0 

•37972 

95,1 

.68807 

52,5 

.4514 

II,! 

.847 

.95197 

138,1 

.38067 

95,2 

.68950 

52,5 

.4503 

11,0 

.848 

•95335 

138,2 

.38162 

95,3 

.6000.2 

52,4 

.4492 

11,0 

.949 

•95473 

138,3 

.38258 

95,5 

.69055 

52,3 

.4481 

11,0 

0.850 

0.95612 

138,4 

1.38353 

95,6 

0.69107 

52,2 

1.4470 

10,9 

• 

tan  gd  u 

«FO' 

sec  gd  u 

«Fo' 

sin  gd  u 

«F0' 

esc  gd  u 

«  Fo' 

SMITHSONIAN  TABLES 


122 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«FO' 

tanhu 

«F0' 

coth  u 

<-FO' 

0.850 

0.95612 

138,4 

1.38353 

95,6 

0.69107 

52,2 

1.4470 

10,9 

.851 

•95750 

138,4 

.38449 

95,7 

.69159 

52,2 

•4459 

10,9 

.852 

.95888 

138,5 

.38545 

95,9 

.69211 

52,1 

•4449 

10,9 

.853 

.96027 

138,6 

.38641 

96,0 

.69263 

52,0 

•  4438 

10,8 

.854 

.96166 

138,7 

.38737 

96,2 

•69315 

52,0 

.4427 

10,8 

0.855 

0.96305 

138,8 

1.38833 

96,3 

0.69367 

51,9 

1.4416 

10,8 

.856 

.96443 

138,9 

.38929 

96,4 

.69419 

5i,8 

.4405 

10,8 

.857 

.96582 

139,0 

.39026 

96,6 

•69471 

5i,7 

•  4395 

10,7 

.858 

.96721 

139,1 

•39122 

96,7 

.69523 

5i,7 

.4384 

10,7 

.859 

.96861 

139,2 

.39219 

96,9 

.69574 

5i,6 

•4373 

10,7 

0.860 

O.97OOO 

139,3 

I.393I6 

97,0 

0.69626 

5i,5 

1.4362 

10,6 

.861 

.97139 

139,4 

.39413 

97,1 

.69677 

5i,5 

•4352 

10,6 

.862 

.97279 

139,5 

.39510 

97,3 

.69729 

5i,4 

-4341 

10,6 

.863 

.97418 

139,6 

.39608 

97,4 

.69780 

5i,3 

.4331 

10,5 

.864 

.97558 

139,7 

•39705 

97,6 

.69831 

51,2 

.4320 

io,5 

0.865 

0.97698 

139,8 

1.39803 

97,7 

0.69882 

51,2 

I.43IO 

io,5 

.866 

.97838 

139,9 

.39901 

97,8 

.69934 

5i,i 

.4299 

10,4 

*•  .867 

.97978 

140,0 

•39999 

98,0 

.69985 

5i,o 

.4289 

10,4 

.868 

.98118 

140,1 

.40097 

98,1 

.70036 

5i,o 

.4278 

10,4 

.869 

.98258 

140,2 

.40195 

98,3 

.70087 

50,9 

.4268 

10,4 

0.870 

0.98398 

140,3 

1.40293 

98,4 

0.70137 

50,8 

1.4258 

10,3 

"  .871 

.98538 

140,4 

.40392 

98,5 

.70188 

50,7 

.4247 

10,3 

.872 

.98679 

140,5 

.40490 

98,7 

.70239 

50,7 

•  4237 

10,3 

.873 

.98819 

140,6 

.40589 

98,8 

.70290 

50,6 

.4227 

10,2 

.874 

.98960 

140,7 

.40688 

99,o 

.70340 

50,5 

•  4217 

10,2 

0.875 

O.99IOI 

140,8 

1.40787 

99,1 

0.70391 

50,5 

1.4206 

10,2 

.876 

.99241 

140,9 

.40886 

99,2 

.70441 

50,4 

.4196 

10,2 

.877 

.99382 

141,0 

.40985 

99,4 

.70491 

50,3 

.4186 

10,1 

.878 

.99523 

141,1 

.41085 

99,5 

.70542 

50,2 

.4176 

10,1 

.879 

.99665 

141,2 

.41184 

99,7 

.70592 

50,2 

.4166 

10,1 

0.880 

0.99806 

I4i,3 

1.41284 

99,8 

0.70642 

50,1 

1.4156 

10,0 

.881 

•99947 

141,4 

.41384 

99,9 

.70692 

5o,o 

.4146 

10,0 

.882 

1.00089 

i4i,5 

.41484 

100,1 

.70742 

50,0 

.4136 

10,0 

.883 

.00230 

141,6 

.41584 

100,2 

.70792 

49,9 

.4126 

IO,O 

.884 

.00372 

I4i,7 

.41684 

100,4 

.70842 

49,8 

.4116 

9,9 

0.885 

1.00514 

141,8 

1.41785 

100,5 

0.70892 

49,7 

1.4106 

9,9 

.886 

.00655 

141,9 

.41886 

100,7 

.70941 

49,7 

.4096 

9,9 

.887 

.00797 

142,0 

.41986 

100,8 

.70991 

49,6 

.4086 

9,8 

.888 

.00939 

142,1 

.42087 

100,9 

.71040 

49,5 

.4076 

9,8 

.889 

.01081 

142,2 

.42188 

IOI,I 

.71090 

49,5 

.4067 

9,8 

0.890 

1.01224 

142,3 

1.42289 

IOI,2 

0.7H39 

49,4 

1.4057 

9,8 

.891 

.01366 

142,4 

.42391 

101,4 

.71189 

49,3 

.4047 

9,7 

.892 

.01508 

142,5 

.42492 

ioi,5 

.71238 

49,3 

.4037 

9,7 

.893 

.01651 

142,6 

.42594 

101,7 

.71287 

49,2 

.4028 

9,7 

.894 

.01794 

142,7 

.42695 

101,8 

.71336 

49,1 

.4018 

9,7 

0.895 

1.01936 

142,8 

1.42797 

101,9 

0.71385 

49,0 

1.4008 

9,6 

.896 

.02079 

142,9 

.42899 

102,1 

.71434 

49,0 

•  3999 

9,6 

.897 

.02222 

I43,o 

.43001 

102,2 

.71483 

48,9 

•  3989 

9,6 

.898 

.02365 

I43,i 

.43104 

102,4 

.71532 

48,8 

.3980 

9,5 

.899 

.O25O8 

143,2 

.43206 

102,5 

.71581 

48,8 

•  3970 

9,5 

0.900 

I.O2652 

143,3 

1.43309 

102,7 

0.71630 

48,7 

I.396I 

9,5 

u 

tan  gd  u 

•  Fo' 

sec  gd  u 

-FO' 

sin  gd  u 

<-F0' 

esc  gd  u 

O.FO' 

SMITHSONIAN  TABLES 


I23 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•IV 

cosh  u 

15 

tanh  u 

™ 

cothu 

•  Fo' 

0.900 

1.02652 

143 

1.43309 

103 

0.71630 

48,7 

I.396I 

9,5 

.901 

.02795 

143 

•434II 

103 

.71678 

48,6 

.3951 

9,5 

.902 

.02938 

144 

.43514 

103 

.71727 

48,6 

•  3942 

9,4 

.903 

.03082 

144 

103 

.71776 

48,5 

.3932 

9,4 

.904 

.03226 

144 

.43720 

103 

.71824 

48,4 

.3923 

9,4 

0.905 

1.03370 

144 

1.43824 

103 

0.71872 

48,3 

I.39I4 

9,4 

.906 

.03513 

144 

•43927 

104 

.71921 

48,3 

.3904 

9,3 

.907 

.03657 

144 

.44031 

104 

.71969 

48,2 

.3895 

9,3 

.908 

.03801 

144 

.44134 

104 

.72017 

48,1 

.3886 

9,3 

.909 

.03946 

144 

.44238 

104 

.72065 

48,1 

.3876 

9,3 

0.910 

1.04090 

144 

1-44342 

104 

0.72113 

48,0 

1.3867 

9,2 

.911 

.04234 

144 

.44446 

104* 

.72161 

47,9 

.3858 

9,2 

.912 

.04379 

145 

.44551 

104 

.72209 

47,9 

.3849 

9,2 

.913 

.04523 

145 

.44655 

105 

.72257 

47,8 

.3840 

9,2 

.914 

.04668 

145 

.44760 

105 

.72305 

47,7 

.3830 

9,1 

0.915 

1.04813 

145 

1.44865 

105 

0.72352 

47,7 

1.3821 

9,1 

.916 

.04958 

145 

.44969 

105 

.72400 

47,6 

.3812 

9,1 

.917 

.05103 

145 

•45075 

105 

.72448 

47,5 

•  3803 

9J 

.918 

.05248 

145 

.45180 

105 

.72495 

47,4 

.3794 

9,0 

.919 

.05393 

145 

.45285 

105 

.72542 

47,4 

.3785 

9,0 

0.920 

1.05539 

145 

1.45390 

106 

0.72590 

47,3 

1.3776 

9,0 

.921 

.05684 

145 

.45496 

106 

.72637 

47,2 

.3767 

9,0 

.922 

.05830 

146 

•  .45602 

106 

.72684 

47,2 

.3758 

8,9 

.923 

•05975 

146 

.45708 

106 

.72731 

47,1 

•  3749 

8,9 

.924 

.06121 

146 

.45814 

106 

.72778 

47,0 

•3740 

8,9 

0.925 

1.06267 

146 

1.45920 

106 

0.72825 

47,0 

I-373I 

8,9 

.926 

.06413 

146 

.46026 

106 

.72872 

46,9 

.3723 

8,8 

.927 

.06559 

146 

.46133 

107 

.72919 

46,8 

8,8 

.928 

.06705 

146 

.46239 

107 

.72966 

46,8 

•  3705 

8,8 

.929 

.06851 

146 

.46346 

107 

.73013 

46,7 

.3696 

8,8 

0.930 

1.06998 

146 

1.46453 

107 

0.73059 

46,6 

1.3687 

8,7 

.931 

.07144 

147 

.46560 

107 

.73106 

46,6 

.3679 

8,7 

.932 

.07291 

147 

.46667 

107 

.73153 

46,5 

.3670 

8,7 

.933 

.07438 

147 

.46775 

107 

.73199 

46,4 

.3661 

8,7 

•934 

.07584 

147 

.46882 

108 

•73245 

46,4 

.3653 

8,6 

0.935 

^•tj^j 

1.07731 

147 

1.46900 

108 

0.73292 

46,3 

1.3644 

8,6 

.936 

.07878 

147 

.47098 

108 

.73338 

46,2 

.3636 

8,6 

•  937 

.08026 

147 

.47206 

icS 

.73384 

46,1 

.3627 

8,6 

.938 

.08173 

147 

.47314 

108 

•73430 

46,1 

.3618 

8,5 

•  939 

.08320 

147 

.47422 

108 

•73476 

46,0 

.3610 

8,5 

0.940 

1.08468 

148 

1-47530 

T08 

0.73522 

45,9 

1.3601 

8,5 

.941 

.08615 

148 

.47639 

109 

•73568 

45,9 

•  3593 

8,5 

.942 

.08763 

148 

.47748 

109 

.73614 

45,8 

.3584 

8,5 

•  943 

.08911 

148 

.47857 

109 

.73660 

45,7 

.3576 

8,4 

•  944 

.00059 

148 

.47966 

109 

•73705 

45,7 

•  3568 

8,4 

0.945 

1.09207 

148 

1.48075 

109 

0.73751 

45,6 

1.3559 

.  8,4 

.946 

.09355 

148 

.48184 

109 

.73797 

45,5 

•  3551 

8,4 

.947 

•09503 

148 

.48293 

IIO 

.73842 

45,5 

•3542 

8,3 

.948 

.09651 

148 

.48403 

1  10 

.73888 

45.4 

.3534 

8,3 

.049 

.09800 

149 

.48513 

IIO 

•73933 

45,3 

.3526 

8,3 

0.950 

1.09948 

149 

1.48623 

IIO 

0.73978 

4*3 

I.35I7 

8,3 

u 

tan  gd  u 

•  Fo' 

sec  gd  u 

.w 

sin  gd  u 

-P.' 

esc  gd  u 

jjW 

SMITHSONIAN  TABLES 


124 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  Fo' 

cosh  u 

•  Fb' 

tanh  u 

«FO' 

coth  u 

U.FO' 

0.950 

1.09948 

149 

1.48623 

no 

0.73978 

45,3 

I.35I7 

8,3 

.951 

.10097 

149 

.48733 

no 

.74024 

45,2 

.3509 

8,2 

.952 

.  10246 

149 

.48843 

no 

.74069 

45,1 

•  3501 

8,2 

•  953 
•954 

.  10395 
.10544 

149 
149 

.48953 
.49064 

no 
in 

.74114 
.74159 

45,1 
45,0 

.3493 
.3485 

8,2 
8,2 

0.955 

1.10693 

149 

I.49I74 

in 

0.74204 

44,9 

1.3476 

8,2 

.956 

.10842 

149 

.49285 

in 

.74249 

44,9 

.3468 

8,1 

•  957 

.10991 

149 

.49396 

in 

.74294 

44,8 

.3400 

8,1 

•958 

.11141 

ISO 

•49507 

in 

.74338 

44,7 

.3452 

8,1 

•959 

.11291 

150 

.49618 

in 

.74383 

44,7 

•  3444 

8,1 

0.960 

I  .  I  1440 

150 

1.49729 

in 

0.74428 

44,6 

1.3436 

8,1 

.961 

.11590 

150 

.49841 

112 

•74472 

44,5 

.3428 

8,0 

.962 

.11740 

ISO 

.49953 

112 

.74517 

44,5 

.3420 

8,0 

.963 

.11890 

150 

.50064 

112 

.74561 

44,4 

.3412 

8,0 

•  964 

.  12040 

150 

.50176 

112 

.74606 

44,3 

.3404 

8,0 

0.965 

1.12190 

150 

I  .  50289 

112 

0.74650 

44,3 

1.3396 

7,9 

.966 

.12341 

ISO 

.50401 

112 

.74694 

44,2 

.3388 

7,9 

.967 

.12491 

151 

.50513 

112 

.74738 

44,1 

.3380 

7,9 

.968 

.  12642 

151 

.50626 

113 

.74782 

44,1 

•  3372 

7.9 

.969 

.  12792 

151 

•50739 

H3 

.74826 

44,0 

.3364 

7,9 

0.970 

I  .  12943 

151 

1.50851 

H3 

0.74870 

43,9 

1.3356 

7,8 

.971 

.13094 

151 

.50964 

H3 

.74914 

43,9 

•  3349 

7,8 

.972 

.13245 

151 

.51078 

H3 

.74958 

43,8 

•  3341 

7,8 

•973 

.13396 

I5i 

.51191 

H3 

-75002 

43,7 

•3333 

7,8 

•  974 

.  13547 

151 

.51304 

114 

.75046 

43,7 

.3325 

7,8 

0.975 

I.I3699 

151 

1.51418 

114 

0.75089 

43,6 

I.33I7 

7,7 

.976 

.  13850 

152 

.51532 

114 

.75133 

43,6 

.3310 

7,7 

.977 

.14002 

152 

.51646 

114 

.75176 

43,5 

•  3302 

7,7 

.978 

.14154 

152 

.51760 

114 

.75220 

43,4 

.3294 

7,7 

.979 

.  14305 

152 

.51874 

114 

.75263 

43,4 

.3287 

7,7 

0.980 

I  .  14457 

152 

1.51988 

144 

0.75307 

43,3 

1.3279 

7,6 

.981 

.14609 

152 

.52103 

H5 

.75350 

43,2 

.3271 

7,6 

.982 

.14761 

152 

.52218 

H5 

•75393 

43,2 

.3264 

7,6 

.983 

.14914 

152 

.52332 

115 

.75436 

43,1 

.3256 

7,6 

.984 

.15066 

152 

.52447 

H5 

•75479 

43,0 

.3249 

7,6 

0.985 

1.15219 

153 

1.52563 

US 

0.75522 

43,0 

1.3241 

7,5 

.986 

•I537I 

153 

.52678 

H5 

.75565 

42,9 

.3234 

7,5 

.987 

.15524 

153 

.52793 

116 

.756o8 

42,8 

.3226 

7,5 

.988 

.15677 

153 

.52909 

116 

.75651 

42,8 

.3219 

7,5 

.989 

.  15830 

153 

.53025 

116 

.75694 

42,7 

.3211 

7,5 

0.990 

I.I5983 

153 

I.53I4I 

116 

0.75736 

42,6 

1.3204 

7,4 

•  991 

.  16136 

153 

.53257 

116 

•75779 

42,6 

.3196 

7,4 

.992 

.16289 

153 

•53373 

116 

.75821 

42,5 

.3189 

7,4 

•  993 

.16443 

153 

.53489 

116 

.75864 

42,4 

.3182 

7,4 

.994 

.16596 

154 

.53606 

117 

.75906 

42,4 

.3174 

7,4 

0.995 

I  .  16750 

154 

1.53722 

117 

0.75949 

42,3 

1.3167 

7,3 

.996 

.16904 

154 

.53839 

117 

•75991 

42,3 

.3159 

7,3 

•  997 

.17058 

154 

.53956 

117 

.76033 

42,2 

•3152 

7,3 

.998 

.17212 

154 

.54073 

117 

.76075 

42,1 

.3145 

7,3 

.999 

.17366 

154 

.54191 

117 

.76117 

42,1 

.3138 

7,3 

I.OOO 

I.I7520 

154 

1.54308 

118 

0.76159 

42,0 

I.3I30 

7,2 

u 

tan  gd  u 

«Fo' 

sec  gd  u 

wF0' 

sin  gd  u 

«F0' 

esc  gd  u 

»F0' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinhu 

•  Fo' 

cosh  u 

«F0' 

tanh  u 

•  FO' 

cothu 

•  Fo' 

1.  000 

I.I7520 

154 

1.54308 

118 

0.76159 

42,0 

I.3I30 

7,2 

.001 

.  17674 

154 

.54426 

118 

.76201 

41,9 

.3123 

7,2 

.002 

.  17829 

155 

•54543 

118, 

.76243 

41,9 

7,2  ' 

.003 

.17984 

155 

.54661 

118 

.76285 

41,8 

.3109 

7,2 

.004 

.18138 

155 

•54779 

118 

.76327 

41,7 

.3102 

7,2 

1.005 

1.18293 

155 

1.54898 

118 

0.76369 

41,7 

1.3094 

7,1 

.006 

.  18448 

155 

.55016 

118 

.76410 

41,6 

.3087 

.007 

.18603 

155 

.55134 

119 

.76452 

41,6 

.3080 

7!  i 

.008 

.18758 

155 

.55253 

119 

.76493 

41,5 

•3073 

7,1 

.009 

.18914 

155 

•55372 

119 

•76535 

41,4 

.3066 

I.OIO 

1.19069 

155 

I-5549I 

119 

0.76576 

41,4 

1.3059 

7,1 

.on 

.19225 

156 

.55610 

119 

.76618 

41,3 

.3052 

7,o 

.012 
.013 

.19380 
.  19536 

156 
156 

•55729 
.55849 

119 

120 

•76659 
.76700 

41,2 
41,2 

.3045 
.3038 

7,o 
7,o 

.014 

.19692 

156 

.55969 

120 

.76741 

41,1 

.3031 

7,o 

1.015 

1.19848 

156 

1.56088 

I2O 

0.76782 

41,0 

1.3024 

7,o 

.016 

.20004 

156 

.56208 

I2O 

.76823 

41,0 

.3017 

6,9 

.017 

.20l6o 

156 

.56328 

I2O 

.76864 

40,9 

.3010 

6,9 

.018 

.20317 

156 

.56449 

I2O 

.76905 

40,9 

.3003 

6,9 

.019 

.20473 

157 

•56569 

I2O 

.76946 

40,8 

.2996 

6,9 

i.  020 

1.20630 

157 

1.56689 

121 

0.76987 

40,7 

1.2989 

6,9 

.021 

.20787 

157 

.56810 

121 

.77027 

40,7 

.2982 

6,91 

.022 

.20944 

157 

-56931 

121 

.77068 

40,6 

.2976 

6,8 

.023 

.2IIOI 

157 

.57052 

121 

.77109 

40,5 

.2969 

6,8! 

.024 

.21258 

157 

.57173 

121 

.77U9 

40,5 

.2962 

6,8 

1.025 

I.2I4I5 

157 

1.57295 

121 

0.77190 

40,4 

1.2955 

6,8 

.026 

.21572 

157 

.57416 

122 

.77230 

40,4 

.2948 

6,8  1 

.027 

.21730 

158 

.57538 

122 

.77270 

40,3 

.2942 

6,7 

.028 

.21887 

158 

.57660 

122 

.77310 

40,2 

.2935 

6,7' 

.029 

.22045 

158 

.57782 

122 

•77351 

40,2 

.2928 

6,7: 

1.030 

I  .  222O3 

158 

1.57904 

122 

0-77391 

40,1 

1.2921 

6,7 

.031 

.22361 

158 

.58026 

122 

.77431 

40,0 

.2915 

6,7! 

.032 

.22519 

158 

.58148 

123 

•77471 

40,0 

.2908 

6,7 

•033 

.22677 

158 

.58271 

123 

•  775" 

39,9 

.2901 

6,6  ; 

.034 

.22836 

158 

.58394 

123 

•77551 

39,9 

.2895 

6,6 

1.035 

1.22994 

159 

1.58517 

123 

0-77591 

39,8 

1.2888 

6,6 

.036 

.23153 

159 

.58640 

123 

.77630 

39,7 

.2882 

6,6 

.037 

.233H 

159 

.58763 

123 

.77670 

39,7 

.2875 

6,6 

.038 

.23470 

159 

.58886 

123 

•77710 

39,6 

.2868 

6,6 

•039 

.23629 

159 

.59010 

124 

•77749 

39,6 

.2862 

6,5 

1.040 

1.23788 

159 

I.59I34 

124 

0.77789 

39,5 

1.2855 

6,5 

.041 

•23947 

159 

.59257 

124 

.77828 

39,4 

•  2849 

6,5 

.042 

.24107 

159 

.59381 

124 

.77868 

39,4 

.2842 

6,5 

.043 

.24266 

160 

.59506 

124. 

.77907 

39,3 

.2836 

6,5 

.044 

.24426 

160 

•59630 

124 

.77946 

39,2 

.2829 

6,5 

1.045 

1.24585 

160 

1-59755 

125 

0.77985 

39,2 

1.2823 

6,4 

.046 

•24745 

160 

.50879 

125 

.78025 

39,1 

.2816 

6,4 

.047 

.24905 

160 

.60004 

125 

.78064 

39,1 

.2810 

6,4 

.048 

.25065 

160 

.60129 

125 

.78103 

39,0 

.2804 

6,4 

.049 

.25225 

160 

.60254 

125 

.78142 

38,9 

.2797 

6,4 

1.050 

1.25386 

160 

1.60379 

125 

0.78181 

38,9 

I.279I 

6,4 

u 

tan  gd  u 

-Fo' 

sec  gd  u 

-Fo' 

tin  gd  u 

•  IV 

esc  gd  u 

-Fo' 

SMITHSONIAN  TABLES 


126 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«Fo' 

cosh  u 

«F0' 

tanh  u 

•  FO' 

coth  u 

O.FO' 

1.050 

1.25386 

160 

1.60379 

125 

0.78181 

38,9 

I.279I 

6,4 

.051 

.25546 

161 

.60505 

126 

.78219 

38,8 

.2785 

6,3 

.052 

.25707 

161 

.60631 

126 

.78258 

38,8 

.2778 

6,3 

•  053 

.25867 

161 

.60756 

126 

.78297 

38,7 

.2772 

6,3 

•  054 

.26028 

161 

.60882 

126 

.78336 

38,6 

.2766 

6,3 

1.055 

1.26189 

161 

I.  61008 

126 

0.78374 

38,6 

1.2759 

6,3 

.056 

.26350 

161 

.61135 

126 

.78413 

38,5 

.2753 

6,3 

.057 

.26511 

161 

.61261 

127 

.78451 

38,4 

.2747 

6,2 

.058 

.26673 

161 

.61388 

127 

.78400 

38,4 

.2741 

6,2 

.059 

.26834 

162 

.61514 

127 

.78528 

38,3 

•2734 

6,2 

i.  060 

1.26996 

162 

1.61641 

127 

0.78566 

38,3 

1.2728 

6,2 

.061 

.27157 

162 

.61768 

127 

.78605 

38,2 

.2722 

6,2 

.062 

.27319 

162 

.61896 

127 

.78643 

38,2 

.2716 

6,2 

.063 

.27481 

162 

.62023 

127 

.78681 

38,1 

.27IO 

6,2 

.064 

.27643 

162 

.62151 

128 

.78719 

38,0 

.2703 

6,1 

1.065 

1.27806 

162 

1.62278 

128 

0.78757 

38,0 

1.2697 

6,1 

.o(j3 

.27968 

162 

.62406 

128 

.  78795 

37,9 

.2691 

6,1 

.067 

.28130 

163 

.62534 

128 

•78833 

37,9 

.2685 

6,1 

.068 

.28293 

163 

.62662 

128 

.78871 

37,8 

.2679 

6,1 

.069 

.28456 

163 

.62791 

128 

.78508 

37,7 

.2673 

6,1 

1.070 

1.28619 

163 

1.62919 

129 

0.78946 

37,7 

1.2667 

6,0 

.071 

.28782 

163 

.63048 

129 

.78984 

37,6 

.2661 

6,0 

.072 

.28945 

163 

.63177 

129 

.79021 

37,6 

.2655 

6,0 

•  073 

.29108 

163 

.63306 

129 

.79059 

37,5 

.2649 

6,0 

.074 

.29271 

163 

.63435 

129 

.79096 

37,4 

.2043 

6,0 

1.075 

1.29435 

164 

1.63565 

129 

0.79134 

37,4 

1.2637 

6,0 

.076 

.29598 

164 

.63694 

130 

.79171 

37,3 

.2631 

6,0 

.077 

.29762 

164 

.63824 

130 

.  79208 

37,3 

.2625 

5,9 

.078 

.29926 

164 

.63954 

130 

.79246 

37,2 

.2619 

5,9 

•  079 

.30090 

164 

.64084 

130 

.79283 

37,1 

.2613 

5,9 

1.080 

1.30254 

164 

1.64214 

130 

0.79320 

37,1 

1.2607 

5,9 

.081 

.30418 

164 

.64344 

130 

•79357 

37,o 

.2601 

5,9 

'  .082 

.30583 

164 

.64475 

131 

•79394 

37,o 

.2595 

5,9 

.083 

.30747 

165 

.64605 

131 

•79431 

36,9 

.2590 

5,8 

.084 

.30912 

165 

.64736 

131 

.79468 

36,8 

.2584 

5,8 

1.085 

I.3I077 

165 

1.64867 

131 

0.79505 

36,8 

1.2578 

5,8 

.086 

.31242 

165 

.64098 

131 

•79541 

36,7 

.2572 

5,8 

.087 

.31407 

165 

.65130 

131 

•  79578 

36,7 

.2566 

5,8 

.088 

.31572 

165 

.65261 

132 

.79615 

36,6 

.2560 

5,8 

.089 

.31737 

165 

.65393 

132 

.79651 

36,6 

.2555 

5,8 

1.090 

I.3I903 

166 

1.65525 

132 

0.79688 

36,5 

1.2549 

5,7 

.091 

.32068 

166 

.65657 

132 

.79724 

36,4 

.2543 

5,7 

.092 

.32234 

166 

.65789 

132 

.79761 

36,4 

.2538 

5,7  ' 

.093 

.32400 

166 

.65921 

132 

.79797 

36,3 

.2532 

5,7 

.094 

.32566 

166 

.66053 

133 

-79833 

36,3 

.2526 

5,7 

1.095 

1.32732 

166 

I.  66186 

133 

0.79870 

36,2 

1.2520 

5,7 

.096 

.32808 

166 

.66319 

133 

.79906 

36,2 

.2515 

5,7 

.097 

.33065 

166 

.66452 

133 

.79942 

36,1 

.2509 

5,6 

.098 

.33231 

167 

.66585 

133 

.79978 

36,0 

.2503 

5,6 

.099 

.33398 

167 

.66718 

133 

.80014 

36,0 

.2498- 

5,6 

I.  100 

1.33565 

167 

1.66852 

134 

0.80050 

35,9 

1.2492 

5,6 

u 

tan  gd  u 

wF0' 

sec  gd  u 

«FO' 

sin  gd  u 

«Fo' 

esc  gd  u 

»Fo' 

SMITHSONIAN  TABLES 


127 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

<oF0' 

cosh  u 

«Fo' 

tanh  u 

«F0' 

cothu 

<-F0' 

I.IOO 

1.33565 

167 

1.66852 

134 

0.80050 

35,9 

1.2492 

5,6 

.101 

•33732 

167 

.66986 

134 

.80086 

35,9 

.2487 

5,6 

.102 

.33899 

167 

.67119 

134 

.80122 

35,8 

.2481 

5,6 

.103 

.34066 

167 

.67253 

134 

.80157 

35,7 

•2475 

5,6 

.104 

.34233 

167 

.67387 

134 

.80193 

35,7 

.2470 

5,5 

1.  105 

I.3440I 

168 

1.67522 

134 

0.80229 

35,6 

1.2464 

5,5 

.106 

.34568 

168 

.67656 

135 

.80264 

35,6 

•  2459 

5,5 

.107 

•34/36 

168 

.67791 

135 

.80300 

35,5 

•  2453 

5,5 

.108 

•34904 

168 

.67926 

135 

•80335 

35,5 

.2448 

5,5 

.109 

.35072 

168 

.68061 

135 

.80371 

35,4 

.2442 

5,5 

I.  IIO 

1.35240 

168 

1.68196 

135 

0.80406 

35,3 

1.2437 

5,5 

.in 

.35408 

168 

.68331 

135 

.80442 

35,3 

.2431 

5,5 

.112 

.35577 

168 

.68467 

136 

•80477 

35,2 

.2426 

5,4 

.113 

•35745 

169 

.68602 

136 

.80512 

35,2 

.2421 

5,4 

.114 

.35914 

169 

.68738 

136 

.80547 

35,1 

.2415 

5,4 

I.H5 

1.36083 

169 

1.68874 

136 

0.80582 

35,1 

1.2410 

5,4 

.116 

.36252 

169 

.69010 

136 

.80617 

35,o 

.2404 

5,4 

.117 

.36421 

169 

.69147 

136 

.80652 

35,0 

•  2399 

5,4 

.118 

.36590 

169 

.69283 

137 

.80687 

34,9 

5,4 

.119 

.36759 

169 

.69420 

137 

.80722 

34,8 

.2388 

5,3 

T.I2O 

1.36929 

170 

1.69557 

137 

0.80757 

34,8 

1.2383 

5,3 

."?! 

.37098 

170 

.69694 

137 

.80792 

34,7 

.2378 

5,3 

.122 

.37268 

170 

.69831 

137 

.80826 

34,7 

.2372 

5,3 

.123 

.37438 

170 

.69968 

137 

.80861 

34,6 

.2367 

5,3 

.124 

.37608 

170 

.70106 

138 

.80896 

34*6 

.2362 

5,3 

1.  125 

1.37778 

170 

1.70243 

138 

0.80930 

34,5 

1.2356 

5,3 

.125 

•  37949 

170 

.70381 

138 

.80965 

34,4 

.2351 

5,3 

.127 

.38119 

171 

.70519 

138 

.80909 

34,4 

.2346 

5,2 

.128 

.38290 

171 

.70658 

138 

.81033 

34,3 

.2341 

5,2 

.129 

.38460 

171 

.70706 

138 

.81068 

34,3 

•  2335 

5,2 

I.I30 

1.38631 

171 

1.70934 

139 

O.8IIO2 

34,2 

1.2330 

5,2 

.131 

.38802 

171 

.71073 

139 

.81136 

34,2 

.2325 

5,2 

.132 

.38973 

171 

.71212 

139 

.81170 

34,1 

.2320 

5,2 

•133 

.39145 

171 

.71351 

139 

.81204 

34,1 

.2315 

5,2 

•134 

.39316 

171 

.71490 

139 

.81238 

34,0 

.2309 

5,2 

1.  135 

1.39488 

172 

1.71630 

139 

0.81272 

33,9 

1.2304 

5,1 

.136 

•  39^59 

172 

.71769 

140 

.81306 

33,9 

.2209 

5,1 

.137 

.39831 

172 

.71909 

140 

.81340 

33,8 

5,i 

.138 

.40003 

172 

•72049 

140 

.81374 

33,8 

.2289 

5,1 

.139 

.40175 

172 

.72189 

140 

.81408 

33,7 

.2284 

5,1 

1.140 

1.40347 

172 

1.72329 

140 

0.81441 

33,7 

1.2279 

5,1 

.141 

.40520 

172 

.72470 

141 

.81475 

33,6 

.2274 

5,1 

.142 

.40692 

173 

.72610 

141 

.81509 

33,6 

.2269 

5,1 

.143 

.40865 

173 

.72751 

141 

.81542 

33,5 

.2264 

5,o 

.144 

.41038 

173 

.72892 

141 

.81576 

33,5 

.2259 

5,o 

1.  145 

1.41211 

173 

1.73033 

141 

0.81609 

33,4 

1.2254 

5,o 

.146 

.41384 

173 

.73175 

141 

.81642 

33,3 

.2249 

5,o 

.147 

.41557 

173 

.73316 

142 

.81676 

33,3 

.2244 

5,o 

.148 

.41731 

173 

.73458 

142 

.81709 

33,2 

.2239 

5,o 

.149 

.41904 

174 

•73599 

142 

.81742 

33,2 

.  233  \ 

5,o 

1.150 

1.42078 

174 

I-7374I 

142 

0.81775 

33,1 

1.2229 

5,0 

u 

tan  gd  u 

-Fo' 

sec  gd  u 

«F0' 

singdu 

»F0' 

csc  gd  u 

wF0' 

SMITHSONIAN   TABLE* 


128 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

<-Fo' 

tanhu 

«FO- 

coth  u 

-IV 

1.150 

1.42078 

174 

I-7374I 

142 

o.  -81775 

33,1 

1.2229 

5,0 

.151 

.42252 

174 

.73884 

142 

.81809 

33,1 

.2224 

4,9 

.152 

.42426 

174 

.74026 

142 

.81842 

33,0 

.2219 

4,9 

.153 

.42600 

174 

.74168 

143 

.81875 

33,0 

.2214 

4,9 

.154 

.42774 

174 

.743H 

143 

.81907 

32,9 

.2209 

4,9 

1.  155 

1.42948 

174 

1.74454 

143 

0.81940 

32,9 

1.2204 

4,9 

.156 

.43123 

175 

.74597 

143 

.81973 

32,8 

.2199 

4,9 

.157 

.43297 

175 

.74740 

143 

.82006 

32,8 

.2194 

4,9 

.158 

.43472 

175 

.74884 

143 

.82039 

32,7 

.2189 

4,9 

.159 

.43647 

175 

.75027 

144 

.82071 

32,6 

.2185 

4,8 

1.160 

1.43822 

175 

I.75I7I 

144 

0.82104 

32,6 

I.  2180 

4,8 

.161 

.43998 

175 

.75315 

144 

.82137 

32,5 

•2175 

4,8 

.162 

.44173 

175 

.75459 

144 

.82169 

32,5 

.2170 

4,8 

.163 

•44349 

176 

.75603 

144 

.82202 

32,4 

.2165 

4,8 

.164 

.44524 

176 

.75748 

145 

.82234 

32,4 

.2160 

4,8 

1.165 

1.44700 

176 

1.75892 

145 

0.82266 

32,3 

1.2156 

4,8 

.166 

.44876 

176 

.76037 

145 

.82299 

32,3 

.2151 

4,8 

.167 

.45052 

176 

.76182 

145 

.82331 

32,2 

.2146 

4,8 

1  68 

.45228 

176 

.76327 

145 

.82363 

32,2 

.2141 

4,7 

[169 

.45405 

176 

.76472 

145 

.82395 

32,1 

.2137 

4,7 

1.170 

I.4558I 

177 

1.76618 

146 

0.82427 

32,1 

1.2132 

4,7 

-171 

.45758 

177 

.76764 

146 

.82459 

32,0 

.2127 

4,7 

.172 

.45935 

177 

.76009 

146 

.82491 

32,0 

.2123 

4,7 

•  173 

.46112 

177 

.77056 

146 

.82523 

3i,9 

.2118 

4,7 

.174 

.46289 

177 

.77202 

146 

.82555 

3i,8 

.2113 

4,7 

1.  175 

1.46466 

177 

1.77348 

146 

0.82587. 

3i,8 

1.2108 

4,7 

.176 

.46644 

177 

•77495 

147 

.82619 

3i,7 

.2104 

4,7 

.177 

.46821 

178 

.77641 

147 

.82650 

3i,7 

.2009 

4,6 

.178 

.46999 

178 

.77788 

147 

.82682 

3i,6 

.2095 

4,6 

.179 

.47177 

178 

•77935 

147 

.82714 

3i,6 

.2090 

4,6 

1.180 

1.47355 

178 

1.78083 

147 

0.82745 

31,5 

1.2085 

4,6 

.181 

•47533 

178 

.78230 

148 

.82777 

3i,5 

.2081 

4,6 

.182 

.47711 

178 

•78378 

148 

.82808 

3i,4 

.2076 

4,6 

.183 

.47890 

179 

.78526 

148 

.82840 

3i,4 

.2072 

4,6 

.184 

.48068 

179 

.78673 

148 

.82871 

3i,3 

.2067 

4,6 

1.185 

1.48247 

179 

1.78822 

148 

0.82902 

3i,3 

1.2062 

4,6 

.186 

.48426 

179 

.78970 

148 

.82933 

31,2 

.2058 

4,5 

.187 

.48605 

179 

.79H9 

149 

.82965 

31,2 

.2053 

4,5 

.188 

.48784 

179 

.79267 

149 

.82996 

3M 

.2049 

4,5 

.189 

.48964 

179 

.79416 

149 

.83027 

3i,i 

.2044 

4,5 

1.190 

I.49I43 

180 

1.79565 

149 

0.83058 

31,0 

1.2040 

4,5 

.191 

.49323 

180 

•  797H 

149 

.83089 

31,0 

.2035 

4,5 

.192 

.49502 

180 

•79864 

150 

.83120 

30,9 

.2031 

4,5 

•  193 

.40682 

180 

.80013 

150 

.83151 

30,9 

.2026 

4>5 

.194 

.49862 

180 

.80163 

150 

.83182 

30,8 

.2022 

4,5 

I.I95 

1.50043 

180 

1.80313 

ISO 

0.83212 

30,8 

1.2017 

4,4 

.196 

.50223 

180 

.80463 

ISO 

.83243 

30,7 

.2013 

4,4 

.197 

.50404 

181 

.80614 

ISO 

.83274 

30,7 

.2009 

4,4 

.198 

.50584 

181 

.80764 

151 

•83304 

30,6 

.2004 

4,4 

.199 

.50765 

'181 

.80915 

I5i 

.83335 

30,6 

.2000 

4,4 

i.  200 

1.50946 

181 

i.  81066 

151 

0.83365 

30,5 

i.  1995 

4,4 

u 

tan  gd  u 

O>FO' 

sec  gd  u 

«FO' 

sin  gd  u 

<oF0' 

esc  gd  u 

wF0' 

SMITHSONIAN  TABLES 


129 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

•  IV 

cosh  u 

«FO' 

tanh  u 

«*FO' 

coth  u 

«F0' 

1.200 

1.50946 

181 

I.  81066 

151 

0.83365 

30,5 

I.I995 

4,4 

.201 

.51127 

181 

.81217 

151 

.83396 

30,5 

.1991 

4,4 

.202 

.51309 

181 

.81368 

151 

.83426 

30,4 

.1987 

4,4 

.203 

.51490 

182 

.81519 

151 

.83457 

30,3 

.1982 

4,4 

.204 

.51672 

182 

.81671 

152 

.83487 

30,3 

.1978 

4,3 

1.205 

I.5I853 

182 

1.81823 

152 

0.83517 

30,2 

I  .  1974 

4,3 

.206 

.52035 

182 

.81974 

152 

.83548 

30,2 

.1969 

4,3 

.207 

.52217 

182 

.82127 

.  152 

.83578 

30,1 

.1965 

4,3 

.208 

.52400 

182 

.82279 

152 

.83608 

30,1 

.1961 

4,3 

.209 

.52582 

182 

.82431 

153 

.83638 

30,0 

.1956 

4,3 

I.2IO 

1.52764 

183 

1.82584 

153 

0.83668 

30,0 

I  .  1952 

4,3 

.211 

.52947 

183 

.82737 

153 

.83698 

29,9 

.1948 

4,3 

.212 

.53130 

183 

.82890 

153 

.83728 

29,9 

•1943 

4,3 

•  213 

.53313 

183 

•83043 

153 

.83758 

29,8 

.1939 

4,3 

.214 

.53496 

183 

.83197 

153 

.83788 

29,8 

.1935 

4,2 

i.  215 

1.53679 

183 

1.83350 

154 

0.83817 

29,7 

I.I93I 

4,2 

.216 

.53863 

184 

.83504 

154 

.83847 

29,7 

.1926 

4,2 

.217 

.54046 

184 

.83658 

154 

.83877 

29,6 

.1922 

4,2 

.218 

.54230 

184 

.83812 

154 

.83506 

29,6 

.1918 

4,2 

.219 

.54414 

184 

.83966 

154 

.83936 

29,5 

.1914 

4,2 

I.22O 

1.54598 

184 

1.84121 

155 

0.83965 

29,5 

1.1910 

4,2 

.221 

.54782 

184 

.84276 

155 

.83995 

29,4 

.1905 

.4,2 

.222 

.54966 

184 

.84430 

155 

.84024 

29,4 

.1901 

4,2 

.223 

.55151 

185 

.84586 

155 

.84054 

29,3 

.1897 

4,2 

.224 

.55336 

185 

.84741 

155 

.84083 

29,3 

.1893 

4,1 

1.225 

1-55520 

185 

1.84896 

156 

0.84112 

29,3 

1.1889 

4,1 

.226 

•55705 

185 

.85052 

156 

.84142 

29,2 

.1885 

4,1 

.227 

.55891 

185 

.85208 

156 

.84171 

29,2 

.1881 

4,1 

.228 

06076 

185 

.85364 

156 

.84200 

29,1 

.1877 

4,1 

.229 

.56261 

186 

.85520 

156 

.84229 

29,1 

.1872 

4,1 

1.230 

1.56447 

186 

1.85676 

156 

0.84258 

29,0 

i.i858 

4,1 

.231 

.56633 

186 

.85833 

157 

.84287 

29,0 

.1864 

4,1 

.232 

.56819 

186 

.85989 

157 

.84316 

28,9 

.1860 

4,1 

•  233 

•57005 

186 

.86146 

157 

.84345 

28,9 

.1856 

4,1 

•  234 

.57191 

186 

.86303 

157 

.84374 

28,8 

.1852 

4,1 

1.235 

i  •  57377 

186 

1.86461 

157 

0.84402 

28,8 

i  .  1848 

4,0 

.236 

.57564 

187 

.86618 

158 

.84431 

28,7 

•  1844 

4,0 

.237 

•  57750 

187 

.86/76 

158 

.84460 

28,7 

.1840 

4,o 

.238 

.  57937 

187 

.86934 

158 

.84488 

28,6  j   .  1836 

4,0 

.239 

.58124 

187 

.87092 

158 

.84517 

28,6 

.1832 

4,0 

1.240 

1.58311 

187 

1.87250 

158 

0.84546 

28,5 

i  .  1828 

4,0 

.241 

.58499 

187 

.87408 

158 

.84574 

28,5 

.1824 

4,0 

.242 

.58686 

188 

.87567 

159 

.84602 

28,4 

.1820 

4,0 

.243 

.58874 

188 

.87726 

159 

.84631 

28,4 

.1816 

4,0 

.244 

.59062 

188 

.87885 

159 

.84659 

28,3 

.1812 

4,0 

1.245 

1.59250 

188 

1.88044 

159 

0.84688 

28,3 

i.  1808 

3,9 

.246 

188 

.88203 

159 

.84716 

28,2 

.1804 

3,9 

.247 

.59626 

188 

.88363 

160 

.84744 

28,2 

.1800 

3,9 

.248 

^59815 

*/^    */ 

189 

.88522 

160 

.84772 

28,1 

.1796 

3,9 

.249 

.60003 

189 

.88682 

160 

.84800 

28,1 

.1792 

3,9 

1.250 

1.60192 

189 

1.88842 

160 

0.84828 

28,0 

1.1789 

3,9 

u 

tan  od  u 

«F0' 

sec  gd  u 

«Fo' 

sin  gd  u 

-FO' 

esc  gd  u 

-Fo' 

SMITHSONIAN  TABLES 


130 


Natural  Hyperbolic  Functions. 


u 

sinhu 

»F0' 

cosh  u 

«Fo' 

tanhu 

*>Fo' 

coth  u 

«Fo' 

1.250 

1.60192 

189 

1.88842 

160 

0.84828 

28,0 

1.1789 

3,9 

.251 

.60381 

189 

.89003 

160 

.84856 

28,0 

.1785 

3,9 

.252 

.60570 

189 

.89163 

161 

.84884 

27,9 

.1781 

3,9 

.253 

.00759 

189 

.89324 

161 

.84912 

27,9 

.1777 

3,9 

.254 

.60949 

189 

.89485 

161 

.84940 

27,9 

.1773 

3,9 

1.255 

1.61138 

190 

1.89646 

161 

0.84968 

27,8 

1.1769 

3,9 

.256 

.61328 

190 

.89807 

161 

.84996 

27,8 

.1765 

3,8 

-257 

.61518 

190 

.89968 

162 

.85023 

27,7 

.1761 

3,8 

.258 

.61708 

190 

.90130 

162 

.85051 

27,7 

.1758 

3,8 

.259 

.61898 

190 

.90292 

162 

.85079 

27,6 

.1754 

3,8 

1.260 

1.62088 

190 

1.90454 

162 

0.85106 

27,6 

1.1750 

3,8 

.261 

.62279 

IQI 

.90616 

162 

.85134 

27,5 

.1746 

3,8 

.262 

.62470 

191 

.90778 

162 

.85161 

27,5 

.1742 

3,8 

.263 

.62661 

I9I 

.90941 

163 

.85189 

27,4 

•  1739 

3,8 

.264 

.62851 

.191 

.9H04 

163 

.85216 

27,4 

.1735 

3,8 

1.265 

1.63043 

191 

1.91267 

163 

0.85244 

27,3 

1.1731 

3,8 

.266 

.63234 

191 

.91430 

163 

.85271 

27,3 

.1727 

3,8 

.267 

.63426 

192 

.91593 

163 

.85298 

27,2 

.1724 

3,7 

.268 

.63617 

192 

.91757 

164 

.85325 

27,2 

.1720 

3,7 

.269 

.63809 

192 

.91920 

164 

.85353 

27,1 

.1716 

3,7 

1.270 

1.64001 

192 

1.92084 

164 

0.85380 

27,1 

1.1712 

3,7 

.271 

.64193 

192 

.92248 

164 

.85407 

27,1 

.1709 

3,7 

.272 

.64386 

192 

.92413 

164 

•85434 

27,0 

.1705 

3,7 

•  273 

.64578 

193 

.92577 

165 

.85461 

27,0 

.1701 

3,7 

.274 

.64771 

193 

.92742 

165 

.85488 

26,9 

.1698 

3,7 

1.275 

1.64964 

193 

1.92907 

165 

0.85515 

26,9 

1.1694 

3,7 

.276 

.65157 

193 

.93072 

165 

.85542 

26,8 

.1690 

3,7 

•  277 

.65350 

193 

.93237 

165 

.85568 

26,8 

.1687 

3,7 

.278 

.65543 

193 

•93402 

166 

.85595 

26,7 

.1683 

3,6 

.279 

.65736 

194 

.93568 

166 

.85622 

26,7 

.1679 

3,6 

1.280 

1.65930 

194 

1.93734 

166 

0.85648 

26,6 

I  .  1676 

3,6 

.281 

.66124 

194 

.93900 

166 

.85675 

26,6 

.1672 

3,6 

.282 

.66318 

194 

.94066 

166 

.85702 

26,6 

.1668 

3,6 

.283 

.66512 

194 

.94233 

167 

.85728 

26,5 

.1665 

3,6 

.284 

.66706 

194 

•94399 

167 

.85755 

26,5 

.1661 

3,6 

1.285 

1.66901 

195 

1.94566 

167 

0.85781 

26,4 

I  .  1658 

3,6 

.286 

.67096 

195 

•94733 

167 

.85808 

26,4 

.1654 

3,6 

.287 

.67200 

195 

.94900 

167 

.85834 

26,3 

.1650 

3,6 

.288 

.67485 

195 

.95068 

167 

.85860 

26,3 

.1647 

3,6 

.289 

.67680 

195 

•95235 

168 

.85886 

26,2 

.1643 

3,6 

1.290 

1.67876 

195 

1.95403 

168 

0.85913 

26,2 

I  .  1640 

.  3,5 

.291 

.68071 

196 

•95571 

168 

.85939 

26,1 

.1636 

3,5 

.292 

.68267 

196 

•95739 

168 

.85965 

26,1 

.1633 

3,5 

•  293 

.68463 

196 

.95907 

168 

.85991 

26,1 

.1629 

3,5 

.294 

.68659 

196 

.96076 

169 

.86017 

26,0 

.1626 

3,5 

1.295 

1.68855 

196. 

1.96245 

169 

0.86043 

26,0 

I  .  1622 

3,5 

.296 

.60051 

196 

.96414 

169 

.86069 

25,9 

.1619 

3,5 

.297 

.69248 

197 

.96583 

169 

.86095 

25,9 

.1615 

3,5 

.298 

.69444 

197 

.96752 

169 

.86121 

25,8 

.1612 

3,5 

•  299 

.69641 

197 

.96922 

170 

.86147 

25,8 

.1608 

3,5 

1.300 

1.69838 

197 

1.97091 

170 

0.86172 

25,7 

1.1005 

3,5 

u 

tan  gd  u 

«FO' 

sec  Qd  u 

»FO' 

sin  gd  u 

w  FO' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«F0' 

tanhu 

coFo' 

cothu 

-FO' 

1.300 

1.69838 

197 

I.9709I 

170 

0.86172 

25,7 

I  .  1605 

3,5 

.301 

.70035 

197 

.97261 

170 

.86198 

25,7 

.  1601 

3,5 

.302 

.70233 

197 

.97431 

170 

.86224 

25,7 

.1598 

3,5 

.303 

.70430 

198 

.97602 

170 

.86249 

25,6 

•  1594 

3,4 

.304 

.70628 

198 

.97772 

171 

.86275 

25,6 

•  I59I 

3,4 

1.305 

1.70826 

198 

1-97943 

171 

0.86300 

25,5 

1.1587 

3,4 

.306 

.71024 

198 

.98114 

171 

.86326 

25,5 

•  1584 

3,4 

.307 

.71222 

198 

.98285 

171 

.86351 

25,4 

.1581 

3,4 

.308 

.71420 

198 

.98456 

i/i 

.86377 

25,4 

.1577 

3,4 

.309 

.71619 

199 

.98628 

172 

.86402 

25,3 

•  1574 

3,4 

1.310 

I.7l8l8 

199 

1.98800 

172 

0.86428 

25,3 

1.1570 

3,4 

.311 

.72017 

199 

.98972 

172 

.86453 

25,3 

.1567 

3,4 

.312 

.72216 

199 

.99M4 

172 

.86478 

25,2 

•  1564 

3,4 

•313 

.72415 

199 

.99316 

172 

.86503 

25,2 

.1560 

3,4 

.314 

.72614 

199 

.99489 

173 

.86528 

25,1 

.1557 

3,4 

1.315 

1.72814 

200 

1.99661 

173 

0.86554 

25,1 

I.  1554 

3,3 

.316 

.73014 

200 

.99834 

173 

.86579 

25,0 

.1550 

3,3 

.317 

.73214 

2OO 

2.00007 

173 

.86604 

25,0 

.1547 

3,3 

.318 

-73414 

2OO 

.00181 

173 

.86629 

25,0 

.1544 

3,3 

.319 

.73614 

200 

•00354 

174 

.86653 

24,9 

.1540 

3,3 

1.320 

I.738I4 

2OI 

2.00528 

174 

0.86678 

24,9 

i  -1537 

3,3 

.321 

.74015 

2OI 

.00702 

174 

.  81.703 

24,8 

•  1534 

3,3 

.322 

.74216 

2O  I 

.00876 

174 

.86728 

24,8 

.1530 

3,3 

•323 

.74417 

201 

.01050 

174 

.86753 

24,7 

.1527 

3,3 

.324 

.74618 

201 

.01225 

175 

.86778 

24,7 

.1524 

3,3 

1.325 

I.748I9 

2OI 

2.01309 

i75 

0.85802 

24,7 

1.1520 

3,3 

.326 

.75021 

2O2 

.01574 

175 

.86827 

24,6 

.1517 

3,3 

.327 

.75222 

202 

.01749 

175 

.86851 

24,6 

.1514 

3,3 

.328 

•75424 

2O2 

.01925 

175 

.86876 

24,5 

.1511 

3,2 

.329 

.75626 

2O2 

.02100 

176 

.86900 

24,5 

.1507 

3,2 

1.330 

1.75828 

2O2 

2.02276 

176 

0.86925 

24,4 

I  .  1504 

3,2 

.331 

.76031 

202 

.02452 

176 

.86949 

24,4 

.1501 

3,2 

.332 

.  76233 

203 

.02628 

i75 

.86974 

24,4 

.1408 

3,2 

.333 

.76436 

203 

.02804 

176 

.86998 

24,3 

.1495 

3,2 

.334 

.76639 

203 

.02981 

177 

.87022 

24,3 

.1491 

3,2 

1.335 

1.76842 

203 

2.03158 

177 

0.87047 

24,2 

1.1488 

3,2 

.336 

.77045 

203 

•03335 

177 

.87071 

24,2 

.1485 

3,2 

•  337 

•77249 

2O4 

.03512 

177 

•87095 

24,1 

.1482 

3,2 

.338 

•77452 

204 

.03689 

177 

.87119 

24,1 

.1479 

3,2 

.339 

.77656 

2O4 

.03867 

178 

.87143 

24,1 

•  1475 

3,2 

1-340 

1.77860 

204 

2.04044 

178 

0.87167 

24,0 

I.I472 

3,2 

•  341 

.78064 

204 

.04222 

178 

.87191 

24,0 

.1469 

3,2 

.342 

.78268 

204 

.04401 

178 

.87215 

23,9 

.1466 

3,1 

•  343 

.78473 

205 

.04579 

178 

.87239 

23,9 

.  1463 

3,1 

•344 

.78677 

205 

.04758 

179 

.87263 

23,9 

.1460 

3,1 

1-345 

1.78882 

205 

2.04936 

179 

0.87287 

23,8 

I.I456 

3,1 

.346 

.79087 

205 

.05115 

179 

.87311 

23,8 

.1453 

3J 

•  347 

.79293 

205 

•05294 

179 

.87334 

23,7 

.  M50 

3,1 

.348 

.79498 

205 

.05474 

179 

.87358 

23,7 

.1447 

3.1 

•  349 

.79704 

206 

.05653 

180 

.87382 

23,6 

.1444 

3,i 

T.350 

1.79909 

206 

2.05833 

180 

0.87405 

23,6 

I  .  1441 

3.1 

u 

tan  ad  u 

-  F,,' 

sec  gd  u 

•  Fo' 

sin  gd  u 

«F,/ 

esc  gd  u 

-Fo' 

SMITHSONIAN  TABLES 


132 


Natural  Hyperbolic  Functions. 


u 

sinh  u   |  w  Fo'    cosh  u 

u>Fo' 

tanh  u 

O>FO' 

cothu 

«F0' 

1.350 

1.79909 

206   2.05833 

180 

0.87405 

23,6 

1.1441 

3,1 

.351 

.80115 

206    .06013 

180 

.87429 

23,6 

.1438 

3,1 

.352 

.80321 

206 

.06194 

180 

.87452 

23,5 

.1435 

3,1 

•  353 

'  .80528 

206 

.06374 

181 

.87476 

23,5 

.1432 

3,1 

•  354 

.80734 

207 

.06555 

181 

.87499 

23,4 

.1429 

3,1 

1.355 

1.80041 

207 

2.06735 

181 

0.87523 

23,4 

1.1426 

3,1 

•  356 

.81148 

207 

.06916 

181 

.87546 

23,4 

.1423 

3,0 

.357 

.81355 

207 

.07098 

181 

.87570 

23,3 

.1419 

3,o 

.358 

.81562 

207 

.07279 

182 

.87593 

23,3 

.1416 

3,0 

•  359 

.81769 

207 

.07461 

182 

.87616 

23,2 

.1413 

3,0 

1.360 

I.8I977 

208 

2.07643 

182 

0.87639 

23,2 

1.1410 

3,o 

.361 

.82184 

208 

.07825 

182 

.87662 

23,2 

.1407 

3,0 

.362 

.82392 

208 

.08007 

182 

.87686 

23,1 

.1404 

3,0 

.363 

.82600 

208 

.08190 

183 

.87709 

23,1 

.1401 

3,0 

•  364 

.82809 

208 

.08372 

.  183 

.87732 

23,0 

.1398 

3,0 

1.365 

1.83017 

209 

2.08555 

183 

0.87755 

23,0 

I  .  1395 

3,0 

.366 

.83226 

209 

.08738 

183 

.87778 

23,0 

3,o 

.367 

.83435 

209 

.08922 

183 

.87801 

22,9 

.1389 

3,0 

.368 

.83644 

209 

.09105 

184 

.87824 

22,9 

.1386 

3,0 

.369 

•83853 

209 

.09289 

184 

.87846 

22,8 

.1384 

3,0 

1.370 

1.84062 

209 

2.09473 

184 

0.87869 

22,8 

1.1381 

3,0 

•  371 

.84272 

2IO 

,09657 

184 

.87892 

22,7 

.1378 

2,9 

•  372 

.84482 

2IO 

.09841 

184 

.87915 

22,7 

.1375 

2,9 

•  373 

.84691 

2IO 

.10026 

185 

.87937 

22,7 

.1372 

2,9 

•  374 

.84902 

2IO 

.1021  I 

185 

.87960 

22,6 

.1369 

2,0 

1.375 

I.85II2 

210 

2.10306 

185 

0.87983 

22,6 

1.1366 

2,9 

.376 

.85322 

211 

.10581 

185 

.88005 

22,6 

.1363 

2,9 

•  377 

•85533 

211 

.10766 

186 

.88028 

22,5 

.1360 

2,9 

.378 

.85744 

211 

.10952 

186 

.88050 

22,5 

.1357 

2,9 

•  379 

.85955 

211 

.11138 

186 

.88073 

22,4 

.1354 

2,9 

1.380 

I.86I66 

211 

2.11324 

186 

0.88095 

22,4 

1.1351 

2,9 

.381 

.86378 

212 

.11510 

186 

.88117 

22,4 

.1348 

2,9 

.382 

.86589 

212 

.11697 

187 

.88140 

22,3 

.1346 

2,9 

.383 

.86801 

212 

.11883 

187 

.88162 

22,3 

.  1343 

2,9 

.384 

.87013 

212 

.12070 

187 

.88184 

22,2 

.1340 

2,9 

1.385 

1.87225 

212 

2.12257 

187 

0.88207 

22,2 

1  .  1337 

2,9 

.386 

.87437 

212 

.12445 

187 

.88229 

22,2 

.1334 

2,8 

.387 

.87650 

213 

.12632 

188 

.88251 

22,1 

.1331 

2,8 

.388 

.87863 

213 

.12820 

188 

.88273 

22,1 

.1328 

2,8 

.389 

.88076 

213 

.13008 

188 

.88295 

22,O 

.1326 

2,8 

1.390 

1.88289 

213 

2.13196 

188 

0.88317 

22,0 

1.1323 

2,8 

.391 

.88502 

213 

.13385 

189 

.88339 

22,O 

.1320 

2,8 

.392 

.88716 

214 

•  13573 

189 

.88361 

21,9 

.1317 

2,8 

•  393 

.88929 

214 

.13762 

189 

.88383 

21,9 

.1314 

2,8 

•  394 

.89143 

214 

.13951 

189 

.88405 

21,8 

.1312 

2,8 

1.395 

1.89357 

214 

2.141-40 

189 

0.88427 

21,8 

1.1309 

2,8 

•  396 

.89571 

214 

.  14330 

190 

.88448 

21,8 

.1306 

2,8 

•  397 

.89786 

215 

.  14520 

190 

.88470 

21,7 

.1303 

2,8 

.398 

.90000 

215 

.14709 

190 

.88492 

21,7 

.1300 

2,8 

•  399 

.90215 

215 

.14900 

190 

.88513 

21,7 

.1298 

2,8 

1.400 

1.00430 

215 

2.15090 

190 

0.88535 

21,6 

i.  1295 

2,8 

u 

tan  gd  u 

«FO' 

sec  gd  u 

-FO' 

sin  gd  u 

«F0' 

csc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


133 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

•  Fo' 

tanh  u 

«Fo' 

coth  u 

•  Fo' 

1.400 

1.90430 

215 

2.15000 

190 

0.88535 

21,6 

1.1295 

2,8 

.401 

.90645 

215 

.15280 

191 

•88557 

21,6 

.1292 

2,8 

.402 

.90861 

215 

•  I547I 

191 

.88578 

21,5 

.1289 

2,7 

.403 

.91076 

216 

.15662 

191 

.88600 

21,5 

.1287 

2,7 

.404 

.91292 

216 

.15853 

191 

.88621 

21,5 

.1284 

2,7 

1.405 

1.91508 

216 

2.16045 

192 

0.88643 

21,4 

1.1281 

2,7 

.406 

.91724 

216 

.  16236 

192 

.88664 

21,4 

.1279 

2,7 

.407 

.91940 

216 

.16428 

192 

.88686 

21,3 

.1276 

2,7 

.408 

-92I57 

217 

.16620 

192 

.88707 

21,3 

.1273 

2,7 

.409 

.92374 

217 

.16812 

192 

.88728 

21,3 

.1270 

2,7 

1.410 

I.9259I 

217 

2.17005 

193 

0.88749 

21,2 

1.1268 

2,7 

.411 

.92808 

217 

.17198 

193 

.88771 

21,2 

.1265 

2,7 

.412 

.93025 

217 

.17391 

193 

.88792 

21,2 

.1262 

2,7 

.413 

.93242 

218 

.17584 

193 

.88813 

21,1 

.1260 

2,7 

.414 

.93460 

218 

.  17777 

193 

.88834 

21,1 

•  1257 

2,7 

1.415 

1.93678 

218 

2.17971 

194 

0.88855 

21,0 

i  .  1254 

2,7 

.416 

.93896 

218 

.  18164 

194 

.88876 

21,0 

.1252 

2,7 

.417 

.94114 

218 

.  18358 

194 

.88897 

21,0 

.1249 

2,7 

.418 

.94333 

219 

.18553 

194 

.88918 

20,9 

.1246 

2,6 

.419 

.94551 

219 

•  18747 

195 

.88939 

20,9 

.1244 

2,6 

1.420 

1.94770 

219 

2.18942 

195 

0.88960 

20,9 

1.1241 

2,6 

.421 

.94989 

219 

.19137 

195 

.88081 

20,8 

.1238 

2,6 

.422 

.95209 

219 

.  19332 

195 

.89002 

20,8 

.1236 

2,6 

423 

.95428 

22O 

.19527 

195 

.89022 

20,8 

•  1233 

2,6 

.424 

.95648 

22O 

.19723 

196 

.89043 

20,7 

.1231 

2,6 

1.425 

1.95867 

22O 

2.19918 

196 

0.89064 

20,7 

i  .  1228 

2,6 

.426 

.96087 

22O 

.20114 

196 

.89084 

20,6 

.1225 

2,6 

.427 

.96308 

220 

.20310 

196 

.89105 

20,6 

.1223 

2,6 

.428 

.96528 

221 

.20507 

197 

.89126 

20,6 

.1220 

2,6 

.429 

.96749 

221 

.20704 

197 

.89146 

20,5 

.1218 

2,6 

1.430 

1.96970 

221 

2.20900 

197 

0.89167 

20,5 

1.1215 

2,6 

.431 

.97191 

221 

.21097 

197 

.89187 

20,5 

.1212 

2,6 

.432 

.97412 

221 

.21295 

197 

.89208 

20,4 

.1210 

2,6 

•  433 

.97633 

221 

.21492 

198 

.89228 

20,4 

.I2O7 

2,6 

•434 

.97855 

222 

.21690 

198 

.89248 

20,3 

.1205 

2,6 

1-435 

1.98076 

222 

2.21888 

198 

0.89269 

20,3 

I.I2O2 

2,5 

.436 

.08298 

,  222 

.22086 

198 

.89289 

20,3 

.I2OO 

2,5 

•  437 

.98521 

222 

.22285 

199 

.89309 

20,2 

.1197 

2,5 

.438 

.98743 

222 

.22483 

199 

.89329 

20,2 

•1195 

2,5 

•  439 

.98966 

223 

.22682 

199 

.89350 

20,2 

.1192 

2,5 

1.440 

1.99188 

223 

2.22881 

199 

0.89370 

2O,  I 

I.II89 

2,5 

.441 

.99411 

223 

.23080 

199 

.89390 

2O,  I 

.1187 

2,5 

.442 

.99635 

223 

.23280 

200 

.89410 

2O,  I 

.1184 

2,5 

•443 

.99858 

223 

.23480 

200 

.89430 

2O,O 

.1182 

2,5 

•444 

2.00082 

224 

.23680 

200 

.89450 

20,O 

.1179 

2,5 

1-445 

2.00305 

224 

2.23880 

200 

0.89470 

2O,O 

1.1177 

2,5 

.446 

.00529 

224 

.24080 

201 

.89490 

19,9 

.1174 

2,5 

•  447 

.00753 

224 

.24281 

2OI 

.89510 

19,9 

.1172 

2,5 

.448 

.00978 

224 

.24482 

201 

.89530 

19,8 

.1109 

2,5 

•449 

.01202 

225 

.24683 

2OI 

.89550 

19,8 

.1167 

2,5 

1.450 

2.01427 

225 

2.24884 

201 

0.89569 

19,8 

I.II65 

2,5 

u 

tan  gd  u 

«F0' 

sec  gd  u 

•  F.' 

tin  gd  u 

•  IV 

csc  gd  u 

«Fo' 

SMITHSONIAN  TABLCD 


134 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«Fo' 

tanh  u 

«F0' 

coth  u 

«Fo' 

1.450 

2.01427 

225 

2.24884 

201 

0.89569 

19,8 

I  .  I  165 

2,5 

.451 

.01652 

225 

.25086 

202 

.89589 

19,7 

.1162 

2,5 

.452 

.01877 

225 

.25288 

202 

.89609 

19,7 

.nob 

2,5 

•453 

.02103 

225 

.25490 

202 

.89628 

19,7 

.1157 

2,4 

•454 

.02328 

226 

.25692 

202 

.89648 

19,6 

.1155 

2,4 

1.  455 

2.02554 

226 

2.25894 

203 

0.89668 

19,6 

1.1152 

2,4 

.456 

.02780 

226 

.26097 

203 

.89687 

19,6 

.1150 

2,4 

•  457 

.03006 

226 

.26300 

203 

.89707 

19,5 

.1147 

2,4 

.458 

.03233 

227 

.26503 

203 

.89726 

19,5 

•  1145 

2,4 

•459 

•03459 

227 

.26706 

203 

.89746 

19,5 

•  1143 

2,4 

1.460 

2.03686 

227 

2.26910 

2O4 

0.89765 

19,4 

i  .  i  140 

2,4 

.461 

.03913 

227 

.27114 

2O4 

.89785 

19,4 

.1138 

2,4 

.462 

.04140 

227 

.27318 

2O4 

.89804 

19,4 

.1135 

2,4 

.463 

.04368 

228 

.27522 

204 

.89823 

19,3 

.ii33 

2,4 

.464 

.04595 

228 

.27726 

205 

.89843 

19,3 

.1131 

2,4 

1.465 

2.04823 

228 

2.27931 

205 

0.89862 

19,2 

i  .  i  128 

2,4 

.466 

.05051 

228 

.28136 

205 

.89881 

19,2 

.1126 

2,4 

.467 

.05280 

228 

.28341 

205 

.89900 

19,2 

.1123 

2,4 

.468 

.05508 

229 

.28547 

206 

.89920 

19,1 

.1121 

2,4 

.469 

.05737 

229 

.28752 

206 

.89939 

19,1 

.1119 

2,4 

1.470 

2.05965 

229 

2.28958 

206 

0.89958 

19,1 

I.III6 

2,4 

.471 

.06195 

229 

.29164 

206 

.89977 

19,0 

.1114 

2,4 

.472 

.06424 

229 

.29370 

206 

.89996 

19,0 

.1112 

2,3 

.473 

.06653 

230 

.29577 

207 

.90015 

19,0 

.IIO9 

2,3 

.474 

.06883 

230 

.29784 

207 

.90034 

18,9 

.1107 

2,3 

1.475 

2.07113 

23O 

2.29991 

207 

0.90053 

18,9 

1.  1105 

2,3 

.476 

.07343 

230 

.30198 

207 

.90072 

18,9 

.IIO2 

2,3 

.477 

.07573 

230 

.30405 

208 

.90090 

18,8 

.IIOO 

2,3 

.478 

.07804 

231 

.30613 

208 

.90109 

18,8 

.1008 

2,3 

•479 

.08034 

231 

.30821 

208 

.90128 

18,8* 

.1095 

2,3 

1.480 

2.08265 

231 

2.31029 

208 

0.00147 

18,7 

I.  1093 

2,3 

.481 

•08497 

231 

.31238 

208 

.90166 

18,7 

.1091 

2,3 

.482 

.08728 

231 

.31446 

209 

.90184 

18,7 

.1088 

2,3 

.483 

.08959 

232 

.31655 

209 

.90203 

18,6 

.1086 

2,3 

.484 

.09191 

232 

,  .31864 

209 

.90221 

18,6 

.1084 

2,3 

1.485 

2.09423 

232 

2.32073 

209 

0.90240 

18,6 

1.1082 

2,3 

.486 

.09655 

232 

.32283 

210 

.90259 

18,5 

.1079 

2,3 

.487 

.09888 

232 

.32493 

2IO 

.90277 

18,5 

.1077 

2,3 

.488 

.  IOI2O 

233 

.32703 

2IO 

.90296 

18,5 

.1075 

2,3 

.489 

.10353 

233 

.32913 

210 

.90314 

18,4 

.1072 

2,3 

1.490 

2.10586 

233 

2.33123 

211 

0.90332 

18,4 

i  .  1070 

2,3 

.491 

.10819 

233 

•33334 

211 

.90351 

18,4 

.1068 

2,2 

.492 

.11053 

234 

.33545 

211 

.90369 

18,3 

.1066 

2,2 

•493 

.11286 

234 

.33756 

211 

.90388 

18,3 

.1063 

2,2 

•  494 

.11520 

234 

.33968 

212 

.00406 

18,3 

.1061 

2,2 

1.495 

2.11754 

234 

2.34179 

212 

0.90424 

18,2 

i  .  1059 

2,2 

.496 

.11089 

234 

•34391 

212 

.00442 

18,2 

.1057 

2,2 

•  497 

.  12223 

235 

.34603 

212 

.90460 

18,2 

.1055 

2,2 

.498 

.  12458 

235 

.34816 

212 

.90479 

18,1 

.1052 

2,2 

.499 

.12693 

235 

.35028 

213 

•90497 

18,1 

.1050 

2,2 

1.500 

2.12928 

235 

2.35241 

213 

0.90515 

18,1 

i  .  1048 

2,2 

u 

tan  gd  u 

wF0' 

sec  gd  u 

«F0' 

sin  gd  u 

O.FO' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


135 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F«/ 

cosh  u 

«FO' 

tanhu 

«F0' 

coth  u 

«F0' 

1.500 

2.12928 

235 

2.35241 

213 

0.90515 

18,1 

I  .  1048 

2,2 

.501 

.13163 

235 

.35454 

213 

.90533 

18,0 

.1046 

2,2 

.502 

•13399 

236 

.35667 

213 

•00551 

18,0 

.1044 

2,2 

.503 

.  13635 

236 

.35881 

214 

.90569 

18,0 

.1041 

2,2 

.504 

.13871 

236 

.36095 

214 

.90587 

17,9 

.1039 

2,2 

1.505 

2.14107 

236 

2.36309 

214 

0.90605 

17,9 

1.  1037 

2,2 

.506 

•  14343 

237 

.36523 

214 

.90623 

17,9 

.1035 

2,2 

.507 

.14580 

237 

.36737 

215 

.90641 

17,8 

.1033 

2,2 

.508 

.14817 

237 

.36952 

215 

.90658 

17,8 

.1030 

2,2 

.509 

.15054 

237 

.37167 

215 

.90676 

17,8 

.1028 

2,2 

1.510 

2.15291 

237 

2.37382 

215 

0.90694 

17,7 

I  .  1026 

2,2 

.511 

•  15529 

238 

•37597 

216 

.90712 

17,7 

.1024 

2,2 

.512 

.15766 

238 

.37813 

216 

.90729 

17,7 

.1022 

2,1 

.513 

.16004 

238 

.38029 

216 

.90747 

17,6 

.1020 

2,1 

.514 

.  16242 

238 

.38245 

216 

.90765 

17,6 

.1018 

2,1 

1.515 

2.16481 

238 

2.38461 

216 

0.90782 

17,6 

I.IOI5 

2,1 

.516 

.16719 

239 

.38678 

217 

.90800 

17,6 

.1013 

2,1 

.517 

.16958 

239 

.38895 

217 

.90817 

17,5 

.IOII 

2,1 

.518 

.17197 

239 

-39II2 

217 

.90835 

17,5 

.1009 

2,1 

.519 

.  17436 

239 

.39329 

217 

.90852 

17,5 

.1007 

2,1 

1.520 

2.17676 

240 

2-39547 

218 

0.90870 

17,4 

I.  1005 

2,1 

.521 

.17915 

240 

.39765 

218 

.90887 

17,4 

.1003 

2,1 

.522 

.18155 

240 

.39983 

218 

.90905 

17,4 

.1001 

2,1 

.523 

.  18395 

240 

.40201 

218 

.90922 

17,3 

.0998 

2,1 

.524 

.18636 

240 

.40419 

219 

.90939 

17,3 

.0996 

2,1 

1.525 

2.18876 

241 

2.40638 

219 

0.90957 

17,3 

1.0094 

•2,1 

.526 

.19117 

241 

.40857 

219 

•90974 

17,2 

.0992 

2,1 

.527 

.19358 

241 

.41076 

219 

.90991 

17,2 

.0000 

2,1 

.528 

.19599 

241 

.41296 

220 

.91008 

17,2 

.0988 

2,1 

.529 

.19840 

.  242 

.41516 

220 

.91025 

I7,i 

.0986 

2,1 

1.530 

2.20082 

242 

2.41736 

220 

0.91042 

I7,i 

1.0984 

2,1 

.531 

.20324 

242 

.41956 

220 

.91060 

I7,i 

.0082 

2,1 

.532 

.20566 

242 

.42176 

221 

.91077 

I7,i 

.0080 

2,1 

•533 

.20808 

242 

•42397 

221 

.91094 

I7,o 

.0978 

2,1 

•  534 

.21051 

243 

.42618 

221 

.91111 

I7,o 

.0976 

2,0 

1.535 

2.21293 

243 

2.42839 

221 

0.91128 

I7,o 

1.0974 

2,0 

.536 

.21536 

243 

.43060 

222 

•9II45 

16,9 

.0972 

2,O 

.537 

.21780 

243 

.43282 

222 

.91161 

16,9 

.0970 

2,0 

.538 

.22023 

244 

.43504 

222 

.9H78 

16,9 

.0968 

2,0 

•  539 

.22267 

244 

.43726 

222 

.91195 

16,8 

.0965 

2,0 

1.540 

2.22510 

244 

2.43949 

223 

O.9I2I2 

16,8 

1.0063 

2,O 

•  541 

.22755 

244 

.44171 

223 

.91229 

16,8 

.0961 

2,O 

•  542 

.22099 

244 

•44394 

223 

.91246 

16,7 

.0959 

2,0 

.543 
•  544 

1  23488 

245 
245 

.44617 
.44841 

223 
223 

.91262 
.91279 

16,7 
16,7 

•0957 
.0955 

2,O 
2,0 

1-545 

2.23733 

245 

2.45064 

224 

0.91296 

16,7 

1.0953 

2,0 

.546 

.23978 

245 

.45288 

224 

.91312 

16,6 

.0951 

2,0 

•  547 

.24224 

246 

•45512 

224 

.91329 

16,6 

•  0949 

2,0 

.548 

.24469 

246 

.45736 

224 

.91345 

16,6 

•  0947 

2,0 

•  549 

.24715 

246 

.45961 

225 

.91362 

16,5 

.0945 

2,0 

1.550 

2.24961 

246 

2.46186 

225 

0.91379 

16,5 

1.0943 

2,0 

u 

tan  gd  u 

«F</ 

sec  gd  u 

«F0' 

sin  gd  u 

«F0' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


136 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

»F0' 

tanh  u 

«FO' 

cothu 

«F0' 

1.550 

2.24961 

246 

2.46186 

225 

0.91379 

16,5 

1.0943 

2,0 

.551 

.25207 

246 

.46411 

225 

.91395 

16,5 

.0942 

2,0 

.552 

.25454 

247 

.46636 

225 

.91411 

16,4 

.0940 

2,0 

.553 

.25701 

247 

.46862 

226 

.91428 

16,4 

.0938 

2,0 

•  554 

.25948 

247 

.47088 

226 

•91444 

16,4 

.0936 

2,0 

1-555 

2.26195 

247 

2.47314 

226 

0.91461 

16,3 

1.0934 

2,0 

.556 

.26442 

248 

.47540 

226 

.91477 

16,3 

.0932 

2,0 

•  557 

.26690 

248 

.47767 

227 

.9U93 

16,3 

.0930 

1,9 

.558 

.26938 

248 

.47993 

227 

.91510 

16,3 

.0928 

1,9 

.559 

.27186 

248 

.48221 

227 

.91526 

16,2 

.0926 

1,9 

1.560 

2.27434 

248 

2.48448 

227 

0.91542 

16,2 

1.0924 

1,9 

.561 

.27683 

249 

.48675 

228 

.91558 

16,2 

.0922 

1,9 

.562 

.27932 

249 

.48903 

228 

.91574 

16,1 

.0920 

1,9 

.563 

.28181 

249 

.49131 

228 

.91591 

16,1 

.0918 

i,9 

.564 

.28430 

249 

.49360 

228 

.91607 

16,1 

.0916 

1,9 

1.565 

2.28679 

250 

12.49588 

229 

0.91623 

16,1 

I.09I4 

1,9 

.566 

.28929 

250 

.49817 

229 

.91639 

16,0 

.0912 

1,9 

.567 

.29179 

250 

.50046 

229 

.91655 

16,0 

.0911 

1,9 

.568 

.29429 

250 

.50275 

220 

.91671 

16,0 

.0909 

1,9 

.569 

.29680 

251 

.50505 

230 

.91687 

15,9 

.0907 

1,9 

1.570 

2.29930 

251 

2.50735 

230 

0.91703 

15,9 

1.0905 

1,9 

•  571 

.30181 

251 

.50965 

230 

.91718 

15,9 

.0903 

1,9 

•  572 

.30432 

251 

.5H95 

230 

.91734 

15,8 

.0901 

1,9 

•  573 

.30683 

251 

.51426 

231 

.91750 

15,8 

.0899 

1,9 

•  574 

•30935 

252 

.51656 

231 

.91766 

15,8 

.0897 

1,9 

1.575 

2.31187 

252 

2.51887 

231 

0.91782 

15,8 

1.0895 

1,9 

.576 

.31439 

252 

.52119 

231 

.91797 

15,7 

.0894 

1,9 

•  577 

.31691 

252 

.52350 

232 

.91813 

15,7 

.0892 

1,9 

.578 

•31943 

253 

.52582 

232 

.91829 

15,7 

.0890 

1,9 

.579 

.32196 

253 

.52814 

232 

.91845 

15,6 

.0888 

1,9 

1.580 

2.32449 

253 

2.53047 

232 

0.91860 

15,6 

1.0886 

1,9 

.581 

.32702 

253 

.53279 

233 

.91876 

15,6 

.0884 

1,8 

.582 

.32956 

254 

.53512 

233 

.91891 

15,6 

.0882 

1,8 

.583 

.33209 

254 

.53745 

233 

.91907 

15,5 

.0881 

1,8 

.584 

.33463 

254 

•53978 

233 

.91922 

15,5 

.0879 

1,8 

1.585 

2.33717 

254 

2.54212 

234 

0.91938 

15,5 

1.0877 

1,8 

.586 

.33972 

254 

.54446 

234 

.91953 

15,4 

•  0875 

1,8 

.587 

.34226 

255 

.54680 

234 

.91969 

15,4 

•  0873 

1,8 

.588 

.34481 

255 

.54914 

234 

•91984 

15,4 

.0871 

1,8 

.589 

.34736 

255 

.55149 

235 

.92000 

15,4 

.0870 

1,8 

1.500 

2.34991 

255 

2.55384 

235 

0.92015 

15,3 

1.0868 

1,8 

•  591 

.35247 

256 

•55619 

235 

.92030 

15,3 

.0866 

1,8 

.592 

•35502 

256 

.55854 

236 

.92046 

15,3 

.0864 

1,8 

•  593 

.35758 

256 

.56090 

236 

.92061 

15,2 

.0862 

1,8 

•  594 

.36015 

256 

.56326 

236 

.92076 

15,2 

.0861 

1,8 

1.595 

2.36271 

257 

2.56562 

236 

0.92091 

15,2 

1.0859 

1,8 

.596 

.36528 

257 

.56798 

237 

.92106 

15,2 

.0857 

1,8 

•  597 

.36785 

257 

.57035 

237 

.92122 

15,1 

.0855 

1,8 

.598 

.37042 

257 

.57272 

237 

.92137 

I5,i 

•  0853 

1,8 

.599 

•37299 

258 

.57509 

237 

.92152 

I5,i 

.0852 

1,8 

1.  600 

2.37557 

258 

2.57746 

238 

0.92167 

I5,i 

1.0850 

1,8 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

sin  gd  u 

wF0' 

esc  gd  u 

«•>  Fo' 

SMITHSONIAN  TABLES 


137 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

O.FO' 

cosh  u 

«Fo' 

tanhu 

O.FO' 

coth  u 

O.FO' 

1.  600 

2.37557 

258 

2.57746 

238 

0.92167 

15,1 

1.0850 

1,8 

.601 

.3/815 

258 

.57984 

238 

.92182 

15,0 

.0848 

1,8 

.602 

.38073 

258 

.58222 

238 

.92197 

15,0 

.0846 

i3 

.603 

.38331 

258 

.58460 

238 

.92212 

15,0 

.0845 

1,8 

.604 

.38590 

259 

.58699 

239 

.92227 

14,9 

.0843 

1,8 

1.605 

2.38849 

259 

2.58937 

239 

0.92242 

14,9 

1.0841 

1,8 

.606 

.39108 

259 

.59176 

239 

.92257 

14,9 

.0839 

1,7 

.607 

.39367 

259 

.59416 

239 

.92272 

14,9 

.0838 

,7 

.608 

.39626 

260 

.59655 

240 

.92286 

14,8 

.0836 

,7 

.609 

'  .39886 

260 

.59895 

240 

.92301 

14,8 

.0834 

,7 

1.610 

2.40146 

260 

2.60135 

240 

0.92316 

14,8 

1.0832 

,7 

.611 

.40406 

260 

.60375 

240 

.92331 

14,8 

.0831 

,7 

.612 

.40667 

261 

.60616 

241 

.92346 

H,7 

.0829 

,7 

.613 

.40928 

261 

.60857 

241 

.92360 

14,7 

.0827 

,7 

.614 

.41189 

261 

.61098 

241 

.92375 

14,7 

.0825 

,7 

1.615 

2.41450 

261 

2.61339 

241 

0.92390 

14,6 

1.0824 

1,7 

.616 

.41711 

262 

.61581 

242 

.92404 

14,6 

.0822 

1,7 

.617 

.41973 

262 

.61822 

242 

.92419 

14,6 

.0820 

1,7 

.618 

.42235 

262 

.62064 

242 

.92433 

14,6 

.0819 

1,7 

.619 

.42497 

262 

.62307 

242 

.92448 

14,5 

.0817 

1,7 

1.620 

2.42760 

263 

2.62549 

243 

0.92462 

14,5 

1.0815 

1,7 

.621 

.43022 

263 

.62792 

243 

.92477 

14,5 

.0814 

1,7 

.622 

.43285 

263 

.63035 

243 

.92491 

14,5 

.0812 

1,7 

.623 

.43548 

263 

.63279 

244 

.92506 

14,4 

.0810 

1,7 

.624 

.43812 

264 

.63522 

244 

.92520 

14,4 

.0808 

1,7 

1.625 

2.44075 

264 

2.63767 

244 

0.92535 

14,4 

1.0807 

1,7 

.626 

•44339 

264 

.64011 

244 

.92549 

14,3 

.0805 

1,7 

.627 

.44603 

264 

.64255 

245 

.92563 

14,3 

.0803 

1,7 

.628 

.44868 

264 

.64500 

•245 

.92578 

14,3 

.0802 

1,7 

.629 

.45132 

265 

.64745 

245 

.92592 

14,3 

.0800 

1,7 

1.630 

2.45397 

265 

2.64900 

245 

0.92606 

14,2 

1.0708 

1,7 

.631 

.45662 

265 

.65236 

246 

.92620 

14,2 

.0797 

1,7 

.632 

.45928 

265 

.65482 

246 

•92635 

14,2 

.0795 

1,7 

.633 

.46193 

266 

'  .65728 

246 

.92649 

14,2 

.0793 

1,6 

.634 

.46459 

266 

.65974 

246 

.92663 

I4,i 

.0792 

1,6 

1.635 

2.46725 

266 

2.66221 

247 

0.92677 

I4,i 

1.0790 

1,6 

.636 

.46992 

266 

.66467 

247 

.92691 

14,1 

.0789 

1,6 

.637 

.47258 

267 

.66715 

247 

.92705 

14,1 

.0787 

1,6 

.638 

.47525 

267 

.66962 

248 

.92/19 

14,0 

.0785 

1,6 

•639 

•47792 

267 

.67210 

248 

.92733 

14,0 

.0784 

1,6 

1.640 

2.48059 

267 

2.67457 

248 

0.92747 

14,0 

1.0782 

1,6 

.641 

.48327 

268 

.67706 

248 

.92761 

14,0 

.0780 

1,6 

.642 

.48595 

268 

.67954 

249 

.92775 

13,9 

•0779 

1,6 

.643 

.48863 

268 

.68203 

249 

.92789 

12,9 

.0777 

1,6 

.644 

.49131 

268 

.68452 

249 

.92803 

13,9 

.0776 

1,6 

1.645 

2.40400 

269 

2.68701 

249 

0.92817 

13,9 

1.0774 

1,6 

.646 

.40669 

269 

.68951 

250 

.92831 

13,8 

•  0772 

1,6 

.647 

.49938 

269 

.69200 

250 

.92844 

13,8 

.0771 

1,6 

.648 

.50207 

269 

.6945] 

250 

.92858 

13,8 

.0769 

1,6 

.649 

.50477 

270 

.69701 

250 

.92872 

13,7 

.0768 

1,6 

1.650 

2.50746 

270 

2.69951 

251 

0.92886 

13,7 

1.0766 

1,6 

u 

tan  gd  u 

•  Fo' 

sec  gd  u 

-FO' 

sin  gd  u 

•  Fo' 

esc  gd  u 

-FO' 

SMITHSONIAN  TABLE* 


J38 


Natural  Hyperbolic  Functions. 


u 

sinhu 

w  Fo' 

cosh  u 

-Fo' 

tanh  u 

»Fo' 

coth  u 

«F0' 

1.650 

2.50746 

270 

2.69951 

251 

0.92886 

13,7 

1.0766 

1,6 

.651 

.51017 

270 

.70202 

251 

.92899 

13,7 

.0764 

1,6 

.652 

.51287 

270 

.70454 

251 

.92913 

13,7 

.0763 

1,6 

.653 

.51557 

271 

.70705 

252 

.92927 

13,6 

.0761 

1,6 

.654 

.51828 

271 

.70957 

252 

.92940 

13,6 

.0760 

1,6 

1.655 

2.52099 

271 

2.71209 

252 

0.92954 

13,6 

1.0758 

1,6 

.656 

.52371 

271 

.71461 

252 

.92968 

13,6 

.0756 

1,6 

.657 

.52642 

272 

.71713 

253 

.92981 

13,5 

•0755 

1,6 

.658 

.52914 

272 

.71966 

253 

.92995 

13,5 

.0753 

1,6 

.659 

.53186 

272 

.72219 

253 

.93008 

13,5 

.0752 

1,6 

1.660 

2.53459 

272 

2.72472 

253 

O.93O22 

13,5 

1.0750 

•1,6 

.661 

•53731 

273 

.72726 

254 

•93035 

13,4 

•  0749 

1,6 

.662 

.54004 

273 

.72980 

254 

.93049 

13,4 

•  0747 

i,5 

.663 

.54277 

273 

.73234 

254 

.93062 

13,4 

.0746 

i,5 

.664 

•54551 

273 

.73489 

255 

•93075 

13,4 

•  0744 

1,5 

1.665 

2.54824 

274 

2.73743 

255 

0.93089 

13,3 

1.0742 

1,5 

.666 

.55098 

274 

.73998 

255 

.93102 

13,3 

.0741 

i,5 

.667 

.55372 

274 

.74253 

255 

.93115 

13,3 

•  0739 

1,5 

.668 

.55647 

275 

.74509 

256 

.93129 

13,3 

.0738 

i,5 

.669 

•55921 

275 

.74765 

256 

.93142 

13,2 

.0736 

i,5 

1.670 

2.56196 

275  . 

2.75021 

256 

0.93155 

13,2 

1.0735 

1,5 

.671 

.56471 

275   .75277 

256 

.93168 

13,2 

•0733 

i,5 

.672 

.56747 

276   .75534 

257 

.93182 

13,2 

.0732 

i,5 

.673 

.57022 

276 

.75791 

257 

.93195 

13,1 

.0730 

i,5 

.674 

.57298 

276 

.76048 

257 

.93208 

13,1 

.0729 

1,5 

1.675 

2.57574 

276 

2.76305 

258 

0.93221 

I3J 

1.0727 

1,5 

.676 

.57851 

277 

.76563 

258 

.93234 

13,1 

.0726 

i,5 

.677 

.58127 

277 

.76821 

258 

.93247 

I3,o 

.0724 

1,5 

.678 

.58404 

277 

.77079 

258 

.93260 

I3,o 

.0723 

i,5 

.679 

.58682 

277 

.77338 

259 

.93273 

I3,o 

.0721 

i,5 

i.  680 

2.58959 

278 

2.77596 

259 

0.93286 

I3,o 

1.0720 

1,5 

.681 

.59237 

278 

.77856 

259 

.93299 

I3,o 

.0718 

1,5 

.682 

.59515 

278 

.78115 

260 

-933I2 

12,9 

.0717 

1,5 

.683 

•59793 

278 

.78375 

260 

.93325 

12,9 

.0715 

1,5 

.684 

.60072 

279 

.78635 

260 

.93338 

12,9 

.0714 

1,5 

1.685 

2.60350 

279 

2.78895 

260 

0-93351 

12,9 

1.0712 

1,5 

.686 

.60629 

279 

.79155 

261 

.93364 

12,8 

.0711 

1,5 

.687 

.60909 

279 

.79416 

25  1 

.93376 

12,8 

.0709 

1,5 

.688 

.61188 

280 

.79677 

261 

.93389 

12,8 

.0708 

i,5 

.689 

.61468 

280 

.79938 

261 

•93402 

12,8 

.0706 

1,5 

i.  600 

2.61748 

280 

2.80200 

262 

0.934IS 

12,7 

1.0705 

1,5 

.691 

.62028 

280 

.80462 

262 

•93427 

12,7 

.0703 

1,5 

.692 

.62309 

281 

.80724 

262 

•93440 

12,7 

.0702 

1,5 

.693 

.62590 

281 

.80087 

263 

•93453 

12,7 

.0701 

1,5 

.694 

.62871 

•281 

.81249 

263 

.93465 

12,6 

.0699 

1,4 

1.695 

2.63152 

282 

2.81512 

263 

0.93478 

12,6 

1.0698 

1,4 

.696 

.63434 

282 

.81776 

263 

.93491 

12,6 

.0696 

1,4 

.697 

.63716 

282 

.82039 

264 

•93503 

12,6 

.0695 

1,4 

.698 

.63998 

282 

.82303 

264 

.93516 

12,5 

.0693 

i,4 

•  699 

.64280 

283 

.82567 

264 

.93528 

12,5 

.0692 

1,4 

1.700 

2.64563 

283 

2.82832 

265 

0.93S4I 

12,5 

1.0691 

1,4 

u 

tan  gd  u 

*>  FO'   sec  Qd  u 

wF0' 

sin  gd  u 

coFo' 

esc  gd  u 

*>FO' 

SMITHSONIAN  TABLES 


139 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanh  u 

-FO* 

coth  u 

-FO' 

1.700 

2.64563 

283 

2.82832 

265 

0.93541 

12,5 

1.0691 

1,4 

.701 

.64846 

283 

.83096 

265- 

•93553 

12,5 

.0689 

1,4 

.702 

.65129 

283 

.83361 

265 

.93566 

12,5 

.0688 

1,4 

.703 

.65413 

284 

.83627 

265 

•935/8 

12,4 

.0686 

1,4 

.704 

•65697 

384 

.83892 

266 

•93591 

12,4 

.0685 

1,4 

1.705 

2.65981 

284 

2.84158 

266 

0.93603 

12,4 

1.0683 

1,4 

.706 

.66265 

284 

.84424 

266 

.93615 

12,4 

.0682 

1,4 

.707 

.66550 

285 

.84690 

267 

.93628 

12,3 

.O68l 

1,4 

.708 

.66834 

285 

.84957 

267 

.93640 

12,3 

.0679 

1,4 

.709 

.67119 

285 

.85224 

267 

.93652 

12,3 

.0678 

1,4 

r.7io 

2.67405 

285 

2.85491 

267 

0.93665 

12,3 

1.0676 

1,4 

.711 

.67690 

286 

.85759 

268 

.93677 

12,2 

.0675 

1,4 

.712 

.67976 

286 

.86027 

268 

.93689 

12,2 

.0674 

1,4 

.713 

.68262 

286 

.86295 

268 

.93701 

12,2 

.0672 

1,4 

.714 

.68549 

287 

* 

.86563 

269 

.93714 

12,2 

.0671 

1,4 

1.715 

2.68836 

287 

2.86832 

269 

0.93726 

12,2 

1.0669 

1,4 

.716 

.69123 

287 

.87101 

269 

.93738 

12,1 

.0668 

1,4 

.717 

.69410 

287 

.87370 

269 

•93750 

12,1 

.0667 

1,4 

.718 

.69697 

288 

.87640 

270 

.93762 

12,1 

.0665 

1,4 

.719 

.69985 

288 

.87910 

270 

.93774 

12,1 

.0664 

1,4 

1.720 

2.70273 

288 

2.88180 

270 

0.93786 

12,0 

1.0663 

1,4 

.721 

.70561 

288 

.88450 

271 

.93798 

12,0 

.0661 

1,4 

.722 

.70850 

289 

.88721 

271 

.93810 

12,0 

.0660 

1,4 

.723 

.7H39 

289 

.88992 

271 

.93822 

1  2,O 

.0658 

1,4 

.724 

.71428 

289 

.89263 

271 

.93834 

12,0 

.0657 

1,4 

1.725 

2.7I7I7 

290 

2.89535 

272 

0.93846 

11,9 

1.0656 

1,4 

.726 

.72007 

290 

.89807 

272 

.93858 

11,9 

.0654 

1,4 

.727 

.72297 

290 

.90079 

272 

.93870 

11,9 

.0653 

1,3 

.728 

.72587 

290 

.90351 

273 

.93882 

11,9 

.0652 

1,3 

.729 

.72878 

291 

.90624 

273 

.93894 

11,8 

.0650 

1,3 

1.730 

2.73168 

291 

2.90897 

273 

0.93906 

11,8 

1.0649 

1,3 

.731 

.73460 

291 

.91170 

273 

.93917 

11,8 

.0648 

1,3 

•  732 

•73751 

291 

.91444 

274 

.93929 

11,8 

.0646 

1,3 

•  733 

.74042 

292 

.91718 

274 

.93941 

11,8 

.0645 

1,3 

•  734 

•74334 

292 

.91992 

274 

•93953 

n,7 

.0644 

1,3 

1-735 

2.74626 

292 

2.92266 

275 

0.93964 

n,7 

1.0642 

1,3 

.736 

.74919 

293 

.92541 

275 

.93976 

n,7 

.0641 

1,3 

•  737 

.75211 

293 

.92816 

275 

.93988 

n,7 

.0640 

1,3 

.738 

•  75504 

293 

.93092 

276 

•93999 

11,6 

.0638 

,3 

•  739 

.75708 

293 

.93367 

276 

.94011 

n,6 

.0637 

,3 

1.740 

2.7^091 

294 

2.93643 

276 

0.94023 

11,6 

1.0636 

,3 

.741 

.76385 

294 

.93919 

276 

.94034 

11,6 

•0634 

,3 

•  742 

.76679 

294 

.94196 

277 

.94046 

11,6 

.0633 

,3 

.743 

•76973 

294 

•94473 

277 

•94057 

n,5 

.0632 

,3 

•  744 

.77268 

295 

•94750 

277 

.94069 

ii,5 

.0631 

,3 

1.745 

2.77563 

295 

2.95027 

278 

0.94080 

n,5 

1.0629 

,3 

.746 

295 

.95305 

278 

.94092 

n,5 

.0628 

,3 

•  747 

'78153 

296 

.95583 

278 

.94103 

11,4 

.0627 

,3 

.748 

.78449 

396 

.95861 

278 

.94H5 

TI.4 

.0625 

,3 

•  749 

.78745 

296 

.96140 

279 

.94126 

11,4 

.0624 

,3 

1-750 

2.79041 

296 

2.96419 

279 

0.94138 

11,4 

1.0623 

1,3 

u 

tan  od  u 

«F0' 

tec  gd  u 

-FO' 

tin  od  u 

«r; 

csc  od  u 

«F,/ 

SMITHSONIAN  TABLES 


I40 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«F0' 

tanhu 

«F0' 

cothu 

«F0' 

1.750 

2.79041 

296 

2.96419 

279 

0.94138 

11,4 

1.0623 

1,3 

.751 

.79338 

297 

.96698 

279 

.94149 

11,4 

.0621 

1.3 

.752 

.79635 

297 

.96978 

280 

.94160 

ii,3 

.0620 

1,3 

•  753 

.79932 

297 

.97257 

280 

.94172 

n,3 

.0619 

1,3 

•  754 

.80229 

298 

•97537 

280 

.94183 

ii,3 

.0618 

1,3 

1.755 

'2.80527 

298 

2.97818 

281 

0.94194 

n,3 

I.  0616 

1,3 

.756 

.80825 

298 

.98098 

281 

.94205 

ii,3 

.0615 

1,3 

•  757 

.81123 

298 

.98379 

281 

.94217 

11,2 

.0614 

1,3 

•  758 

.81422 

299 

.98661 

281 

.94228 

11,2 

.0613 

1,3 

.759 

.81721 

299 

.98942 

282 

•94239 

11,2 

.0611 

1,3 

1.760 

2.82020 

299 

2.99224 

282 

0.94250 

11,2 

I.  0610 

1,3 

.761 

.82319 

300 

.99506 

282 

.94261 

1  1,1 

.0669 

1,3 

.762 

.82619 

300 

.99789 

283 

.94273 

11,1 

.0608 

1,3 

.763 

.82919 

300 

3.00072 

283 

.94284 

11,1 

.0606 

1,2 

.764 

.83219 

300 

.00355 

283 

.94295 

11,1 

.0605 

1,2 

1.765 
.766 

2.83519 
.83820 

301 
301 

3.00638 
.00922 

284 
284 

0.94306 

.94317 

11,1 

II,O 

1.0604 
.0603 

1,2 
1,2 

.767 

.84121 

301 

.01206 

284 

.94328 

11,0 

.0601 

1,2 

.768 

.84422 

301 

.01490 

284 

•94339 

11,0 

.0600 

1,2 

.769 

.84724 

302 

.01774 

285 

•94350 

11,0 

.0599 

1,2 

1.770 

2.85026 

302 

3.02059 

285 

0.94361 

11,0 

1.0598 

1,2 

•  771 

.85328 

302 

.02344 

285 

.94372 

10,9 

.0596 

1,2 

•  772 

.85631 

303 

.02630 

286 

.94383 

10,9 

.0595 

1,2 

•  773 

.85933 

303 

.02916 

286 

.94394 

10,9 

.0594 

1,2 

•  774 

.86237 

303 

.03202 

286 

.94405 

10,9 

.0593 

1,2 

1.775 

2.86540 

303 

3.03488 

287 

0.04416 

10,9 

1.0591 

1,2 

.776 

.86844 

304 

.03775 

287 

.94426 

10,8 

.0590 

1,2 

•  777 

.87147 

304 

.04062 

287 

•94437 

10,8 

.0589 

1,2 

.778 

.87452 

304 

.04349 

287 

.94448 

10,8 

.0588 

1,2 

.779 

.87756 

305 

.04637 

288 

.94459 

10,8 

.0587 

1,2 

1.780 

2.88o6l 

305 

3.04925 

288 

0.04470 

10,8 

1.0585 

1,2 

.781 

.88366 

305 

.05213 

288 

.94480 

10,7 

.0584 

1,2 

.782 

.88671 

306 

.05501 

289 

.94491 

10,7 

.0583 

1,2 

.783 

.88977 

306 

.05790 

289 

.94502 

10,7 

.0582 

1,2 

.784 

.89283 

306 

.06079 

289 

.94513 

10,7 

.0581 

1,2 

1.785 

2.89589 

306 

3-06369 

290 

0.94523 

10,7 

1.0579 

1,2 

.786 

.89896 

307 

.06659 

290 

•94534 

10,6 

.0578 

1,2 

.787 

.90202 

307 

.06949 

290 

.94544 

10,6 

.0577 

1,2 

.788 

.90510 

307 

.07239 

291 

.94555 

10,6 

.0576 

1,2 

.789 

.90817 

308 

.07530 

291 

.94565 

10,6 

•0575 

1,2 

1.790 

2.91125 

308 

3.07821 

291 

0.94576 

10,6 

1.0574 

1,2 

•  791 

.91433 

308 

.08112 

291 

.94587 

10,5 

.0572 

1,2 

.792 

.91741 

308 

.08403 

292 

•94597 

io,5 

.0571 

1,2 

•793 

.92049 

309 

.08695 

292 

.94608 

io,5 

.0570 

1,2 

.794 

.92358 

309 

.08988 

292 

.94618 

io,5 

.0569 

1,2 

1.795 

2.92667 

309 

3.09280 

293 

0.94629 

10,5 

1.0568 

1,2 

.796 

.92977 

310 

.09573 

293 

.94639 

10,4 

.0566 

1,2 

•  797 

.93287 

310 

.09866 

293 

.94649 

10,4 

.0565 

1,2 

.798 

•93597 

3io 

.10160 

294 

.94660 

10,4 

.0564 

1,2 

•  799 

.93907 

3io 

.10453 

294 

.94670 

10,4 

.0563 

1,2 

1.800 

2.94217 

3ii 

3.10747 

294 

0.94681 

10,4 

1.0562 

1,2 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«F0' 

sin  gd  u 

<oF0' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


141 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanh  u 

«Fr 

coth  u 

»F0' 

1.800 

2.94217 

311 

3-10747 

294 

0.94681 

10,4 

I.O5O2 

1,2 

.801 

.94528 

311 

.11042 

295 

.94691 

10,3 

.0561 

1,2 

.802 

.94840 

311 

.11336 

295 

.94701 

10,3 

.0560 

1,2 

.803 

.95151 

312 

.11631 

295 

.94712 

10,3 

.0558 

1*1 

.804 

.95463 

312 

.11927 

295 

.94722 

10,3 

.0557 

1,1 

1.805 

2.95775 

312 

3.12222 

296 

0.94732 

10,3 

1.0556 

1,1 

.806 

.96087 

313 

.12518 

296 

.94742 

10,2 

.0555 

1,1 

.807 

.96400 

313 

.  12814 

296 

.94753 

10,2 

.0554 

1,1 

.808 

.96713 

313 

.13111 

297 

.94763 

10,2 

.0553 

1,1 

.809 

.97026 

313 

.13408 

297 

•94773 

10,2 

.0552 

1,1 

1.810 

2.97340 

314 

3.13705 

297 

0.94783 

10,2 

1.0550 

1,1 

.811 

.97654 

314 

.14003 

298 

•94793 

10,1 

.0549 

1,1 

.812 

.97968 

314 

.14300 

298 

.94803 

10,1 

.0548 

1,1 

.813 

.98282 

315 

.14599 

298 

.94814 

10,1 

•0547 

1,1 

.814 

.98597 

315 

.14897 

299 

.94824 

10,1 

.0546 

1,1 

1.815 

2.98912 

315 

3.I5I96 

299 

0.94834 

10,1 

1.0545 

1,1 

.816 

.99227 

315 

.15495 

299 

.94844 

IO,O 

.0544 

1,1 

.817 

•99543 

316 

.  15794 

300 

.94854 

IO,O 

•0543 

1,1 

.818 

•99859 

316 

.16094 

300 

.94864 

IO,O 

.0541 

1,1 

.819 

3.00175 

316 

.  16394 

300 

.94874 

10,0 

.0540 

1,1 

1.820 

3-00492 

317 

3.16694 

300 

0.94884 

10,0 

1.0539 

1,1 

.821 

.00808 

317 

.16995 

301 

.94894 

IO,0 

.0538 

1,1 

.822 

.01126 

317 

.17296 

301 

.94904 

9,9 

.0537 

1,1 

.823 

.01443 

318 

.  17597 

301 

.94914 

9,9 

.0536 

1,1 

.824 

.01761 

318 

.17899 

302 

.94924 

9,9 

.0535 

1,1 

1.825 

3.02079 

318 

3.18201 

302 

0.94933 

9,9 

1.0534 

1,1 

.826 

.02397 

319 

.  18503 

302 

•94943 

9,9 

.0533 

1,1 

.827 

.02716 

319 

.18805 

303 

•94953 

9,8 

.0532 

1,1 

.828 

.03035 

319 

.19108 

303 

.94963 

9,8 

•0530 

1,1 

.829 

•03354 

319 

.19411 

303 

.94973 

9,8 

.0529 

1,1 

1.830 

3-03674 

320 

3.I97I5 

304 

0.94983 

9,8 

1.0528 

1,1 

.831 

.03994 

320 

.20019 

304 

.94092 

9,8 

.0527 

1,1 

.832 

.04314 

320 

.20323 

304 

.95002 

9,7 

.0526 

1,1 

.833 

.04634 

321 

.20627 

305 

•95012 

9,7 

.0525 

1,1 

.834 

.04955 

321 

.20932 

305 

.95022 

9,7 

.0524 

1,1 

1.835 

3.05276 

321 

3-21237 

305 

0.95031 

9,7 

1.0523 

1,1 

.836 

.05597 

322 

306 

.95041 

9,7 

.0522 

1,1 

.837 

.05919 

322 

.21849 

306 

.95051 

9,7 

.0521 

1,1 

.838 

.06241 

322 

.22155 

306 

.95060 

9,6 

.0520 

1,1 

.839 

.06563 

322 

.22461 

307 

.95070 

9,6 

.0519 

1,1 

1.840 

3.06886 

323 

3.22768 

307 

0.95080 

9,6 

1.0518 

1,1 

.841 

.07209 

323 

.23075 

307 

.95089 

9,6 

.0516 

1,1 

.842 

.07532 

323 

.23382 

308 

.95009 

9,6 

•  0515 

1,1 

.843 

.07856 

324 

.23600 

308 

.95108 

9,5 

.0514 

1,1 

.844 

.08180 

324 

.23998 

308 

.95n8 

9,5 

.0513 

1,1 

1.845 

3.08504 

324 

3.24306 

309 

0.95127 

9,5 

1.0512 

1,1 

.  .846 

.08828 

325 

.24615 

309 

.95137 

9,5 

.0511 

I,O 

.847 

.09153 

325 

.24924 

309 

.95146 

9,5 

.0510 

1,0 

.848 

.09478 

325 

.25233 

309 

.95156 

9,5 

.0500 

1,0 

.849 

.09803 

326 

.25543 

310 

.95165 

9,4 

.0508 

I,O 

1.850 

3.10129 

326 

3.25853 

310 

0.95175 

94 

1.0507 

I,O 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«F0' 

sin  gd  u 

«F0' 

esc  gd  u 

»FY 

SMITHSONIAN  TABLES 


142 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

O.FO' 

cosh  u 

»Fo' 

tanhu 

»Fo* 

coth  u 

<«>  FO' 

1.850 

3.IOI29 

326 

3.25853 

310 

0.95175 

9,4 

1.0507 

1,0 

.851 

.  10455 

326 

.26163 

310 

.95184 

9,4 

.0506 

1,0 

.852 

.10781 

326 

.26474 

311 

.95193 

9,4 

.0505 

1,0 

.853 

.11108 

327 

.26785 

311 

.95203 

9,4 

.0504 

1,0 

.854 

.11435 

327 

.27096 

311 

.95212 

9,3 

.0503 

1,0 

1.855 

3.11762 

327 

3.27408 

312 

0.95221 

9,3 

1.0502 

1,0 

.856 

.12090 

328 

.27719 

312 

.95231 

9,3 

.0501 

1,0 

.857 

.12418 

328 

.28032 

312 

.95240 

9,3 

.0500 

1,0 

.858 

.  12746 

328 

.28344 

313 

.95249 

9,3 

.0409 

I,O 

.859 

.  13074 

329 

.28657 

313 

.95259 

9,3 

.0498 

1,0 

1.860 

3.13403 

329 

3.28970 

313 

0.95268 

9,2 

1.0497 

1,0 

.861 

•  13732 

329 

.29284 

314 

•95277 

9,2 

.0496 

I,O 

.862 

.14062 

330 

.29598 

314 

.95286 

9,2 

.0495 

1,0 

.863 

.  14392 

330 

.29912 

314 

.95296 

9,2 

•  0494 

1,0 

.864 

.14722 

330 

.30227 

315 

.95305 

9,2 

.0493 

1,0 

1.865 

3.15052 

331 

3.30542 

315 

0.95314 

9,2 

1.0492 

1,0 

.866 

.15383 

331 

.30857 

315 

•95323 

9,1 

.0491 

,0 

.867 

.15714 

331 

.3H72 

316 

•95332 

9,1 

.0490 

,o 

.868 

.16045 

331 

.31488 

316 

•95341 

9,1 

.0489 

,o 

.869 

.16377 

332 

.31804 

316 

•95350 

9,1 

.0488 

1,0 

1.870 

3.16709 

332 

3.32I2I 

317 

0.95359 

9,1 

1.0487 

1,0 

.871 

.  17041 

332 

.32438 

317 

.95368 

9,0 

.0486 

,0 

.872 

.  17374 

333 

.32755 

317 

.95378 

9,o 

.0485 

1,0 

.873 

.17706 

333 

.33073 

318 

.95387 

9,0 

.0484 

1,0 

.874 

.18040 

333 

.33390 

318 

.95396 

9,0 

.0483 

1,0 

1.875 

3.18373 

344 

3.33709 

318 

0.95405 

9,0 

1.0482 

1,0 

.876 

.  18707 

334 

.34027 

319 

.95414 

9,o 

.0481 

1,0 

.877 

.19041 

334 

.34346 

319 

•95422 

8,9 

.0480 

I,O 

.878 

.  19376 

335 

.34665 

319 

•95431 

8,9 

.0479 

I,O 

•879 

.19711 

335 

.34985 

320 

•95440 

8,9 

.0478 

1,0 

i.  880 

3.20046 

335 

3.35305 

320 

0.95449 

8,9 

1.0477 

,o 

.881 

.20381 

336 

.35625 

320 

.95458 

8,9 

.0476 

,o 

.882 

.20717 

336 

.35946 

321 

.95467 

8,9 

.0475 

1,0 

.883 

.21053 

336 

.36266 

321 

.95476 

8,8 

.0474 

,o 

.884 

.21390 

337 

.36588 

321 

.95485 

8,8 

.0473 

I,O 

1.885 

3.21726 

337 

3.36909 

322 

0.95493 

8,8 

1.0472 

1,0 

.886 

.22063 

337 

.37231 

322 

.95502 

8,8 

.0471 

1,0 

.887 

.22401 

338 

•37553 

322 

•955II 

8,8 

.0470 

1,0 

.888 

.22738 

338 

.37876 

323 

•95520 

8,8 

.0469 

I,O 

.889 

.23076 

338 

.38199 

323 

.95529 

8,7 

.0468 

1,0 

1.890 

3.234IS 

339 

3.38522 

323 

0.95537 

8,7 

1.0467 

1,0 

.891 

.23753 

339 

.38846 

324 

.95546 

8,7 

.0466 

1,0 

.892 

.24093 

339 

.39170 

324 

•95555 

8,7 

.0465 

1,0 

.893 

•24432 

339 

•39494 

324 

.95563 

8,7 

.0464 

1,0 

.894 

.24772 

340 

.39818 

325 

•95572 

8,7 

.0463 

0,9 

1.895 

3.25112 

340 

3.40143 

325 

o.9558i 

8,6 

1.0462 

0,9 

.896 

.25452 

340 

.40469 

325 

.95589 

8,6 

.0461 

0,9 

.897 

.25792 

341 

.40794 

326 

.95598 

8,6 

.0460 

0,9 

.898 

.26133 

341 

.41120 

326 

.95607 

8,6 

.0460 

0,9 

.899 

.26475 

341 

.41447 

326 

.95615 

8,6 

.0459 

0,9 

1.900 

3.26816 

342 

3.41773 

327 

0.95624 

8,6 

1.0458 

0,9 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«F«/ 

sin  gd  u 

«F0' 

esc  gd  u 

•  FO' 

SMITHSONIAN  TABLES 


143 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

wF0' 

cosh  u 

«FO' 

tanh  u 

«FO' 

cothu 

»F,' 

1.900 

3.26816 

342 

3.41773 

327 

0.95624 

8,6 

1.0458 

0,9 

.001 

.27158 

342 

.42100 

327 

.95632 

8,5 

•  0457 

0,9 

.902 

.27500 

342 

.42427 

328 

.95641 

8,5 

.0456 

0,9 

.903 

.27843 

343 

.42755 

328 

.95649 

8,5 

.0455 

0,9 

.904 

.28186 

343 

.43083 

328 

.95658 

8,5 

.0454 

0,9 

1.905 

3.28529 

343 

3.43412 

329 

0.95666 

8,5 

1.0453 

0,9 

.906 

.28873 

344 

•43740 

329 

.95675 

8,5 

•  0452 

0,9 

.907 

.29217 

344 

.44069 

329 

.95683 

8,4 

.0451 

0,9 

.908 

.29561 

344 

.44399 

330 

.95692 

8,4 

.0450 

o,9 

.909 

.29906 

345 

.44728 

330 

•95700 

8,4 

.0449 

0,9 

1.910 

3.30250 

345 

3.45058 

330 

0.95709 

8,4 

i  .0448 

o,9 

.911 

.30596 

345 

331 

.95717 

8,4 

.0447 

0,9 

.912 

.30941 

346 

.45720 

331 

.95725 

8,4 

•0447 

o,9 

.913 

.31287 

346 

.46051 

331 

.95734 

8,4 

.0446 

0,9 

.914 

.31633 

346 

.46382 

332 

.95742 

8,3 

•  0445 

0,9 

1.915 

3-31980 

347 

3.46714 

332 

0.95750 

8,3 

1.0444 

0,9 

.916 

.32327 

347 

•47046 

332 

•95759 

8,3 

.0443 

0,9 

.917 

.32674 

347 

•47379 

333 

.95767 

8,3 

.0442 

0,9 

.918 

.33021 

348 

.47712 

333 

•95775 

8,3 

.0441 

0,9 

.919 

.33369 

348 

•48045 

333 

.95783 

8,3 

.0440 

0,9 

1.920 

3.33718 

348 

3.48378 

334 

0.95792 

8,2 

'1.0439 

0,9 

.921 

.34066 

349 

.48712 

334 

.95800 

8,2 

.0438 

0,9 

.922 

•34415 

349 

.40046 

334 

.95808 

8,2 

.0438 

0,9 

.923 

.34764 

349 

.49381 

335 

.95816 

8,2 

.0437 

0,9 

.924 

.35H4 

350 

.49716 

335 

.95825 

8,2 

.0436 

0,9 

1.925 

3.35464 

350 

3.50051 

335 

0.95833 

8,2 

1.0435 

0,9 

.926 

.35814 

350 

•50387 

336 

.95841 

8,1 

.0434 

0,9 

.927 

.36164 

351 

.50723 

336 

.95849 

8,1 

.0433 

0,9 

.928 

.36515 

351 

.51059 

337 

.95857 

8,1 

.0432 

0,9 

.929 

.36867 

351 

.51396 

337 

.95865 

8,1 

.0431 

0,9 

1.930 

3.37218 

352 

3.51733 

337 

0.95873 

8,1 

1.0430 

0,9 

.931 

.37570 

352 

.52070 

.95881 

8,1 

.0430 

0,9 

.932 

.37922 

352 

.52408 

338 

.95890 

8,1 

.0429 

0,9 

•933 

.38275 

353 

.52746 

338 

.95898 

8,0 

.0428 

0,9 

•934 

.38628 

353 

.53085 

339 

.95906 

8,0 

.0427 

0,9 

1-935 

3.38981 

353 

3.53423 

339 

0.959U 

8,0 

1.0426 

0,9 

.936 

•39335 

354 

.53763 

339 

.95922 

8,0 

•  0425 

0,9 

•937 

.39689 

354 

.54102 

.340 

•95930 

8,0 

.0424 

0,9 

.938 

.40043 

354 

.54442 

340 

.95938 

8,0 

•0423 

0,9 

•939 

.40397 

355 

.54782 

340 

•95945 

7,9 

•0423 

0,9 

1.940 

3.40752 

355 

3.55123 

341 

•  0.95953 

7,9 

1.0422 

o,9 

.941 

.41108 

355 

.55464 

341 

.95961 

7,9 

.0421 

0,9 

•942 

.41463 

356 

.55805 

341 

.95969 

7,9 

.0420 

0,9 

•943 

.41819 

356 

.56147 

342 

•95977 

7,9 

.0419 

0,9 

.944 

.42176 

356 

.56489 

342 

.95985 

7,9 

.0418 

o,9 

1.945 

3.42532 

357 

3.56831 

343 

0.95993 

7,9 

1.0417 

0,9 

.946 

.947 

.42889 
.43247 

a 

.57174 
.57517 

343 
343 

.96001 
.96009 

7,8 
7,8 

.0417 
.0416 

0,9 
0,9 

.948 

.43604 

358 

.57860 

344 

.96016 

7,8 

.0415 

0,9 

.949 

.43962 

358 

.58204 

344 

.96024 

7,8 

.0414 

0,9 

1.950 

3.44321 

359 

3.58548 

344 

0.96032 

7,8 

1.0413 

0,8 

u 

tan  gd  u 

»Fo' 

sec  gd  u 

•  FO' 

sin  gd  u 

•  Fo' 

esc  gd  u 

•  FO' 

SMITHSONIAN  TABLC« 


144 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

»Fc' 

cosh  u 

•  FO' 

tanhu 

«F0' 

cothu 

-IV 

1.950 

3.44321 

359 

3.58548 

344 

0.96032 

7,8 

1.0413 

0,8 

.951 

.44679 

359 

.58893 

345 

.96040 

7,8 

.0412 

.952 

.45038 

359 

.59237 

345 

.96047 

7,7 

.0412 

•953 

.45398 

360 

.59583 

345 

.96055 

7,7 

.0411 

•  954 

.45758 

360 

.59928 

346 

.96063 

7,7 

.0410 

1-955 

3.46118 

360 

3.60274 

346 

0.96071 

7,7 

1.0409 

0,8 

.956 

.46478 

361 

.60620 

346 

.96078 

7,7 

.0408 

•957 

.46839 

261 

.60967 

347 

.96086 

7,7 

.0407 

•958 

.47200 

361 

.61314 

347 

.96094 

7,7 

.0407 

•959 

.47562 

362 

.61662 

348 

.96101 

7,6 

.0406 

1.960 

3.47923 

362 

3.62009 

348 

0.96109 

7,6 

1.0405 

0,8 

.961 

.48286 

362 

.62357 

348 

.96117 

7,6 

.0404 

.962 

.48648 

363 

.62706 

349 

.96124 

7,6 

.0403 

.963 

.49011 

363 

.63055 

349 

.96132 

7,6 

.0402 

.964 

.49374 

363 

.63404 

349 

.96139 

7,6 

.0402 

1.965 

3.49738 

364 

3.63753 

350 

0.96147 

7,6 

1.0401 

0,8 

.966 

.50102 

364 

.64103 

350 

.96155 

7,5 

.0400 

.967 

.50466 

364 

.64454 

350 

.96162 

7,5 

.0399 

.968 

.50831 

365 

.64804 

351 

.96170 

7,5 

.0398 

.969 

.51196 

365 

.65155 

35i 

.96177 

7,5 

.0397 

1.970 

3.5I56I 

366 

3.65507 

352 

0.96185 

7,5 

1.0397 

0,8- 

.971 

.51927 

366 

.65858 

352 

.96192 

7,5 

.0306 

•  972 

.52293 

366 

.66211 

352 

.96199 

7,5 

-0395 

.973 

.52659 

367 

.66563 

353 

.96207 

7,4 

.0394 

.974 

.53026 

367 

'.66916 

353 

.96214 

7,4 

.0393 

1-975 

3-53393 

367 

3.67269 

353 

0.96222 

7,4 

1.0393 

0,8 

.976 

.53760 

368 

.67623 

354 

.96229 

7,4 

.0392 

•977 

.54128 

368 

.67977 

354 

.96237 

7,4 

.0391 

.978 

.54496 

368 

.68331 

354 

.96244 

7,4 

.0390 

.979 

•54855 

369 

.68686 

355 

.9^251 

7,4 

.0389 

1.980 

3.55234- 

369 

3.69041 

355 

0.96259 

7,3 

1.0389 

0,8 

.981 

.55603 

369 

.69396 

356 

.962^66 

7,3 

.0388 

.982 

•55972 

370 

.69752 

356 

.96273 

7,3 

.0387 

.983 

.56342 

370 

.70108 

356 

.96281 

7,3 

.0386 

.984 

.56713 

370 

.70465 

357 

.96288 

7,3 

.0386 

1.985 

3.57083 

37i 

3.70821 

357 

0.96295 

7,3 

1.0385 

0,8 

.986 

.57454 

37i 

.71179 

357 

.06302 

7,3 

.0384 

.987 

.57826 

372 

.71536 

358 

.96310 

7,2 

.0383 

.988 

.58197 

372 

.71894 

358 

.96317 

7,2 

.0382 

.989 

.58569 

372 

•72253 

359 

.96324 

7,2 

.0382 

1.990 

3.58042 

373 

3.72611 

359 

0.96331 

7,2 

1.0381 

0,8 

.991 

•59315 

373 

.72971 

359 

.96339 

7,2 

.0380 

.992 

.59588 

373 

.73330 

360 

.96346 

7,2 

.0379 

•993 

.60061 

374 

.73690 

360 

.96353 

7,2 

.0379 

.994 

•60435 

374 

.74050 

360 

.96360 

7,1 

.0378 

1.995 

3.60809 

374 

3-744II 

361 

0.96367 

7,1 

1.0377 

0,8 

.996 

.61184 

375 

•74772 

361 

.96374 

7,i 

.0376 

•  997 

.61559 

375 

.75133 

362 

.96382 

7,i 

.0375 

.998 

.61934 

375 

•75495 

362 

.96389 

7,i 

.0375 

•999 

.62310 

376 

.75857 

362 

.96396 

7,i 

.0374 

2.OOO 

3.62686 

376 

3.76220 

363 

0.96403 

7,i 

1.0373 

0,8 

U 

tan  gd  u 

•  Fo' 

sec  gd  u 

«  F0' 

sin  gd  u 

•  Fo' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


145 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

-FO' 

tanh  u 

»Fo 

coth  u 

«F«' 

2.0OO 

3.62686 

376 

3  .  76220 

363 

0.96403 

7,i 

1-0373 

r   0,8 

.OOI 

.63062 

377 

.76582 

363 

.96410 

7ti 

.0372 

.002 

.63439 

377 

.76940 

363 

.96417 

7,o 

.0372 

.003 

.63816 

.77309 

364 

.96424 

7,o 

.0371 

.004 

.64194 

378 

.77673 

364 

.96431 

7,o 

.0370 

2.005 

3.64572 

378 

3./8038 

365 

0.96438 

7,o 

1.0369 

0,8 

.006 

.64950 

378 

.78402 

365 

.96445 

7,o 

.0369 

0,8 

.007 

.65328 

379 

.78768 

365 

.96452 

7,o 

.0368 

o,7 

.008 

.65707 

379 

.79133 

366 

.96459 

7,o 

.0367 

.009 

.66087 

379 

•79499 

366 

.96466 

6,9 

.0366 

2.0IO 

3.66466 

380 

3.79865 

366 

0.96473 

6,9 

1.0366 

0,7 

.Oil 

.66846 

380 

.80232 

367 

.96480 

6,9 

.0365 

.012 

.67227 

38i 

.80599 

367 

.96487 

6,9 

.0364 

.013 

.67608 

38i 

.80966 

368 

.96493 

6,9 

.0363 

.014 

.67989 

38i 

.81334 

368 

.06500 

6,9 

.0363 

2.015 

3.68370 

382 

3.81702 

368 

0.96507 

6,9 

1.0362 

o,7 

.016 

.68752 

382 

.82071 

369 

.96514 

6,9 

.0361 

.017 

.69134 

382 

.82440 

369 

.96521 

6,8 

.0360 

.018 

.69517 

383 

.82809 

370 

.96528 

6,8 

.0360 

.019 

.69900 

383 

.83179 

370 

.96535 

6,8 

.0359 

2.O2O 

3.70283 

384 

3.83549 

370 

0.96541 

6,8 

1.0358 

o,7 

.021 

.70667 

384 

.83919 

371 

.96548 

6,8 

.0358 

.022 

.71051 

384 

.84290 

371 

.96555 

6,8 

•0357 

.023 

.71436 

385 

.84662 

371 

.96562 

6,8 

.0356 

.024 

.71821 

385 

.85033 

372 

.96568 

6,7 

.0355 

2.025 

3.72206 

385 

3.85405 

372 

0.96575 

6,7 

1.0355 

o,7 

.026 

.72591 

386 

.85778 

373 

.96582 

6,7 

.0354 

.027 

.72977 

386 

.86150 

373 

.96589 

6,7 

.0353 

.028 

.73364 

387 

.86524 

373 

.96595 

6,7 

.0352 

.029 

.73750 

387 

.86897 

374 

.96602 

6,7 

.0352 

2.030 

3.74138 

387 

3.87271 

374 

0.96609 

6,7 

1.0351 

o,7 

.031 

.74525 

388 

.87645 

375 

.96615 

6,7 

•  0350 

.032 

•74913 

388 

.88020 

375 

.96622 

6,6 

•  0350 

.033 

•75301 

388 

.88395 

375 

.96629 

6,6 

•  0349 

.034 

.75090 

389 

.88771 

376 

.96635 

6,6 

•  0348 

2.035 

3.76079 

389 

3.89147 

376 

0.96642 

6,6 

1-0347 

o,7 

.036 

.76468 

390 

.89523 

376 

.96648 

6,6 

•  0347 

•  037 

.76858 

390 

.89900 

377 

.96655 

6,6 

•  0346 

.038 

.77248 

390 

.90277 

377 

.96662 

6,6 

•  0345 

•  039 

.77638 

391 

.90654 

378 

.96668 

6,6 

•  0345 

2.040 

3.78029 

391 

3.91032 

378 

0.96675 

6,5 

1-0344 

o,7 

.041 

.78420 

391 

.91410 

378 

.96681 

6,5 

.0343 

.042 

.78812 

392 

.91789 

379 

.96688 

6,5 

•  0343 

•  043 

.79204 

392 

.92168 

379 

.96694 

6,5 

.034-' 

•044 

.79596 

393 

.92547 

380 

.96701 

6,5 

.0341 

2.045 

3.79989 

393 

3.92927 

380 

0.96707 

6,5 

1.0340 

o,7 

.046 

.80382 

393 

.93307 

380 

.96714 

6,5 

•  0340 

.047 

.80776 

394 

.93688 

38r 

.96720 

6,5 

•  0339 

.048 

.81169 

394 

.94069 

38i 

.96727 

6,4 

.0338 

.049 

.81564 

394 

.94450 

382 

.06733 

6,4 

.0338 

2.050 

3.81958 

395 

3-94832 

382 

0.96740 

6,4 

1.0337 

o,7 

u 

tan  gd  u 

«F0' 

sec  gd  u 

«FO' 

tin  gd  u 

•  Fo* 

esc  gd  u 

»FV 

SMITHSONIAN  TABLES 


146 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«Fo' 

cosh  u 

<-FO' 

tanh  u 

«F0' 

coth  u 

«F0' 

2.050 

3.81958 

395 

3.94832 

382 

0.96740 

6,4 

1.0337 

o,7 

.051 

.82353 

395 

.95214 

382 

.96746 

6,4 

.0336 

.052 

.82749 

396 

•95597 

383 

.96752 

6,4 

.0336 

/  -053 

.83145 

396 

•95979 

383 

.96759 

6,4 

.0335 

•  054 

.83541 

396 

.96363 

384 

.96765 

6,4 

•0334 

2.055 

3.83937 

397 

3.96747 

384 

0.96771 

.6,4 

1.0334 

o,7 

.056 

.84334 

397 

.97131 

3«4 

.96778 

6,3 

•0333 

.057 

.84732 

398 

•97515 

385 

.96784 

6,3 

.0332 

.058 

.85129 

398 

.97900 

385 

.96790 

6,3 

.0332 

•  059 

.85527 

398 

.98285 

386 

.96797 

6,3 

.0331 

2.060 

3.85926 

399 

3.98671 

386 

0.96803 

6,3 

1.0330 

o,7 

.061 

.86325 

399 

.99057 

386 

.96809 

6,3 

.0330 

.062 

.86724 

399 

•99444 

387 

.96816 

6,3 

.0329 

.063 

.87124 

400 

.99831 

387 

.96822 

6,3 

.0328 

.064 

.87524 

400 

4.00218 

388 

.96828 

6,2 

.0328 

2.065 

3.87924 

401 

4.00606 

388 

0.06834 

6,2 

1.0327 

o,7 

.066 

.88325 

401 

.00994 

388 

.96841 

6,2 

.0326 

.067 

.88726 

401 

.01382 

389 

.96847 

6,2 

.0326 

.068 

.89128 

402 

.01771 

389 

.96853 

6,2 

.0325 

.069 

.89530 

402 

.02161 

390 

.96859 

6,2 

.0324 

2.070 

3.89932 

403 

4.02550 

390 

0.96865 

6,2. 

1.0324 

o,7 

.071 

.90335 

403 

.02941 

390 

.96872 

6,2 

.0323 

.072 

.90738 

403 

.03331 

391 

.96878 

6,1 

.0322 

.073 

.91141 

404 

.03722 

391 

.96884 

6,1 

.0322 

.074 

.91545 

404 

.04113 

392 

.96890 

6,1 

.0321 

2.075 

3.91950 

405 

4.04505 

392 

0.96896 

6,1 

1.0320 

o,7 

.076 

.92354 

405 

.04897 

392 

.96902 

6,1 

.0320 

0,6 

.077 

.92759 

405 

.05290 

393 

.96908 

6,1 

.0319 

.078 

.93165 

406 

.05683 

393 

.06914 

6,1 

.0318 

.079 

•93571 

406 

.06076 

394 

.96920 

6,1 

.0318 

2.080 

3-93977 

406 

4.06470 

394 

0.06926 

'   6,1 

1.0317 

0,6 

.081 

.94384 

407 

.06864 

394 

.96933 

6,0 

.0316 

.082 

.94791 

407 

.07259 

395 

.96939 

6,0 

.0316 

.083 

.95198 

408 

.07654 

395 

.96945 

6,0 

.0315 

.084 

.95606 

408 

.08049 

396 

.96951 

6,0 

.0315 

2.085 

3.96014 

408 

4.08445 

396 

0.96957 

6,0 

1.0314 

0,6 

.086 

.96423 

409 

.08841 

396 

.96963 

6,0 

.0313 

.087 

.96832 

409 

.09238 

397 

.96969 

6,0 

.0313 

.088 

.97241 

410 

.00635 

397 

.96975 

6,0 

.0312 

.089 

.97651 

410 

.10032 

398 

.96980 

5,9 

.0311 

2.000 

3.08061 

410 

4-10430 

398 

0.96986 

5,9 

1.0311 

0,6 

.091 

.98472 

411 

.10828 

398 

.95992 

5,9 

.0310 

.092 

.98883 

411 

.11227 

399 

.96998 

5,9 

.0309 

•  093 

.99294 

412 

.11626 

399 

.97004 

5,9 

.0309 

.094 

.99706 

412 

.  12026 

400 

.97010 

5,9 

.0308 

2.095 

4.OOII9 

412 

4.12426 

400 

0.97016 

5,9 

1.0308 

0,6 

.006 

.00531 

413 

.12826 

401 

.97022 

5,9 

.0307 

.097 

.00944 

413 

.13227 

401 

.97028 

5,9 

.0306 

.098 

.01358 

414 

.  13628 

401 

.97034 

5,8 

.0306 

.099 

.01771 

414 

.14029 

402 

.97039 

5,8 

.0305 

2.100 

4.02186 

414 

4.I443I 

402 

0.97045 

5,8 

1.0304 

0,6 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

sin  gd  u 

«F0' 

esc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


147 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«FO' 

tanh  u 

»  Fo' 

coth  u 

~  Fo' 

2.IOO 

4.02186 

414 

4.I443I 

402 

0.97045 

5,8 

1.0304 

0,6 

.IOI 

.02600 

415 

.14834 

403 

.97051 

5,8 

.0304 

.102 

.03015 

415 

.  15237 

403 

.97057 

5,8 

.0303 

.103 

.03431 

416 

.15640 

403 

.97063 

5,8 

•  0303 

.104 

•03847 

416 

.16043 

404 

.97068 

5,8 

.0302 

2.105 

4.04263 

416 

4.16447 

404 

0.97074 

5,8 

I.030I 

0,6 

.106 

.04680 

417 

.16852 

405 

.97080 

5,8 

.0301 

.107 

.05097 

417 

.17257 

405 

.97086 

5,7 

.0300 

.108 

.05514 

4l8 

.17662 

406 

.97091 

5,7 

.0300 

.109 

.05932 

418 

.18068 

406 

.97097 

5,7 

.0299 

2.IIO 

4.06350 

418 

4.  18474 

406 

0.97103 

5,7 

1.0298 

0,6 

.III 

.06769 

419 

.  18881 

407 

.97109 

5,7 

.0298 

.112 

.07188 

419 

.19288 

407 

.97H4 

5,7 

.0297 

•113 

.07607 

420 

.19695 

408 

.97120 

5,7 

.0297 

.114 

.08027 

42O 

.20103 

408 

.97126 

5,7 

.0296 

2.  115 

4.08448 

421 

4.20511 

408 

0.97I3I 

5,7 

1.0295 

0,6 

.116 

.08868 

421 

.20920 

409 

.97137 

5,6 

.0295 

.117 

.09289 

421 

.21329 

409 

.97143 

5,6 

.0294 

.118 

.097H 

422 

.21738 

410 

.97148 

5,6 

.0294 

.119 

.  10133 

422 

.22148 

410 

.97154 

5,6 

.0293 

2.120 

4.I05S5 

423 

4.22558 

411 

0.97159 

5,6 

1.0292 

0,6 

.121 

.10978 

423 

.22969 

411 

.97165 

5,6 

.0292 

.122 

.11401 

423 

.23380 

411 

.97171 

5,6 

.0291 

.123 

.11825 

424 

.23792 

412 

.97176 

5,6 

.0291 

.124 

.  12249 

424 

.24204 

412 

.97182 

5,6 

.0290 

2.I2S 

4.12673 

425 

4.24617 

413 

0.97187 

5,5 

1.0289 

0,6 

.126 

.13098 

425 

.25029 

413 

.97193 

5,5 

.0289 

.127 

.  13523 

425 

.25443 

414 

.97198 

5,5 

.0288 

.128 

•  13949 

426 

.25856 

414 

.97204 

5,5 

.0288 

.129 

.  14375 

426 

.26271 

414 

.97209 

5,5 

.0287 

2.130 

4.14801 

427 

4.26685 

415 

0.97215 

5,5 

1.0286 

0,6 

.131 

.15228 

427 

.27100 

415 

.97220 

5,5 

.0286 

.132 

.15656 

428 

.27516 

416 

.97226 

5,5 

.0285 

.133 

.16083 

428 

.27932 

416 

.97231 

5,5 

.0285 

.134 

.16512 

428 

.28348 

417 

.97237 

5,4 

.0284 

2.135 

4.16940 

429 

4-28765 

417 

0.97242 

5,4 

1.0284 

0,6 

.136 

.17369 

429 

.29182 

417 

.97248 

5,4 

.0283 

.137 

.17798 

430 

.29599 

418 

.97253 

5,4 

.0282 

.138 

.  18228 

430 

.30017 

418 

.97258 

5,4 

.0282 

.139 

.18658 

430 

.30436 

419 

.97264 

5,4 

.0281 

2.140 

4.19089 

431 

4.30855 

419 

0.97269 

5,4 

1.0281 

0,6 

.141 

.19520 

431 

.31274 

420 

.97275 

5,4 

.0280 

.142 

.10952 

432 

.31694- 

420 

.97280 

5,4 

.0280 

.143 

.20384 

432 

.32114 

420 

.97285 

5,4 

.0279 

.144 

.20816 

433 

.32534 

421 

.97291 

5,3 

.0278 

2.145 

4.21249 

433 

4.32955 

421 

0.97296 

5,3 

1.0278 

0,6 

.146 

.21682 

433 

.33377 

422 

.97301 

5,3 

.0277 

.147 

.22115 

434 

•33799 

422 

.97307 

5,3 

.0277 

.148 

.22549 

434 

.34221 

423 

.97312 

5,3 

.0276 

.149 

.22084 

435 

.34644 

423 

.97317 

5,3 

.0276 

2.150 

4.23419 

435 

4.35067 

423 

0.97323 

5,3 

1.0275 

0,6 

u 

tan  od  u 

«Fo' 

sec  od  u 

«Fo' 

sin  gd  u 

»tv 

esc  0d  u 

•»F«' 

SMITHSONIAN  TABLES 


148 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

-Fa' 

cosh  u 

»Fo" 

tanh  u 

«F0 

coin  u 

«Fo' 

2.150 

4.23419 

435 

4.35067 

423 

0.97323 

5,3 

1.0275 

0,6 

.151 

.23854 

435 

•35491 

424 

.97328 

5,3 

.0275 

.152 

.24290 

436 

.35915 

424 

•97333 

5,3 

.0274 

.153 

.24726 

436 

.36339 

425 

.97338 

5,3 

.0273 

•  154 

.25162 

437 

.36764 

425 

•97344 

5,2 

.0273 

2.155 

4.25599 

437 

4.37190 

426 

0.97349 

5,2 

1.0272 

0,6 

.156 

.26037 

438 

.37615 

426 

•97354 

5,2 

.0272 

0,6 

•  157 

.26475 

438 

.38042 

426 

.97359 

5,2 

.0271 

o,5 

.158 

.26913 

438 

.38468 

427 

.97365 

5,2 

.0271 

o,5 

.159 

.27352 

439 

.38896 

427 

•97370 

5,2 

.0270 

o,5 

2.160 

4.27791 

439 

4.39323 

428 

0.97375 

5,2 

I.027O 

o,5 

.161 

.28230 

440 

.39751 

428 

.97380 

5,2 

.0269 

.162 

.28670 

440 

.40180 

429 

•97385 

5,2 

.0268 

.163 

.29111 

441 

.40608 

429 

•97390 

5,2 

.0268 

.164 

-29551 

441 

.41038 

430 

.97396 

5,1 

.0267 

2.165 

4.29993 

441 

4.41468 

430 

0.97401 

5,1 

1.0267 

0,5 

.166 

.30434 

442 

.41898 

430 

.97406 

5,1 

.0266 

.167 

.30876 

442 

.42328 

431 

•974II 

5,1 

.0266 

.168 

.31319 

443 

.42760 

431 

.97416 

5,1 

.0265 

.169 

.31762 

443 

.43191 

432 

.97421 

5,1 

.0265 

2.170 

4.32205 

444 

4.43623 

432 

0.97426 

5,1 

1.0264 

o,S 

.171   .32649 

444 

.44056 

433 

•97431 

5,1 

.0264 

.172 

.33093 

444 

.44488 

433 

•97436 

5,i 

.0263 

.173 

.33538 

445 

.44922 

434 

.97441 

5,i 

.0263 

.174 

.33983 

445 

•45355 

434 

.97446 

5,o 

.0262 

2.175 

4.34429 

446 

4.45790 

434 

0.97452 

5,o 

1.0262 

o,5 

.176 

.34875 

446 

.46224 

435 

•97457 

5,o 

.0261 

.177 

•35321 

447 

.46659 

435 

.97462 

5,o 

.0260 

.178 

.35768 

447 

.47095 

436 

.97467 

5,o 

.0260 

.179 

.36215 

448 

.47531 

436" 

.97472 

5,o 

.0259 

2.180 

4.36663 

448 

4.47967 

437 

0.97477 

5,o 

1.0259 

o,5 

.181 

•37III 

448 

.48404 

437 

.97482 

5,o 

.0258 

.182 

•37560 

449 

.48842 

438 

.97487 

5,o 

.0258 

.183 

.38009 

449 

.49279 

438 

.97491 

5,o 

.0257 

.184 

.38459 

450 

.49718 

438 

.97496 

4,9 

.0257 

2.185 

4.38909 

450 

4.50156 

439 

0.97501 

4,9 

1.0256 

o,5 

.186 

•39359 

451 

.50595 

439 

.97506 

4,9 

.0256 

.187 

.39810 

451 

.51035 

440 

•975II 

4,9 

.0255 

.188 

.40261 

451 

.51475 

440 

.97516 

4,9 

•0255 

.189 

.40713 

452 

.51916 

441 

•97521 

4,9 

.0254 

2.190 

4.4H65 

452 

4.52356 

441 

0.97526 

4,9 

1.0254 

0,5 

.191 

.41617 

453 

.52798 

442 

.97531 

4,9 

•0253 

.192 

.42070 

453 

.53240 

442 

.97536 

4,9 

.0253 

.193 

.42524 

454 

.53682 

443 

•97541 

4,9 

.0252 

.194 

.42978 

454 

.54125 

443 

•97545 

4,8 

.0252 

2.195 

4.43432 

455 

4.54568 

443 

0.97550 

4,8 

1.0251 

0,5 

.196 

.43887 

455 

•55012 

444 

.97555 

4,8 

.0251 

.197 

.44342 

455 

.55456 

444 

.97560 

4,8 

.0250 

.198 

•44798 

456 

•55900 

445 

.97565 

4,8 

.0250 

.199 

.45254 

456 

.56345 

445 

.97570 

4,8 

.0249 

2.200 

4.457H 

457 

4.56791 

446 

0.97574 

4,8 

1.0249 

o,5 

U 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

sin  gd  u 

coFo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


149 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F.' 

cosh  u 

«-F0' 

tanhu 

«Fo' 

coth  u 

-Fo' 

2.2OO 

4-457II 

457 

4.56791 

446 

0.97574 

4,8 

1.0249 

o,5 

.2OI 

.46168 

457 

•57237 

446 

•97579 

4,8 

.0248 

.202 

.46625 

458 

.57683 

447 

.97584 

4,8 

.0248 

.203 

.4/083 

458 

.58130 

447 

.97589 

4,8 

.0247 

.204 

•47541 

459 

.58577 

448 

•97593 

4,8 

.0247 

2.2O5 

4.48000 

459 

4.59025 

448 

0.97598 

4,7 

1.0246 

o,5 

.206 
.207 

.48459 
.48919 

459 
460 

•59473 
•59922 

448 
449 

.97603 
.97608 

4,7 

4,7 

.0246 
.0245 

.208 

•49379 

460 

.60371 

449 

.97612 

4,7 

.0245 

.209 

.49840 

461 

.60821 

450 

.97617 

4,7 

.0244 

2.2IO 

4.50301 

461 

4.61271 

450 

0.97622 

4,7 

1.0244 

o,5 

.211 

.50762 

462 

.61721 

451 

.97626 

4,7 

.0243 

.212 

.51224 

462 

.62172 

451 

•97631 

4,7 

.0243 

.213 

.51687 

463 

.62624 

452 

.97636 

4,7 

.0242 

.214 

•52149 

463 

.63076 

452 

.97640 

4,7 

.0242 

2.2IS 

4.52613 

464 

4-63528 

453 

0.97645 

4,7 

1.0241 

o,5 

.216 

•53077 

464 

.63981 

453 

.97650 

4,6 

.0241 

.217 

•53541 

464 

.64434 

454 

.97654 

4,6 

.0240 

.218 

•54005 

465 

.64888 

454 

.97659 

4,6 

.0240 

.219 

•54471 

465 

.65342 

454 

.97664 

4,6 

.  .0239 

2.22O 

4.54936 

466 

4.65797 

455 

0.97668 

4,6 

1.0239 

0,5 

.221 

•55402 

466 

.66252 

455 

.97673 

4,6 

.0238 

.222 

.55869 

467 

.66708 

456 

.97678 

4,6 

.0238 

.223 

.56336 

467 

.67164 

456 

.97682 

4,6 

.0237 

.224 

.56803 

468 

.67620 

457 

.97687 

4,6 

.0237 

2.225 

4.57271 

468 

4.68078 

457 

0.97691 

4,6 

1.0236 

0,5 

.226 

•57739 

469 

.68535 

458 

.97606 

4,6 

.0236 

.227 

.58208 

469 

.68993 

458 

.97700 

4,5 

•  0235 

.228 

.58677 

469 

.69451 

459 

.97705 

4,5 

.0235 

.229 

.59147 

470 

.69910 

459 

.97709 

4,5 

.0234 

2.230 

4.59617 

470 

4.70370 

460 

0.97714 

4,5 

1.0234 

o,5 

.231 

.60087 

471 

.70830 

460 

.97718 

4,5 

.0233 

.232 

•60559 

471 

.71290 

461 

.97723 

4,5 

.0233 

.233 

.61030 

472 

.71751 

461 

•97727 

4,5 

.0233 

.234 

.61502 

472 

.72212 

462 

•97732 

4,5 

.0232 

2.235 

4.61974 

473 

4.72674 

462 

0.97736 

4,5 

1.0232 

o,5 

.236 

.62447 

473 

.73136 

462 

.97741 

4,5 

.0231 

•  237 

.62921 

474 

•73599 

463 

•97745 

4,5 

.0231 

.238 

.63395 

474 

.74062 

463 

•97750 

4,4 

.0230 

.239 

.63869 

475 

.74525 

464 

•97754 

4,4 

.0230 

2.240 

4-64344 

475 

4.74989 

464 

0-97759 

4,4 

1.0229 

o,5 

.241 

.64819 

475 

.75454 

465 

.97763 

4,4 

.0229 

.242 

.65295 

476 

.75919 

465 

•97768 

4,4 

.0228 

.243 

.65771 

476 

.76385 

466 

•97772 

4,4 

.0228 

.244 

.66247 

477 

.76851 

466 

.97776 

4,4 

.0227 

2.245 

4.66724 

477 

4.77317 

467 

0.97781 

4,4 

1.0227 

o,5 

.246 

.67202 

478 

.77784 

467 

.97785 

4,4 

.0227 

.247 

.67680 

478 

.78252 

468 

•97790 

4,4 

.0226 

.248 

.68158 

479 

.78719 

468 

•97794 

4,4 

.0226 

.249 

.68637 

479 

.79188 

469 

.97798 

4,4 

.0225 

2.250 

4.69117 

480 

4.79657 

469 

0.97803 

4,3 

1.0225 

o,5 

u 

tan  gd  u 

«Fo' 

tec  gd  u 

•  Fo' 

sin  ad  u 

•  Fo' 

esc  ad  u 

«F0' 

SMITHSONIAN  T*ai.r« 


150 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

»F0' 

cosh  u 

«F0' 

tanh  u 

«F0" 

coth  u 

«Fo' 

2.250 

4.69117 

480 

4.79657 

469 

0.97803 

4,3 

I.O225 

o,5 

.251 

•69597 

480 

.80126 

470 

.97807 

4,3 

.O224 

.252 

.70077 

481 

.80596 

470 

.97811 

4,3 

.O224 

.253 

.70558 

48l 

.81066 

471 

.978l6 

4,3 

.O223 

-  .254 

.71039 

482 

.81537 

471 

.97820 

4,3 

.0223 

o,5 

2.255 

4.71521 

482 

4.82008 

472 

0.97824 

4,3 

I.O222 

0,4 

.256 

.72003 

482 

.82480 

472 

.97829 

4,3 

.O222 

.257 

.72486 

483 

.82952 

472 

.97833 

4,3 

.O222 

.258 

.72069 

483 

.83425 

473 

.97837 

4,3 

.O22I 

•  259 

.73453 

484 

.83898 

473 

.97841 

4,3 

.0221 

2.260 

4-73937 

484 

4.84372 

474 

0.97846 

4,3 

I.O22O 

OA 

.261 

.74422 

485 

.84846 

474 

.97850 

4,3 

.O22O 

.262 

.74907 

485 

.85321 

475 

.97854 

4,2 

.O2I9 

.263 

•75392 

486 

.85796 

475 

.97858 

4,2 

.O2I9 

.264 

.75878 

486 

.86272 

476 

.97863 

4,2 

.0218 

2.265 

4.76365 

487 

4.86748 

476 

0.97867 

4,2 

I.  02l8 

0,4 

.266 

.76852 

487 

.87224 

477 

.97871 

4,2 

.0218 

.267 

•77339 

488 

.87701 

477 

.97875 

4,2 

.0217 

.268 

.77827 

488 

.88179 

478 

.97879 

4,2 

.O2I7 

.269 

.78316 

489 

.88657 

478 

.97884 

4,2 

.0216 

2.270 

4.78804 

489 

4.89136 

479 

0.97888 

4,2 

I.  02l6 

0,4 

.271 

.79294 

490 

.89615 

479 

.97892 

4,2 

.O2I5 

.272 

.79784 

490 

.90094 

480 

.97896 

4,2 

.O2I5 

.273 

.80274 

491 

.90574 

480 

.97900 

4,2 

.0214 

•  274 

.80765 

491 

•91055 

481 

.97905 

4,1 

.O2I4 

2.275 

4.81256 

492 

4.91536 

481 

0.97909 

4,1 

I.O2I4 

0,4 

.276 

.81748 

492 

.92017 

482 

.97913 

4,1 

.0213 

.277 

.82240 

492 

.92499 

482 

.97917 

4,1 

.0213 

.278 

.82733 

493 

.92982 

483 

.97921 

4,1 

.O2I2 

.279 

.83226 

493 

.93465 

483 

.97925 

4,1 

.O2I2 

2.280 

4.83720 

494 

4.93948 

484 

0.97929 

4,1 

I.  021  I 

0,4 

.281 

.84214 

494 

.94432 

484 

•97933 

4,1 

.O2II 

.282 

.84709 

495 

.94917 

485 

•97937 

4,1 

.O2I  I 

.283 

.85204 

495 

.95402 

485 

•97942 

4,1 

.O2IO 

.284 

.85699 

496 

.95887 

486 

.97946 

4,1 

.O2IO 

2.285 

4.86196 

496 

4.96373 

486 

0.97950 

4,1 

I.O2O9 

0,4 

.286 

.86692 

497 

.96859 

487 

•97954 

4,1 

.O2O9 

.287 

.87189 

497 

.97346 

487 

.97958 

4,o 

.0208 

.288 

.87687 

498 

.97834 

488 

.97962 

4,0 

.0208 

.289 

.88185 

498 

.98322 

488 

.97966 

4,0 

.0208 

2.290 

4.88684 

499 

4.98810 

489 

0.97970 

4,0 

I.O2O7 

0,4 

.291 

.89183 

499 

.99299 

489 

.97974 

4,0 

.O2O7 

.292 

.89682 

500 

.99789 

490 

.97978 

4,0 

.0206 

•  293 

.90182 

500 

5.00279 

490 

.97982 

40 

.02O6 

.294 

.90683 

501 

.00769 

491 

.97986 

4,0 

.O2O6 

2.295 

4.91184 

5oi 

5.01260 

491 

0.97990 

4,o 

I.O2O5 

0,4 

.296 

.91685 

502 

.01751 

492 

.97994 

4,0 

.O2O5 

.297 

.92187 

502 

.02243 

492 

.97998 

4,0 

.O2O4 

.298 

.92690 

503 

.02736 

493 

.98002 

4,0 

.02O4 

.299 

.93193 

503 

.03229 

493 

.98006 

3,9 

.0203 

2.300 

4.93696 

504 

5.03722 

494 

0.98010 

3,9 

1.0203 

0,4 

u 

tan  gd  u 

«Fo' 

sec  gd  u 

•  Fo' 

sin  gd  u 

«F0' 

csc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

<-FO' 

tanh  u 

•  F«* 

cothu 

«FO' 

2.300 

4.93096 

504 

5.03722 

494 

0.98010 

3,9 

1.0203 

0,4 

.301 

.94200 

504 

.04216 

494 

.98014 

3,9 

.0203 

.302 

•94705 

505 

.04710 

495 

.98018 

3,9 

.0202 

.303 

.95210 

505 

.05205 

495 

.98021 

3,9 

.O2O2 

.304 

.95715 

506 

.05701 

496 

.98025 

3,9 

.O2OI 

2.305 

4.96221 

506 

5.06197 

496 

0.08029 

3,9 

I.  0201 

04 

.306 

.96727 

507 

.06693 

497 

.98033 

3,9 

.02OI 

.307 

•97234 

507 

.07100 

497 

.98037 

3,9 

.O2OO 

.308 

•97742 

508 

.07688 

498 

.98041 

3,9 

.02OO 

.309 

.98250 

508 

.08186 

498 

•98045 

3,9 

.0199 

2.310 

4.98758 

509 

5.08684 

499 

0.98049 

3,9 

I.OI99 

0,4 

.311 

.99267 

509 

.09183 

499 

.98053 

3,9 

.0109 

.312 

.99777 

5io 

.09683 

500 

.08056 

3,8 

.0108 

.313 

5.00286 

5io 

.  10183 

500 

.08060 

3,8 

.0198 

.314 

.00797 

5ii 

.10683 

501 

.98064 

3,8 

.0197 

2.315 

5.01308 

5ii 

5  •  ii  184 

50i 

0.98068 

3,8 

1.  0197 

0,4 

.316 

.01819 

512 

.11686 

502 

.98072 

3,8 

.0197 

.317 

.02331 

512 

.12188 

502 

.98076 

3,8 

.0196 

.318 

.02844 

513 

.12691 

503 

.98079 

3,8 

.0196 

.319 

•03357 

513 

.13194 

503 

.98083 

3,8 

.0195 

2.320 

5.03870 

514 

5.13697 

504 

0.98087 

3,8 

I.  0195 

0,4 

.321 

.04384 

5H 

.  14202 

504 

.98091 

3,8 

.0195 

.322 

.04898 

515 

.14706 

505 

.98095 

3,8 

.0194 

.323 

.05413 

5i5 

.15211 

505 

.98098 

3,8 

.0194 

.324 

.05929 

5i6 

.15717 

506 

.98102 

3,8 

.0193 

2.325 

5-06445 

5i6 

5.16223 

506 

0.98106 

3,8 

1.0193 

0,4 

.326 

.06961 

517 

.  16730 

507 

.98110 

3,7 

.0193 

.327 

.07478 

517 

.  17237 

507 

.08113 

3,7 

.0192 

.328 

.07996 

5i8 

.17745 

508 

.98117 

3,7 

.0192 

.329 

.08514 

5i8 

.18253 

509 

.98121 

3,7 

.0192 

2.330 

5.09032 

519 

5.18762 

509 

0.98124 

3,7 

1.0191 

0,4 

.331 

.09551 

519 

.  19271 

5io 

.98128 

3,7 

.0191 

.332 

.10071 

520 

.19781 

5io 

.98132 

3,7 

.0190 

•333 

.10591 

520 

.20291 

5H 

.98136 

3,7 

.0190 

.334 

.mil 

521 

.20802 

5ii 

•98139 

3,7 

.0190 

2-335 

5-11632 

521 

5.21314 

512 

0.98143 

3,7 

1.0189 

0,4 

.336 

.12154 

522 

.21825 

512 

.98147 

3,7 

.0189 

•  337 

.  12676 

522 

.22338 

5T3 

.98150 

3,7 

.0188 

.338 

.13199 

523 

.22851 

513 

.08154 

3,7 

.0188 

•339 

.  13722 

523 

.23364 

514 

.98158 

3,7 

.0188 

2.340 

5.14245 

524 

5.23878 

514 

0.98161 

3,6 

1.0187 

0,4 

•  341 

.  M770 

524 

.24393 

515 

.98165 

3,6 

.0187 

•  342 

.15294 

525 

.24908 

515 

.98169 

3,6 

.0187 

•  343 

.15819 

525 

.25423 

5i6 

.98172 

3,6 

.0186 

•344 

•  16345 

526 

.25939 

5i6 

.98176 

3,6 

.0186 

2.345 

5.16871 

526 

5.26456 

517 

0.98179 

3,6 

1.0185 

0,4 

.346 

.17398 

527 

.26973 

517 

.98183 

3,6 

.0185 

•  347 

.  17925 

527 

.27491 

5i8 

.98187 

3,6 

.0185 

.348 

.18453 

528 

.28009 

5i8 

.98190 

3,6 

.0184 

•  349 

.18981 

529 

.28528 

519 

•98194 

3,6 

.0184 

2.350 

5.I95IO 

529 

5.20047 

520 

O.o8l97 

3,6 

I.  0184 

0,4 

u 

tan  gd  u 

•Fo' 

sec  od  u 

•  Fo' 

sin  gd  u 

•  Ft* 

esc  ad  u 

•Fo' 

SMITHSONIAN  TABLCS 


152 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«Fu' 

cosh  u 

<-Fo' 

tanhu 

»F0' 

coth  u 

<"  Fo' 

2.350 

5.I95IO 

529 

5.20047 

520 

0.98197 

3,6 

1.0184 

0,4 

.351 

.20039 

530 

.29567 

520 

.98201 

3,6 

.0183 

.352 

.20569 

530 

.30087 

521 

.98204 

3,6 

.0183 

•  353 

.2IIOO 

531 

.30608 

521 

.98208 

3,6 

.0182 

.^54 

.21630 

531 

.3H29 

522 

.98212 

3,5 

.0182 

2.355 

5.22162 

532 

5.3I65I 

522 

0.98215 

3,5 

1.0182 

0,4 

.356 

.22694 

532 

.32174 

523 

.98219 

3,5 

.Oi8l 

.357 

.23226 

533 

.32697 

523 

.08222 

3,5 

.Ol8l 

•  358 

.23759 

533 

•33220 

524 

.98226 

3,5 

.Ol8l 

•  359 

.24293 

534 

•33744 

524 

.98229 

3,5 

.0180 

2.360 

5.24827 

534 

5.34209 

525 

0.98233 

3,5 

1.0180 

0,4 

.361 

.25361 

535 

•34794 

525 

.98236 

3,5 

.0180 

.362 

.25896 

535 

.35319 

526 

.98240 

3,5 

.0179 

.363 

.26432 

536 

.35845 

526 

.98243 

3,5 

.0179 

.364 

.26968 

536 

.36372 

527 

.98247 

3,5 

.0178 

2.365 

5.27504 

537 

5.36899 

528 

0.98250 

3,5 

1.0178 

0,4 

.366 

.28042 

537 

.37427  :  528 

.98254 

3,5 

.0178 

.367 

.28579 

538 

.37955   529 

.98257 

3,5 

.0177 

.368 

.29118 

538 

.38484  1  529 

.98261 

3,4 

.0177 

.369 

.29656 

539 

.39014 

530 

.98264 

3,4 

.0177 

2.370 

5.30196 

540 

5.39544 

530 

0.98267 

3,4 

1.0176 

0,4 

•  371 

•30735 

540 

.40074  !  531 

.98271 

3,4 

.0176 

•  372 

.31276 

541 

.40605   531 

.98274 

3,4 

.0176 

•  373 

.31817 

541 

.4H37  I   532 

.98278 

3,4 

•0175 

•  374 

.32358 

542 

.41669 

532 

.98281 

3,4 

•0175 

2.375 

5.32900 

542 

5.42201 

533 

0.98285 

3,4 

1.0175 

0,4 

.376 

•33442 

543 

.42735    533 

.98288 

3,4 

.0174 

0,4 

•  377 

.33985 

543 

.43268    534 

.98291 

3,4 

.0174 

0,4 

.378 

.34529 

544 

.43803    535 

.98295 

3,4 

.0173 

o,3 

•  379 

.35073 

544 

.44337 

535 

.98298 

3,4 

.0173 

0,3 

2.380 

5.35618 

545 

5.44873 

536 

0.98301 

3,4 

1.0173 

0,3 

.381 

.36163 

545 

.45409 

536 

•98305 

3,4 

.0172 

.382 

.36708 

546 

•45945 

537 

.98308 

3,4 

.0172 

•  383 

.37255 

546 

.46482 

537 

.98311 

3,3 

.0172 

.384 

.37801 

547 

.47020 

538 

.98315 

3,3 

.0171 

2.385 

5.38349 

548 

5.47558 

538 

0.98318 

3,3 

1.0171 

.  0,3 

.386 

.38897 

548 

.48096 

539 

.98322 

3,3 

.0171 

.387 

•39445 

549 

•48635 

539 

•98325 

3,3 

.0170 

.388 

•39994 

549 

.49175 

540 

.98328 

3,3 

.0170 

.389 

•40543 

550 

.49715 

541 

.98331 

3,3 

.6170 

2.390 

5.41093 

550 

5.50256 

541 

0.08335 

3,3 

1.0169 

o,3 

•  391 

.41644 

551 

.50798    542 

.98338 

3,3 

.0169 

•  392 

.42195 

551 

.51339  !   542 

.98341 

3,3 

.0169 

•  393 

.42746 

552 

.51882  :   543 

.98345 

3,3 

.0168 

•  394 

.43299 

552 

.52425    543 

.98348 

3,3 

.0168 

2.395 

5.43851 

553 

5.52969    544 

0.98351 

3,3 

1.0168 

o,3 

.396 

.44405 

554 

.53513  1   544 

.98354 

3,3 

.0167 

.397 

.44958 

554 

.54057  '   545 

.98358 

3,3 

.0167 

.398 

.45513 

555 

.54603    546 

.98361 

3,3 

.0167 

•  399 

.46068 

555 

.55148 

546 

•98364 

3,2 

.0166 

2.400 

5.46623 

556 

5.55095 

547 

0.98367 

3,2 

i.  0166 

o,3 

u 

tan  gd  u 

«-Fo' 

sec  gd  u    <•»  F</ 

sin  ad  u 

«Fo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


153 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

-FO' 

tanhu 

«F0f 

coth  u 

«F0' 

2.400 

5.46623 

556 

5.55695 

547 

0.98367 

3,2 

I.  Ol66 

0,3 

.401 

.47179 

556 

.56242 

547 

.98371 

3,2 

.0166 

.402 

•47735 

557 

.56789 

548 

.98374 

3,2 

.0165 

.403 

.48292 

557 

•57337 

548 

.98377 

3,2 

.0165 

.404 

.48850 

558 

.57886 

549 

.98380 

3,2 

.0165 

2.405 

5.49408 

558 

5.58435 

549 

0.98384 

3,2 

1.0164 

o,3 

.406 

.49967 

559 

•58984 

550 

.98387 

3,2 

.0164 

.407 

.50526 

560 

.59535 

551 

•98390 

3,2 

.   .0164 

.408 

.51086 

560 

.60086 

551 

.98393 

3,2 

.0163 

.409 

.51646 

56i 

.60637 

552 

.98396 

3,2 

.0163 

2.410 

5.52207 

56i 

5.61189 

552 

0.98400 

3,2 

I.OI63 

0,3 

.411 

.52769 

562 

.61741 

553 

.98403 

3,2 

.Ol62 

.412 

562 

.62294 

553 

.98406 

3,2 

.Ol62 

.413 

.53893 

563 

.62848 

554 

.98409 

3,2 

.0162 

.414 

•  544-56 

563 

.63402 

554 

.98412 

3,2 

.Ol6l 

2.415 

5-55020 

564 

5.63957 

555 

0.98415 

3J 

1.0161 

o,3 

.416 

.55584 

565 

.64512 

556 

.98418 

3,1 

.0161 

.417 

.56149 

565 

.65068 

556 

.98422 

3,1 

.0160 

.418 

.56715 

566 

.65624 

557 

.98425 

3,1 

.0160 

.419 

.57280 

566 

.66181 

557 

.98428 

3,1 

.0160 

2.420 

5.57847 

567 

5.66739 

558 

0.98431 

3,1 

1.0159 

o,3 

.421 

.58414 

567 

.67297 

558 

.98434 

3,1 

.0159 

.422 

.58981 

568 

.67856 

559 

•98437 

3J 

.0159 

.423 

•59550 

568 

.68415 

56o 

•98440 

3,1 

.0158 

.424 

.60118 

569 

.68975 

560 

.98443 

3,1 

.0158 

2.425 

5.60688 

570 

5.69535 

56i 

0.98446 

3,1 

1.0158 

o,3 

.426 

.61257 

570 

.70096 

56i 

.98450 

3,1 

•  0157 

.427 

.61828 

571 

.70658 

562 

.98453 

3,1 

•  0157 

.428 

.62399 

57i 

.71220 

562 

.98456 

3,1 

•0157 

.429 

.62970 

572 

.71783 

563 

.98459 

3,1 

•0157 

2.430 

5.63542 

572 

5.72346 

564 

0.98462 

3J 

1.0156 

0,3 

.431 

.64115 

573 

.72910 

564 

•98465 

3,0 

.0156 

.432 

.64688 

573 

•73474 

565 

.98468 

3,0 

.0156 

•433 

.65262 

574 

•74039 

565 

•08471 

3,o 

•  0155 

•434 

.65836 

575 

•74605 

566 

.98474 

3,0 

•  0155 

2.435 

5.66411 

575 

5.75I7I 

566 

0.98477 

3,o 

1.0155 

o,3 

.436  !  .66986 

576 

.75738 

567 

.08480 

3,o 

•  0154 

•  437 

•67563 

576 

•76305 

568 

.08483 

3,o 

.0154 

.438 

.68139 

577 

•76873 

568 

.98485 

3,0 

.0154 

•  439 

.68716 

577 

•77441 

569 

.98489 

3,0 

.0153 

2.440 

5.69294 

578 

5.78010 

569 

0.98492 

3,0 

i.  0153 

o,3 

.441 

.69872 

579 

.78580 

570 

.98495 

3,o 

•  0153 

.442 

.70451 

579 

.79150 

570 

.98498 

3,o 

.0152 

•  443 

.71031 

580 

•79721 

571 

.98501 

3,o 

.0152 

.444 

.71611 

58o 

.80292 

572 

.98504 

3,0 

.0152 

2.445 

5.72I9I 

58i 

5.80864 

572 

0.98507 

3,0 

1.0152 

0,3 

.446 

.72772 

58i 

.81436 

573 

.98510 

3,0 

.0151 

•  447 

•73354 

582 

.82009 

573 

.98513 

3,0 

.0151 

.448 

.73936 

583 

.82583 

574 

.98516 

2,9 

.0151 

.449 

.74519 

583 

.83157 

575 

.98519 

2,9 

.0150 

2.450 

5.75103 

584 

5.83732 

575 

0.98522 

2,9 

1.0150 

0,3 

u 

tan  gd  u 

<-  F,,' 

sec  gd  u 

-Fo' 

sin  gd  u 

«F0' 

esc  gd  u 

•  FO' 

SMITHSONIAN  TABLCS 


154 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«Fo' 

cosh  u 

»F0' 

tanhu 

«-FO' 

cothu 

«FO' 

2.450 

5.75103 

584 

5.83732 

575 

0.98522 

2,9 

1.0150 

0,3 

.451 

.75687 

584 

576 

.98525 

2,9 

.0150 

.452 

.76271 

585 

.84883 

576 

.98528 

2,9 

.0149 

/  .453 

.76856 

585 

.85460 

577 

.98530 

2,9 

.0149 

•454 

•77442 

586 

.86037 

577 

.98533 

2,9 

.0149 

2.455 

5.78029 

587 

5.86615 

578 

0.98536 

2,9 

1.0149 

0,3 

.456 

.78615  ' 

587 

.87193 

579 

.98539 

2,9 

.0148 

•457 

.79203 

588 

.87772 

579 

'.98542 

2,9 

.0148 

.458 

.79791 

588 

.88352 

580 

.98545 

2,9 

.0148 

•459 

.80380 

589 

.88932 

580 

.98548 

2,9 

.0147 

2.460 

5.80969 

590 

5.89512 

58i 

0.98551 

2,9 

I.  0147 

0,3 

.461 

.81559 

590 

.90094 

582 

.98554 

2,9 

.0147 

.462 

.82149 

59i 

.90675 

582 

.98556 

2,9 

.0146 

.463 

.82740 

59i 

.91258 

583 

.98559 

2,9 

.0146 

.464 

.83332 

592 

.91841 

583 

.98562 

2,9 

^  .0146 

2.465 

5.83924 

592 

5.92425 

584 

0.98565 

2,8 

1.0146 

0,3 

.466 

.84516 

593 

.93009 

585 

.98568 

2,8 

.0145 

.467 

.85110 

594 

.93594 

585 

.98571 

2,8 

.0145 

.468 

.85704 

594 

.94179 

586 

.98574 

2,8 

.0145 

.469 

.86298 

595 

.94765 

586 

.98576 

2,8 

.0144 

2.470 

5.86893 

595 

5-95352 

.587 

O.Q8579 

•  2,8 

1.0144 

0,3 

.471 
.472 

.87489 
.88085 

596 

597 

•95939 
.96527 

ft 

.98582 
.98585- 

2,8 
2,8 

.0144 

.0144 

•  473 

.88682 

597 

.97H5 

589 

.98588 

2,8 

.0143 

•474 

.89279 

498 

.97704 

589 

.98590 

2,8 

.0143 

2.475 

S.89877 

598 

5.98294 

590 

0.98593 

2,8 

I.  0143 

0,3 

.476 

.90476 

599 

.98884 

59i 

.98596 

2,8 

.0142 

•477 

•91075 

599 

.99474 

59i 

.98599 

2,8 

.0142 

.478 

.91675 

600 

6.00066 

592 

.98602 

2,8 

.0142 

•  479 

.92275 

601 

.00658 

592 

.98604 

2,8 

.0142 

2.480 

5.92876 

601 

6  .01250 

593 

0.98607 

2,8 

1.0141 

0,3 

.481 

.93478 

602 

.01844 

593 

.98610 

2,8 

.0141 

.482 

.94080 

602 

.02437 

594 

.98613 

2,8 

.0141 

.483 

.94682 

603 

.03032 

595 

.98615 

2,7 

.0140 

.484 

.95286 

604 

.03627 

595 

.98618 

2,7 

.0140 

2.485. 

5.95890 

604 

6.04222 

596 

0.08621 

2,7 

1.0140 

0,3 

.486 

.96494 

605 

.04818 

596 

.98624 

2,7 

.0140 

•487 

.97099 

605 

•05415 

597 

.98626 

2,7 

.0139 

.488 

.97705 

606 

.06013 

598 

.98629 

2,7 

.0139 

.489 

.08311 

607 

.06611 

598 

.98632 

2,7 

.0139 

2.490 

5.98918 

607 

6.07209 

599 

0.98635 

2,7 

1.0138 

0,3 

.491 

.99526 

608 

.07809 

000 

.9S637 

2,7 

.0138 

.492 

6.00134 

608 

.08408 

600 

.98640 

2,7 

.0138 

•  493 

.00743 

609 

.00009 

601 

.98643 

2,7 

.0138 

•494 

.01352 

610 

.09610 

601 

.98645 

2,7 

.0137 

2.495 

6.01962 

610 

6.IO2II 

602 

0.98648 

2,7 

I.  0137 

0,3 

.496 

.02572 

611 

.  10814 

603 

.98651 

2,7 

.0137 

•  497 

.03183 

611 

.11417 

603 

.98653 

2,7 

.0136 

.498 

•03795 

612 

.  12020 

604 

.98656 

2,7 

.0136 

.499 

.04408 

613 

.  12624 

604 

.98659 

2,7 

.0136 

2.500 

6.05020 

613 

6.13229 

605 

0.98661 

2,7 

1.0136 

Q,3 

u 

tan  gd  u 

«FO' 

sec  gd  u 

-PC' 

sin  gd  u 

«Fo' 

csc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


155 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

•  IV 

tanh  u 

W  Fo' 

coth  u 

~  Fo' 

2.500 

6.05020 

6l3 

6.  13229 

605 

0.98661 

2,7 

1.0136 

0,3 

.501 

.05634 

614 

.13834 

606 

.98664 

2,7 

.0135 

.502 

.06248 

614 

.14440 

606 

.98667 

2,6 

.0135 

.503 

.06863 

615 

.15047 

607 

.98669 

2,6 

.0135 

.504 

.07478 

616 

.15654 

607 

.98672 

2,6 

.0135 

2.505 

6.08004 

616 

6.16262 

608 

0.98675 

2,6 

I.  0134 

0,3 

.506 

.08711 

617 

.16870 

609 

.98677 

2,6 

.0134 

.507 

.09328 

617 

.17479 

609 

.98680 

2,6 

.0134 

.508 

.09946 

618 

.18089 

610 

.98683 

2,6 

.0134 

.509 

.  10564 

619 

.18699 

611 

.98685 

2,6 

.0133 

2.510 

6.IH83 

619 

6.19310 

611 

0.98688 

2,6 

1.0133 

0,3 

.511 

.  1  1803 

620 

.19921 

612 

.98690 

2,6 

.0133 

.512 

.  12423 

621 

•20534 

612 

.98693 

2,6 

.0132 

.513 

.13044 

621 

.21146 

613 

.98696 

2,6 

.0132 

.514 

.13665 

622 

.21760 

614 

.98698 

2,6 

.0132 

2.515 

6.14287 

622 

6.22374 

614 

0.98701 

2,6 

1.0132 

0,3 

.516 

.  14910 

623 

.22988 

615 

.98703 

2,6 

.0131 

.517 

•15533 

624 

.23603 

616 

.98706 

2,6 

.0131 

.518 

.16157 

624 

.24219  !   616 

.08708 

2,6 

.0131 

.519 

.  16782 

625 

.24836 

617 

.98711 

2,6 

.0131 

2.520 

6.17407 

625 

6.25453 

617 

0.98714 

2,6 

1.0130 

0,3 

.521 

.18033 

626 

.26071 

618 

.08716 

2,6 

.0130 

.522 

.18659 

627 

.26689 

619 

.98719 

2,5 

.0130 

.523 

.19286 

627 

.27308 

619 

.98721 

2,5 

.0130 

.524 

.19914 

628 

.27927 

620 

.98724 

2,5 

.0129 

2.525 

6.20542 

629 

6.28548 

621 

0.98726 

2,5 

1.0129 

0,3 

.526 

.21171 

629 

.29169 

621 

.98729 

2,5 

.0129 

.527 

.21800 

630 

.29750 

622 

.98/31 

2,5 

.0128 

.528 

.22430 

630 

.30412 

622 

.98734 

2,5 

.0128 

.529 

.23061 

631 

.31035 

623 

.98736 

2,5 

.0128 

2.530 

6.23692 

632 

6.31658 

624 

0.98739 

2,5 

1.0128 

0,3 

.531 

.24324 

632 

.  32282 

624 

.98741 

2,5 

.0127 

.532 

.24957 

633 

.32907 

625 

.98744 

2,5 

.0127 

•  533 

.25590 

634 

.33532 

626 

.98746 

2,5 

.0127 

•  534 

.26224 

634 

.34158 

626 

.08749 

2,5 

.0127 

2.535 

6.26858 

635 

6.34785 

627 

0.98751 

2,5 

1.0126 

0,3 

.536 

•27494 

635 

.35412 

627 

.98754 

2,5 

.0126 

•  537 

.28129 

636 

.30040 

628 

.98756 

2,5 

.0126 

.538 

.28766 

637 

.36668 

629 

.98759 

2,5 

.0126 

.539 

.29403 

637 

.37297 

629 

.98761 

2,5 

.0125 

2.540 

6.30040 

638 

6.37927 

630 

0.98764 

2,5 

I.  0125 

0,3 

•  541 

.30678 

639 

.38557 

631 

.98766 

2,5 

.0125 

0,3 

•  542 

.31317 

639 

.39188 

631 

.98769 

2,4 

.0125 

0,3 

•  543 

.31957 

640 

.39820 

632 

.98771 

2,4 

.0124 

o,3 

•  544 

.32597 

640 

.40452 

633 

.98773 

2,4 

.0124 

0,2 

2.545 

6.33238 

641 

6.41085 

633 

0.98776 

2,4 

1.0124 

0,2 

.546 

.33879 

642 

.41719 

634 

.98778 

2,4 

.0124 

is 

.34521 
.35164 

642 
643 

.42353 
.42088 

635 
635 

.98781 
.98783 

A4 

2,4 

.0123 
.0123 

.549 

.35807 

644 

.43623 

•636 

.98786 

24 

.0123 

2.550 

6.30451 

644 

6.44259 

636 

0.98788 

2,4 

1.0123 

CX2 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

tin  gd  u 

«F0' 

csc  gd  u 

•  Fo' 

SMITHSONIAN  TABLE* 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

w  py> 

cosh  u 

O.FO' 

tanh  u 

«F0' 

coth  u 

«F0' 

2.550 

6.36451 

644 

6.44259 

636 

0.98788 

2,4 

I.OI23 

0,2 

.551 

.37096 

645 

.44896 

637 

.98790 

2,4 

.OI22 

\-552 

.37741 

646 

.45533 

638 

•98793 

2,4 

.0122 

•  553 

.38387 

646 

.46172 

638 

.98795 

2,4 

.OI22 

•  554 

.39033 

647 

.46810 

639 

.98798 

2,4 

.OI22 

2.555 

6.39680 

647 

6.47450 

640 

0.98800 

2,4 

I.OI2I 

0,2 

.556 

.40328 

648 

.48090 

640 

.98802 

2,4 

.OI2I 

•  557 

.40977 

649 

.48730 

641 

.98805 

2,4 

.OI2I 

.558 

.41626 

649 

•49372 

642 

.98807 

2,4 

.OI2I 

•  559 

.42275 

650 

.50014 

642 

.98810 

2,4 

.OI2O 

2.560 

6.42926 

651 

6.50656 

643 

0.98812 

2,4 

I.OI2O 

0,2 

.561 

•43577 

651 

.51299 

644 

.98814 

2,4 

.OI2O 

.562 

.44228 

652 

.51943 

644 

.98817 

2,4 

.OI2O 

.563 

.44880 

653 

.52588 

645 

.98819 

2,3 

.OI2O 

.564 

.45533 

653 

.53233 

646 

.98821 

2,3 

.0119 

2.565 

6.46187 

654 

6.53879 

646 

0.98824 

2,3 

I.OII9 

0,2 

.566 

.46841 

655 

.54525 

647 

.98826 

2,3 

.OI  19 

.567 

.47496 

655 

.55173 

647 

.98828 

2,3 

.OII9 

.568 

.48152 

656 

.55820 

648 

.98831 

2,3 

.0118 

.569 

.48808 

656 

.56469 

649 

.98833 

2,3 

.0118 

2.570 

6.49464 

657 

6.57118 

649 

0.98835 

2,3 

I.OIlS 

0,2 

•  571 

.50122 

658 

.57768 

650 

.98838 

2,3 

.0118 

•  572 

.50780 

658 

.58418 

651 

.98840 

2,3 

.OII7 

•  573 

.51439 

659 

.59069 

651 

.98842 

2,3 

.OII7 

.574 

.52098 

660 

•59721 

652 

•98845 

2,3 

.OII7 

2.575 

6.52758 

660 

6.60374 

653 

0.98847 

2,3 

I.OII7 

0,2 

.576 

.53419 

661 

.61027 

653 

.98849 

2,3 

.OIl6 

•  577 

.54080 

662 

.61680 

654 

.98851 

2,3 

.OIl6 

.578 

•54742 

662 

.62335 

655 

.98854 

2,3 

.OIl6 

.579 

.55405 

663 

.62990 

655 

.98856 

2,3 

.OIl6 

2.580 

6.56068 

664 

6.63646 

656 

0.98858 

2,3 

I.  0115 

0,2 

.581 

.56732 

664 

.64302 

657 

.98860 

2,3 

.0115 

.582 

•57397 

665 

.64959 

657 

.98863 

2,3 

:oii5 

.583 

.58062 

666 

-.65617 

658 

.98865 

2,3 

.0115 

.584 

.58728 

666 

.66275 

659 

.98867 

2,3 

.0115 

2.585 

6.59395 

667 

6.66934 

659 

0.98870 

2,2 

1.0114 

0,2 

.586 

.60062 

668   .67594 

660 

.98872 

2,2 

.0114 

.587 

.60730 

668   .68254 

661 

•98874 

2,2 

.0114 

.588 

.61398 

669 

.68915 

661 

.98876 

2,2 

.0114 

.589 

.62068 

670 

.69577 

662 

.98878 

2,2 

.0113 

2.590 

6.62738 

670 

6.70240 

663 

0.98881 

2,2 

1.0113 

0,2 

.591 

.63408 

671 

.70903 

663 

.98883 

2,2 

.0113 

.592 

•64079 

672 

.71566 

664 

.98885 

2,2 

.0113 

•  593 

.64751 

672 

.72231 

665 

.98887 

2,2 

.0113 

•  594 

.65424 

673 

.72876 

665 

.98890 

2,2 

.0112 

2.595 

6.66097 

674 

6.73562 

666 

0.98892 

2,2 

I.OII2 

0,2 

.596 

.66771 

674 

.74228 

667 

.98894 

2,2 

.OII2 

•  597 

.67446 

675 

.74895 

667 

.98896 

2,2 

.0112 

•  598 

.68121 

676 

.75563 

668 

.98898 

2,2 

.0111 

•  599 

.68797 

676 

.76231 

669 

.98901 

2,2 

.OI  1  1 

2.600 

6.69473 

677 

6.76901 

669 

0.98903 

2,2 

I.OIII 

0,2 

u 

tan  gd  u 

«FO' 

sec  gd  u 

wF0' 

sin  gd  u 

wF</ 

csc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


157 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

<•»  Fi/ 

cosh  u 

wF0' 

tanhu 

<-F0' 

coth  u 

•  Fo' 

2.600 

6.69473 

677 

6.76901 

669 

0.98903 

2,2 

I.OIII 

0,2 

.601 

.70150 

678 

•77570 

670 

.98905 

2,2 

.0111 

.602 

.70828 

678 

.78241 

671 

•98907 

2,2 

.OIIO 

.603 

.71507 

679 

.78912 

67* 

.98909 

2,2 

.OIIO 

.604 

.72186 

680 

.79584 

672 

.98911 

2,2 

.OIIO 

2.605 

6.72866 

680 

6.80256 

673 

0.98914 

2,2 

I.  OIIO 

0,2 

.606 

•73547 

681 

.80930 

674 

.98916 

2,2 

.OIIO 

.607 

.74228 

682 

.81604 

674 

.98918 

2,2 

.0109 

.608 

.74910 

682 

.82278 

675 

.98920 

2,1 

.0109 

.609 

•75593 

683 

.82953 

676 

.98922 

2,1 

.0109 

2.610 

6.76276 

684 

6.83629 

676 

0.98924 

2,1 

1.0109 

0,2 

.611 

.76960 

684 

.84306 

677 

.98926 

2,1 

.0109 

.612 

.77644 

685 

.84983 

678 

.98929 

2,1 

.0108 

.613 

•78330 

686 

.85661 

678 

•9^931 

2,1 

.0108 

.614 

.79016 

686 

.86340 

679 

•98933 

2,1 

.0108 

2.615 

6.79702 

687 

6.87019 

680 

0.98935 

2,1 

1.0108 

0,2 

.616 

.80300 

688 

.87699 

680 

•Q8937 

2,1 

.0107 

.617 

.81078 

688 

.88380 

681 

.98939 

2,1 

.0107 

.618 

.81767 

689 

.89061 

682 

.98941 

2,1 

.0107 

.619 

.82456 

690 

.89744 

682 

.98943 

2,1 

.0107 

2.620 

6.83146 

690 

6.90426 

683 

0.98946 

2,1 

1.0107 

0,2 

.621 

.83837 

691 

.91110 

684 

.98948 

2,1 

.0106 

.622 

.84528 

692 

.91794 

685 

.98950 

2,1 

.0106 

.623 

.85220 

692 

.92479 

685 

.98952 

2,1 

.0106 

.624 

.85913 

693 

.93164 

686 

.98954 

2,1 

.0106 

2.625 

6.86607 

694 

6.93851 

687 

0.98956 

2,1 

1.0106 

0,2 

.626 

.87301 

695 

.94538 

687 

.98958 

2,1 

.0105 

.627 

.87996 

695 

.95225 

688 

.98960 

2,1 

.0105 

.628 

.88691 

696 

.95914 

689 

.98962 

2,1 

.0105 

.629 

.89388 

697 

.96603 

689 

.98964 

2,1 

.0105 

2.630 

6.90085 

697 

6.97292 

690 

0.98966 

2,1 

1.  0104 

0,2 

.631 

.90782 

698 

.97983 

691 

.98968 

2,1 

.0104 

.632 

.91481 

699 

.98674 

691 

.98970 

2,O 

.0104 

.633 

.92180 

699 

.99366 

692 

.98972 

*  2,0 

.0104 

.634 

.92879 

700 

7.00058 

693 

.98974 

2,0 

.0104 

2.635 

6.93580 

701 

7.00752 

694 

0.98977 

2,0 

1.0103 

0,2 

.636 

.94281 

701 

.01446 

694 

.98979 

2,0 

.0103 

.637 

.94983 

702 

.02140 

695 

.98981 

2,0 

.0103 

.638 

.95685 

703 

.02835 

696 

.98983 

2,O 

.0103 

.639 

.96388 

704 

.03532 

696 

.98985 

2,0 

.0103 

2.640 

6.97092 

704 

7.04228 

697 

0.98987 

2,0 

I.OI02 

0,2 

.641 

•97797 

705 

.04926 

698 

.98989 

2,O 

.0102 

.642 

.98502 

706 

.05624 

699 

.98991 

2,0 

.0102 

.643 

.99208 

706 

.06323 

699 

.98993 

2,0 

.OIO2 

.644 

.99915 

707 

.07022 

700 

.98995 

2,0 

.OIO2 

2.645 

7.00622 

708 

7.07723 

701 

0.98997 

2,0 

I.OIOI 

0,2 

.646 

.01330 

7o8 

.08423 

701 

.98999 

2,0 

.OIOI 

.647 

.02039 

709 

.09125 

702 

.99001 

2,0 

.0101 

.648 

.02748 

710 

.09828 

703 

.99003 

2,0 

.OIOI 

.649 

.03458 

711 

.10531 

703 

.09005 

2,O 

.OIOI 

2.650 

7.04169 

7ii 

7-II234 

704 

0.99007 

2,0 

I.OIOO 

0,2 

u 

tan  gd  u 

•  Fo' 

sec  gd  u 

•  Fo' 

•ingdu 

«F,/ 

csc  gd  u 

•  FO' 

SMITHSONIAN  TABLES 


158 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanh  u 

«FO 

coth  u  . 

•  Fa' 

2.650 

7.04169 

711 

7.11234 

704 

0.99007 

2,0 

I.OIOO 

0,2 

\  .651 

.04881 

712 

.11939 

705 

.99009 

2,0 

.0100 

\652 

•05593 

713 

.  12544 

706 

.99011 

2,0 

.0100 

.653 

.06306 

713 

.  13350 

706 

.90013 

2,0 

.0100 

.654 

.07020 

7U 

.  14057 

707 

.99015 

2,0 

.0100 

2.655 

7-07734 

715 

7.14764 

708 

0.99016 

2,O 

1.0099 

0,2 

.656 

.08449 

715 

.  15472 

708 

.99018 

2,0 

.0099 

.657 

.09165 

7l6 

.16181 

709 

.99020 

1,9 

.0099 

.658 

.09882 

717 

.16891 

710 

.99022 

i,9 

.0099 

.659 

.10599 

718 

.17601 

711 

.99024 

1,9 

.0099 

2.660 

7.11317 

718 

7-18312 

711 

0.99026 

1,9 

1.0098 

0,2 

.661 

.  12036 

719 

.19024 

712 

.99028 

1,9 

.0098 

.662 

.  12755 

720 

.  19736 

713 

.99030 

1,9 

.0098 

.663 

.  13475 

720 

.20449 

713 

.09032 

1,9 

.0098 

.664 

.14196 

721 

.21163 

714 

.99034 

1,9 

.0098 

2.665 

7.14918 

722 

7.21877 

715 

0.99036 

1,9 

1.0097 

0,2 

.666 

.  15640 

723 

.22593 

7l6 

.99038 

i,9 

.0097 

.667 

.  16363 

723 

.23309 

7i6 

.99040 

1,9 

.0097 

.668 

.17086 

724 

.24025 

717 

.09042 

1,9 

.0097 

.669 

.17811 

725 

.24743 

7l8 

.99044 

1,9 

.0097 

2.670 

7.18536 

725 

7-25461 

719 

0.99045 

i,9 

1.0096 

0,2 

.671 

.  19262 

726 

.26180 

719 

.99047 

i,9 

.0096 

.672 

.19988 

727 

.26900 

720 

.99049- 

1,9 

.0096 

.673 

.20715 

728 

.27620 

721 

.99051 

i,9 

.0096 

.674 

•21443 

728 

.28341 

721 

•99053 

1,9 

.0096 

2.675 

7.22172 

729 

7-29063 

722 

0,99055 

1,9 

1.0095 

0,2 

.676 

.22902 

730 

.29785 

723 

.99057 

i,9 

.0095 

.677 

.23632 

731 

.30509 

724 

.99059 

1,9 

.0095 

.678 

,.24363 

731 

.31233 

724 

.99060 

1,9 

.0095 

.679 

.25094 

732 

.31957 

725 

.99062 

1,9 

.0095 

2.680 

7-25827 

733 

7.32683 

726 

0.09064 

1,9 

1.0094 

0,2 

.681 

.26560 

733 

•33409 

727 

.99066 

1,9 

.0094 

.682 

.27293 

734 

.34136 

727 

.Q9068 

i,9 

.0094 

.683 

.28028 

735 

.34864 

728 

.09070 

1,9 

.0094 

.684 

.28763 

736 

.35592 

729 

.99072 

1,8 

.0094 

2.685 

7.29499 

736 

7.36321 

729 

0.09073 

1,8 

1.0094 

0,2 

.685 

.30236 

737 

.37051 

730 

•99075 

1,8 

.0093 

.687 

.30973 

738 

.37782 

73i 

.99077 

1,8 

.0093 

.688 

.31711 

739 

.38513 

732 

.99079 

1,8 

.0093 

.689 

•32450 

739 

.39245 

732 

.99081 

1,8 

.0093 

2.600 

7.33190 

740 

7.39978 

733 

0.99083 

1,8 

1.0093 

0,2 

.691 

•33930 

741 

.40711 

734 

.90084 

1,8 

.0092 

.692 

•34671 

74i 

.41446 

735 

.99085 

1,8 

.0092 

.693 

.35413 

742 

.42181 

735 

.90088 

1,8 

.0092 

.694 

.36156 

743 

.42917 

736 

.99090 

1,8 

.0092 

2.695 

7.36899 

744 

7.43653 

737 

0.99092 

1,8 

1.0092 

0,2 

.696 

.37643 

744 

.44390 

738 

.99094 

1,8 

.0091 

.697 

.38388 

745 

.45128 

738 

.00095 

1,8 

.0091 

.698 

.39133 

746 

.45867 

739 

.99097 

1,8 

.0091 

.699* 

.39879 

747 

.46607 

740 

.99099 

1,8 

.0091 

2.700 

7.40626 

747 

7-47347 

741 

0.99101 

1,8 

1.0091 

0,2 

u 

tan  gd  u 

«F0' 

sec  gd  u 

-Fo' 

sin  gd  u 

«-Fo' 

esc  gd  u 

<-F</ 

SMITHSONIAN  TABLES 


159 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«F0' 

tanh  u 

«FO' 

cothu 

W  Fo' 

2.700 

7.40626 

747 

7-47347 

741 

0.99101 

1,8 

1.0091 

0,2 

.701 

.41374 

748 

.48088 

741 

.99103 

1,8 

.0091 

.702 

.42122 

749 

.48830 

742 

.99104 

1,8 

.0090 

.703 

.42872 

750 

•49572 

743 

•  99io5 

1,8 

.0090 

.704 

.43622 

750 

.50315 

744 

.99108 

1,8 

.0090 

2.705 

7.44372 

751 

7.51059 

744 

0.99110 

1,8 

I.OOOO 

0,2 

.706 

.45124 

752 

.51804 

745 

.99IH 

1,8 

.0090 

.707 

.45876 

753 

.52550 

746 

•99113 

1,8 

.0089 

.708 

.46629 

753 

.53206 

747 

•99115 

1,8 

.0089 

.709 

.47383 

754 

•54043 

747 

.99117 

1,8 

.0089 

2.710 

7.48I37 

755 

7.54791 

748 

0.99118 

1,8 

1.0089 

0,2 

.711 

.48892 

756 

•55539 

749 

.99120 

1,8 

.0089 

.712 

.49648 

756 

.56288 

750 

.99122 

1,7 

.0089 

.713 

.50405 

757 

.57038 

750 

.99124 

1,7 

.0088 

.714 

.51162 

758 

.57789 

75i 

.99125 

i,7 

.0088 

2.715 

7.51920 

759 

7.58541 

752 

0.99127 

1,7 

1.0088 

O,2 

.716 

.52679 

759 

.59293 

753 

.09129 

i,7 

.0088 

.717 

•53439 

760 

.60046 

753 

.99131 

i,7 

.0088 

.718 

.54199 

76i 

.60800 

754 

.99132 

i,7 

.0088 

.719 

.54960 

762 

.61555 

755 

.99134 

i,7 

.0087 

2.720 

7-55722 

762 

7.62310 

756 

0.09136 

1,7 

1.0087 

0,2 

.721 

.56485 

763 

.63066 

756 

.99138 

i,7 

.0087 

.722 

.57249 

764 

.63823 

757 

•99139 

i,7 

.0087 

.723 

.58013 

765 

.64580 

758 

.99MI 

i,7 

.0087 

.724 

.58778 

765 

.65339 

759 

•99143 

i,7 

.0086 

2.725 

7-59543 

766 

7.66098 

760 

0.99144 

i,7 

1.0086 

0,2 

.726 

.60310 

767 

.66858 

760 

.99146 

i,7 

.0086 

.727 

.61077 

768 

.67619 

761 

.99148 

i,7 

.0086 

.728 

.61845 

768 

.68380 

762 

.59150 

i,7 

.0086 

.729 

.62614 

769 

.69142 

763 

.09151 

i,7 

.0086 

2.730 

7.63383 

770 

7.69905 

763 

0.09153 

1,7 

1.0085 

0,2 

.731 

.64154 

771 

.70669 

764 

•99155 

i,7 

.0085 

.732 

.64925 

77i 

.7U34 

765 

.09156 

1,7 

.0085 

•  733 

.65697 

772 

.72199 

766 

.99158 

1,7 

.0085 

•  734 

.66469 

773 

.72965 

766 

.99160 

i,7 

.0085 

2.735 

7.67242 

774 

7-73732 

767 

0.99161 

i,7 

1.0085 

0,2 

.736 

.68017 

774 

•74500 

768 

.99163 

1,7 

.0084 

.737 

.68791 

775 

.75268 

769 

.59165 

1,7 

.0084 

-738 

.69567 

776 

.76037 

770 

.99166 

i,7 

.0084 

•  739 

•70344 

777 

.76807 

770 

.99168 

i,7 

.0084 

2.740 

7.7II2I 

778 

7.77578 

771 

0.99170 

1,7 

1.0084 

0,2 

.741 

.71899 

778 

.78349 

772 

.99171 

i,7 

.0084 

.742 

.72677 

779 

.79122 

773 

.99173 

1,6 

.0083 

•  743 

•73457 

780 

.79895 

773 

•9PI75 

1,6 

.0083 

•  744 

.74237 

78i 

.80668 

774 

.99176 

1,6 

.0083 

2.745 

7.75018 

78i 

7.81443 

775 

0.99178 

1,6 

1.0083 

0,2 

.746 

.75800 

782 

.82219 

776 

.99179 

1,6 

.0083 

•  747 

.76583 

783 

.82955 

777 

.99181 

1,6 

.0083 

.748 

.77366 

784 

.83772 

777 

.09183 

1,6 

.0082 

•  749 

.78150 

785 

.84549 

778 

.99184 

1,6 

.0082 

• 

2.750 

7.78935 

785 

7.85328 

779 

0.99186 

1,6 

1.0082 

0,2 

u 

tan  gd  u 

«Fo' 

•ec  gd  u 

«F0' 

sin  gd  u 

«F0' 

csc  gd  u 

-FO' 

SMITHSONIAN  TABLES 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

w  F0' 

tanh  u 

"Fo 

coth  u 

«Fo' 

2.750 

7.78935 

785 

7.85328 

779 

0.99186 

1,6 

1.0082 

0,2 

.751 

.79721 

786 

.86107 

780 

.99188 

1,6 

.0082 

\  .752 

.80507 

787 

.86887 

78i 

.99189 

1,6 

.0082 

•  753 

.81295 

788 

.87668 

78i 

.99191 

1,6 

.0082 

•  754 

.82083 

788 

.88450 

782 

.99192 

*6 

.0081 

2.755 

7.82872 

789 

7.89232 

783 

0.99194 

1,6 

I.OOSI 

0,2 

•  756 

.83661 

790 

.90016 

784 

.09196 

1,6 

.0081 

•  757 

.84452 

791 

.90800 

784 

•99197 

1,6 

.Oo8l 

.758 

.85243 

792 

.91585 

785 

.99199 

1,6 

.0081 

•  759 

.85035 

792 

.92370 

786 

.99200 

1,6 

.008I 

2.760 

7.86828 

793 

7.93157 

787 

O.992O2 

1,6 

I.OoSo 

0,2 

.761 

.87621 

794 

•93944 

788 

.99204 

1,6 

.0080 

.762 

.88415 

795 

.94732 

788 

.99205 

,6 

.0080 

.763 

.89211 

796 

•95521 

789 

.99207 

,6 

.0080 

.764 

.90006 

796 

.96310 

790 

.99208 

,6 

.0080 

2.765 

7.90803 

797 

7.97IOI 

791 

O.992IO 

,6 

I.OOSO 

0,2 

.766 

.91601 

798 

.97892 

792 

.99212 

,6 

.0079 

.767 

.92399 

799 

.98684 

792 

.99213 

,6 

.0079 

.768 

.93198 

799 

•99477 

793 

.99215 

,6 

.0079 

.769 

.93998 

800 

8.00270 

794 

.99216 

,6 

.0079 

2.770 

7-94799 

801 

8.01065 

795 

0.99218 

,6 

1.0079 

0,2 

•  771 

.95600 

802 

.01860 

796 

.99219 

,6 

.0079 

.772 

.96402 

803 

.02656 

756 

.99221 

,6 

.0079 

•  773 

.97205 

803 

.03453 

797 

.99222 

,5 

.0078 

•  774 

.98009 

804 

.04250 

798 

.99224 

,5 

.0078 

2.775 

7.98814 

805 

8.05049 

799 

0.99226 

,5 

1.0078 

0,2 

.776 

.99619 

806 

.  05848 

800 

.99227 

,5 

.0078 

.777 

8.00426 

807 

.06648 

800 

.99229 

,5 

.0078 

.778 

.01233 

807 

.07449 

801 

.99230 

,5 

.0078 

•  779 

.O2O40 

808 

.08251 

802 

.99232 

,5 

.0077 

2.780 
.781 

8.02849 
.03659 

809 
810 

8.09053 
.09856 

803 

804 

0.99233 
.99235 

,5 
,5 

1.0077 
.0077 

O,2 

.782 

.04469 

811 

.10660 

804 

.99236 

,5 

.0077 

.783 

.05280 

811 

.11465 

805 

.99238 

,5 

.0077 

.784 

.06092 

812 

.12271 

806 

.99239 

,5 

.0077 

2.785 

8.06904 

813 

8.13077 

807 

0.99241 

,5 

1.0077 

0,2 

.786 

.07718 

814 

.13885 

808 

.99242 

,5 

.0076 

.787 

.08532 

815 

.14693 

809 

•99244 

,5 

.0076 

.788 

.09347 

816 

.  15502 

809 

.99245 

,5 

.0076 

.789 

.  10163 

816 

.16311 

810 

•99247 

,5 

.0076 

2.700 

8.10980 

817 

8.17122 

811 

0.99248 

,5 

1.0076 

0,2 

.791 

.11797 

818 

.  17933 

812 

.09250 

,5 

.0076 

•  792 

.12616 

819 

.  18746 

813 

.99251 

,5 

.0075 

•  793 

.13435 

820 

.  19559 

813 

.99253 

,5 

.0075 

.794 

.  14255 

820 

.20373 

814 

.99254 

,5 

.0075 

2.795 

8.15076 

821 

8.21187 

815 

0.99256 

,5 

1.0075 

O,2 

.796 

.15897 

822 

.22003 

816 

.99257 

,5 

.0075 

0,2 

•  797 

.  16720 

823 

.22819 

817 

.09259 

,5 

.0075 

0,2 

.798 

.17543 

824 

.23636 

818 

.£Q26o 

,5 

.0075 

0,2 

.799 

.18367 

824 

•24454 

818 

.99262 

i,5 

.0074 

0,1 

2.800 

8.19192 

825 

8.25273 

819 

0.99263 

1,5 

1.0074 

0,1 

u 

tan  gd  u 

wF0' 

sec  gd  u 

*>Fo' 

sin  gd  u 

wF0' 

esc  cd  u 

»Fo' 

SMITHSONIAN  TABLES 


161 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«F0' 

tanhu 

«Fo' 

coth  u 

«F0' 

2.800 

8.  19192 

825 

8.25273 

819 

0.99263 

i,5 

1.0074 

0,1 

.801 

.20018 

826 

.26092 

820 

.99265 

T,5 

.0074 

.802 

.20844 

827 

.26913 

821 

.99266 

i,5 

.0074 

.803 

.21671 

828 

.27734 

822 

.99268 

i,5 

.0074 

.804 

.22499 

829 

.28556 

822 

.99269 

i,5 

.0074 

2.805 

8.23328 

829 

8.29379 

823 

0.09270 

i,5 

1.0073 

0,1 

.806 

.24158 

830 

.30203 

824 

.99272 

i,5 

.0073 

.807 

.24989 

831 

.31027 

825 

.99273 

i,4 

.0073 

.808 

.25820 

832 

.31853 

826 

.99275 

i,4 

.0073 

.809 

.26653 

833 

.32679 

827 

.99276 

M 

.0073 

2.810 

8.27486 

834 

8.33506 

827 

0.09278 

1,4 

1.0073 

0,1 

.811 

.28320 

834 

•34334 

828 

.99279 

1,4 

.0073 

.812 

.29154 

835 

.35163 

829 

.99281 

1,4 

.0072 

.813 

.29990 

836 

.35992 

830 

.99282 

1,4 

.0072 

.814 

.30826 

837 

.36823 

831 

•59283 

1,4 

.0072 

2.815 

8.31664 

838 

8.37654 

832 

0.99285 

1,4 

1.0072 

0,1 

.816 

.32502    838 

.38486 

833 

.99286 

1,4 

.0072 

.817 

•33341    839 

.39319 

833 

.99288 

1,4 

.0072 

.818 

.34180    840 

•40153 

834 

.99289 

1,4 

.0072 

.819 

.35021 

84I 

•40987 

835 

.99291 

1,4 

.0071 

2.820 

8.35862 

842 

8.41823 

836 

0.99292 

1,4 

1.0071 

0,1 

.821 

.36704    843 

.42659 

837 

•99293 

1,4 

.0071 

.822 

.37548    843 

.43496 

838 

.99295 

1,4 

.0071 

.823 

.38391 

844 

.44334 

838 

.99296 

1,4 

.0071 

.824 

.39236 

845 

.45173 

839 

.99298 

1,4 

.0071 

2.825 

8.40082 

846 

8.46013 

840 

0.99299 

1,4 

1.0071 

0,1 

.826 

.40928 

847 

.46853 

84I 

•99300 

1,4 

.0070 

.827 

.41776 

848 

.47695 

842 

•  99302 

1,4 

.0070 

.828 

.42624 

849 

.48537 

843 

.99303 

1,4 

.0070 

.829 

•43473 

849 

.49380 

843 

•99305 

1,4 

.0070 

2.830 

8.44322 

850 

8.50224 

844 

0.59306 

1,4 

1.0070 

0,1 

.831 

.45173 

85I 

.51068 

845 

•99307 

1,4 

.0070 

.832 

.46025 

852 

.51914 

846 

.99309 

1,4 

.0070 

.833 

.46877 

853 

.52760 

847 

.99310 

1,4 

.0069 

.834 

.47730 

854 

.53008 

848 

•993II 

1,4 

.0069 

2.835 

8.48584 

854 

8.54456 

849 

0.99313 

1,4 

1.0069 

0,1 

.836 

•49439 

855 

.55305 

849 

.99314 

1,4 

.0069 

.837 

.50295 

856 

.56155 

8^0 

.99316 

1,4 

.0069 

.838 

.51151 

857 

.57006 

851 

.99317 

1,4 

.0069 

.839 

.52009 

858 

.57857 

852 

.99318 

1,4 

.0069 

2.840 

8.52867 

859 

8.58710 

853 

0.99320 

1,4 

1.0069 

0,1 

.841 

.53726 

860 

.59563 

854 

•99321 

1,4 

.0068 

.842 

.54586 

860 

.60417 

855 

.99322 

1,4 

.0068 

.843 

•55447 

861 

.61272 

855 

.99324 

1,3 

.0068 

.844 

.56309 

862 

.62128 

856 

.99325 

1,3 

.0068 

2.845 

8.57I7I 

863 

8.62085 

857 

0.99326 

1,3 

1.0068 

0,1 

.846 

.58035 

864 

.63842 

858 

.99328 

1,3 

.0068 

.847 

.58899 

865 

.64701 

859 

•99329 

i,3 

.0068 

.848 

.59764 

866 

.65560 

860 

•99330 

i,3 

.0067 

.849 

.60630 

866 

.66420 

861 

•  99332 

1,3 

.0067 

2.850 

8.61497 

867 

8.67281 

861 

0.09333 

1,3 

1.0067 

0,1 

u 

tan  ad  u 

-Fo' 

tec  gd  u 

•ly 

sin  gd  u 

-Fo' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLE* 


162 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«Fo' 

cosh  u 

«F0' 

tanh  u 

*»  Fo'     coth  u 

«F0' 

2.850 

8.61497 

867 

8.67281 

861 

0.99333 

1,3 

1.0067 

0,1 

i  .851 

.62365 

868 

.68143 

862 

•99334 

1,3 

.0067 

\  .852 

.63233 

869 

.69006 

863 

.99336 

1,3 

.0067 

.853 

.64103 

870 

.69870 

864 

.99337 

1,3 

.0067 

.854 

.64973 

871 

.70734 

865 

.09338 

1,3 

.0067 

2.855 

8.65844 

872 

8.71600 

866 

0.99340 

1,3 

1.0066 

0,1 

.856 

.66716 

872 

.72466 

867 

.99341 

1,3 

.0066 

.857 

.67589 

873 

•73333 

868 

.99342 

1,3 

.0066 

.858 

.68463 

874 

.74201 

868 

•99344 

1,3 

.0066 

.859 

.69337 

875 

.75070 

869 

•  99345 

1,3 

.0066 

2.860 

8.70213 

876 

8.75940 

870 

0.99346 

1,3 

1.0066 

0,1 

.861 

.71089 

877 

.76810 

871 

.99348 

1,3 

.0066 

.862 

.71967 

878 

.77682 

872 

.99349 

i,3 

.0066 

.863 

.72845 

•  879 

.78554 

873 

•99350 

i,3 

.0065 

.864 

.73724 

879 

.79428 

874 

•99351 

1,3 

.0065 

2.865 

8.74604 

880 

8.80302 

875 

0.99353 

1,3 

1.0065 

0,1 

.85^ 

.75484 

881 

.81177 

875 

•99354 

1,3 

.0065 

.867 

.76366 

882 

.82053 

876 

•99355 

i,3 

.0065 

.868 

.77248 

883 

877 

•99357 

1,3 

.0065 

.869 

.78132 

884 

.83807 

878 

•99358 

1,3 

.0065 

2.870 

8.70016 

885 

8.84686 

879 

0.99359 

1,3 

1.0065 

0,1 

.871 

.79901 

886 

.85565 

880 

.99360 

1,3 

.0064 

.872 

.80787 

886 

.86446 

881 

.99362 

1,3 

.0064 

.873 

.81674 

887 

.87327 

882 

.99363 

1,3 

.0064 

•  874 

.82562 

888 

.88209 

883 

.99364 

1,3 

.0064 

2.875 

8.83450 

889 

8.89092 

883 

0.99365 

i,3 

1.0064 

0,1 

.876 

.84340 

890 

.89976 

884 

.99367 

i,3 

.0064 

.877 

.85230 

891 

.90861 

885 

.99368 

1,3 

.0064 

.878 

.86122 

892 

.91746 

886 

.99369 

1,3 

.0063 

•  879 

.87014 

893 

.92633 

887 

•99371 

1,3 

.0063 

2.880 

8.87907 

894 

8.93520 

888 

0.99372 

1,3 

1.0063 

o,r 

.881 

.88801 

894 

.94409 

889 

•99373 

1,3 

.0063 

.882 

.89696 

895 

.95298 

890 

•99374 

1,2 

.0063 

.883 

.90591 

896 

.96188 

891 

•99376 

1,2 

.0063 

.884 

.91488 

897 

.97079 

891 

•99377 

1,2 

.0063 

2.885 

8.92386 

898 

8.97971 

892 

0.09378 

1,2 

1.0063 

0,1 

.886 

.93284 

899 

.98864 

893 

•99379 

1,2 

.0062 

.887 

.94183 

900 

.99758 

894 

.99380 

1,2 

.0062 

.888 

.95084 

901 

9.00652 

895 

.09382 

1,2 

.0062 

.889 

.95985 

902 

.01548 

896 

.09383 

1,2 

.0062 

2.890 

8.96887 

902 

9.02444 

897 

0.99384 

1,2 

1.0062 

0,1 

.891 

•97790 

003 

.03342 

898 

•99385 

1,2 

.0062 

.892 

.98693 

004 

.04240 

899 

•99387 

1,2 

.0062 

.893 

.99598 

905 

.05139 

900 

•99388 

1,2 

.0062 

.894 

9.00504 

906 

.06039 

901 

.99389 

1,2 

.0061 

2.895 

9.01410 

007 

9.06940 

901 

0-99390 

1,2 

I.  0061 

0,1 

.896 

.02318 

008 

.07842 

002 

.09391 

1,2 

.0061 

.897 

.03226 

009 

.08745 

903 

.99393 

1,2 

.0061 

.898 

.04135 

910 

.09648 

004 

•99394 

1,2 

.0061 

.899 

.05045 

911 

.  10553 

905 

•  99395 

1,2 

.0061 

2.900 

9.05956 

911 

9.H458 

906 

0.09396 

1,2 

I.  0061 

0,1 

u 

tan  gd  u 

»Fo' 

sec  gd  u 

-FO' 

sin  gd  u 

<»  Fo'    csc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


163 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

«F0' 

cosh  u 

«FO' 

tanh  u 

«Fo' 

coth  u 

«oF0' 

2.900 

9.05956 

911 

9.H458 

906 

0.09396 

1,2 

I.  0061 

0,1 

.001 

.06868 

912 

.  12365 

907 

.99398 

1,2 

.0061 

.902 

.07781 

9U 

.  13272 

908 

•99399 

1,2 

.0060 

.903 

.08695 

914 

.14180 

009 

.99400 

1,2 

.0060 

.904 

.09609 

915 

.15090 

910 

.99401 

1,2 

.0060 

2.905 

9.  10525 

9l6 

9.16000 

911 

0.90402 

1,2 

I.  0060 

0,1 

.906 

.11441 

917 

.16911 

911 

.99403 

1,2 

.0060 

.907 

•  12359 

9l8 

.17823 

912 

.99405 

1,2 

.0060 

.908 

.  13277 

919 

.18735 

913 

.99406 

1,2 

.0060 

.909 

.1410 

92O 

.19649 

914 

.99407 

1,2 

.0060 

2.910 

9.I5II6 

921 

9.20564 

9i5 

0.90408 

1,2 

1.  0060 

0,1 

.911 

.16037 

921 

.21479 

916 

.99409 

1,2 

.0059 

.912 

.10959 

922 

.22396 

917 

•994II 

1,2 

.0059 

.913 

.17882 

923 

.23313 

918 

.99412 

1,2 

.0059 

.914 

.18806 

924 

.24232 

919 

.99413 

1,2 

.0059 

2.915 

9-  19730 

925 

9.25I5I 

920 

0.99414 

1,2 

1.0059 

0,1 

.916 

.20656 

926 

.26071 

921 

.99415 

1,2 

.0059 

.917 

.21583 

927 

.26092 

922 

.99416 

1,2 

.0059 

.918 

.22510 

928 

.27914 

923 

.99418 

1,2 

.0059 

.919 

.23438 

929 

.28837 

923 

.99419 

1,2 

.0058 

2.920 

9.24368 

930 

9.29761 

924 

0.99420 

1,2 

1.0058 

0,1 

.921 

.25298 

93i 

.30686 

925 

.99421 

1,2 

.0058 

.922 

.26229 

932 

.31612 

926 

.99422 

1,2 

.0058 

.923 

.27161 

933 

.32538 

927 

.99423 

1,1 

.0058 

.924 

.28094 

933 

.33466 

928 

.99425 

1,1 

.0058 

2.925 

9.2O028 

934 

9-34395 

929 

0.99426 

I, 

1.0058 

0,1 

.926 

•29963 

935 

.35324 

930 

.99427 

I, 

.0058 

.927 

.30809 

936 

.36254 

931 

.99428 

I, 

.0058 

.928 

.31835 

937 

.37186 

932 

.99429 

I, 

.0057 

.929 

.32773 

938 

.38118 

933 

.99430 

I, 

.0057 

2.930 

9-33712 

939 

9.39051 

934 

0.09531 

I, 

1.0057 

0,1 

.931 

.34651 

940 

.39986 

935 

.99433 

I, 

.0057 

.932 

•35592 

941 

.40921 

936 

.99434 

I, 

.0057 

•  933 

.36533 

942 

.41857 

937 

•99435 

I, 

.0057 

•  934 

•37475 

943 

.42794 

937 

.99436 

I, 

•  0057 

2.935 

9.38419 

944 

9.43732 

938 

0.09437 

I, 

1.0057 

0,1 

.936 

.39363 

945 

.44671 

939 

.99438 

I, 

.0057 

•  937 

.40308 

946 

.45610 

940 

•99439 

I, 

.0056 

.938 

.41254 

947 

.46551 

941 

.99440 

I, 

.0056 

•939 

.42201 

947 

•47493 

942 

•99441 

I, 

.0056 

2.940 

9.43H9 

948 

9.48436 

943 

0.99443 

I. 

1.0056 

0,1 

.941 

.44098 

949 

.49379 

944 

.99444 

I, 

.0056 

.942 

.45048 

950 

.50324 

945 

•99445 

I, 

.0056 

•  943 

•45999 

951 

.51269 

946 

.99446 

I, 

.0056 

•  944 

.46950 

952 

.52216 

947 

•99447 

I, 

.0056 

2.045 

9.47903 

953 

9.53163 

948 

0.09448 

I, 

1.0055 

0,1 

.946 

.48857 

954 

.54H2 

949 

.99449 

I, 

•  0055 

•947 

.49811 

955 

.55061 

950 

.»450 

I, 

.0055 

.948 

.50767 

956 

.56011 

951 

•99451 

I, 

.0055 

.949 

.51723 

957 

.56962 

952 

•99453 

I, 

.0055 

2.950 

9.52681 

958 

9.57915 

953 

0.99454 

1,1 

1.0055 

0,1 

u 

tan  ad  u 

«Fo' 

sec  gd  u 

•  Fo' 

sin  od  u 

«Fo' 

esc  od  u 

-Fo1 

SMITHSONIAN  TABLES 


164 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

»Fo' 

cosh  u 

,F0' 

tanh  u 

«F0' 

coth  u 

«F0' 

2.950 

9.52681 

958 

9.57915 

953 

0.99454 

1.0055 

0,1 

\  .951 

•  53639 

959 

.58868 

954 

.99455 

•  0055 

X.952 

.54598 

960 

.55822 

955 

.99456 

.0055 

•  953 

•55559 

961 

.60777 

956 

•99457 

.0055 

•954 

.56520 

962 

.61733 

957 

•99458 

.0055 

2.955 
.956 

9.57482 
.58445 

963 
964 

9.62600 
.63648 

957 

958 

0-99459 
.99460 

1.0054 
.0054 

0,1 

.957 

•59410 

965 

.64607 

959 

.99461 

.0054 

.958 

.60375 

966 

.65567 

960 

.99462 

.0054 

•959 

.61341 

967 

.66528 

961 

.99463 

.0054 

2.960 

9.62308 

967 

9.67490 

962 

0.99464 

1.0054 

0,1 

.961 

.63276 

968 

.68452 

963 

.99465 

•  0054 

.962 

.64245 

969 

.69416 

954 

.99467 

.0054 

.963 

•65214 

970 

.70381 

965 

.99468 

.0054 

.964 

.66185 

971 

.71347 

966 

.99469 

.0053 

2.965 

9.67157 

972 

9.72313 

967 

0.99470 

1.0053 

0,1 

.966 

.68130 

973 

.73281 

968 

.99471 

.0053 

.967 

.69104 

974 

.74249 

969 

.99472 

.0053 

.968 

.70078 

975 

.75219 

970 

.99473 

.0053 

.969 

.71054 

976 

.76190 

971 

•99474 

IO 

.0053 

2.970 

9.72031 

977 

9.77l6l 

972 

0.99475 

1,0 

1.0053 

0,1 

.971 

.73008 

978 

.78134 

973 

.99476 

1,0 

.0053 

.972 

.73987 

979 

.79107 

974 

•99477 

1,0 

.0053 

.973 

.74967 

980 

.80082 

975 

•99478 

1,0 

.0052 

.974 

.75947 

.81057 

976 

•99479 

1,0 

.0052 

2.975 

9.76929 

982 

9.82034 

977 

0.99480 

1,0 

1.0052 

0,1 

.976 

.77911 

983 

.83011 

978 

.09481 

1,0 

.0052 

•977 

.78895 

984 

.83989 

979 

.99482 

1,0 

.0052 

.978 

.79879 

985 

.84969 

980 

.99483 

1,0 

.0052 

•979 

.80865 

986 

.85949 

p8l 

.99484 

1,0 

.0052 

2.980 

9.81851 

987 

9.86930 

982 

0.99485 

1,0 

1.0052 

0,1 

.981 

.82839 

988 

.87913 

983 

.99486 

I,O 

.0052 

.982 

•83827 

989 

.88896 

984 

.99487 

1,0 

.0052 

.983 

.84816 

990 

.89880 

985 

.99488 

1,0 

.0051 

.984 

•85807 

991 

.90866 

986 

•99489 

1,0 

.0051 

2.985 

9.86798 

992 

9.91852 

987 

0.99490 

1,0 

1.0051 

0,1 

.986 

.87790 

993 

.92839 

988 

•99491 

1,0 

.0051 

.987 

.88784 

994 

.93828 

989 

•99492 

1,0 

.0051 

.988 

.89778 

995 

.94817 

990 

•99493 

1,0 

.0051 

.989 

.90773 

996 

.95807 

991 

•99495 

1,0 

.0051 

2.990 

9.91770 

997 

9.96798 

992 

0.99496 

1,0 

1.0051 

0,1 

.991 

.92767 

998 

•97791 

993 

•99497 

1,0 

•  0051 

•  992 

.93765 

999 

.98784 

994 

.99498 

I,O 

•  0051 

•  993 

.94765 

IOOO 

.99778 

995 

•99499 

1,0 

.0050 

•994 

.95765 

IOOI 

10.00774 

996 

•99500 

1,0 

.0050 

2.  995 

9.96766 

IOO2 

10.01770 

997 

0.99501 

1,0 

1.0050 

0,1 

.996 

.97768 

1003 

.02767 

9C8 

.09502 

1,0 

.0050 

•  997 

.98772 

1004 

•03765 

999 

•99503 

1,0 

.0050 

.998 

.99776 

1005 

.04765 

IOOO 

.99504 

1,0 

.0050 

.999 

10.00781 

IO06 

.05765 

IOOI 

.99504 

1,0 

.0050 

3.000 

10.01787 

IOO7 

10.06766 

IO02 

0.99505 

1,0 

1.0050 

0,1 

u 

tan  gd  u 

wF0' 

sec  gd  u 

«F0' 

sin  gd  u 

«F0' 

esc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


165 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

O»FO' 

tanhu 

«FO' 

coth  u 

»F0' 

3.00 

10.0179 

IO07 

10.0677 

IOO2 

0.99505 

9,9 

1.0050 

1,0 

.01 

10.  1191 

IOI7 

10.1683 

1012 

•99515 

9,7 

.0049 

1,0 

.02 

IO.22I2 

IO27 

10.2700 

IO22 

.99525 

9,5 

.0048 

I,O 

.03 

10.3245 

1037 

10.3728 

1032 

.99534 

9,3 

.0047 

0,9 

.04 

IO.4287 

1048 

10.4765 

1043 

•99543 

9,1 

.0046 

0,9 

3-05 

10.5340 

1058 

10.5814 

1053 

0.99552 

8,9 

1.0045 

0,9 

.06 

10.6403 

1069 

10.6872 

1064 

.99561 

8,8 

.0044 

0,9 

.07 

10.7477 

1079 

10.7942 

1075 

.99570 

8,6 

.0043 

0,9 

.08 

10.8562 

1000 

10.0022 

1086 

.99578 

8,4 

.0042 

0,8 

.09 

10.9658 

IIOI 

11.0113 

1097 

.99587 

8,2 

.0041 

0,8 

3-10 

11.0765 

III2 

11.1215 

1108 

0-99595 

8,1 

1.0041 

0,8 

.11 

11.1882 

1123 

11.2328 

1119 

.99603 

7,9 

.0040 

0,8 

.12 

11.3011 

1135 

11-3453 

1130 

.09611 

7,8 

.0039 

0,8 

•13 

11.4151 

1146 

11.4588 

1142 

.99618 

7,6 

.0038 

0,8 

•14 

H.5303 

1157 

n.5736 

ii53 

.99626 

7,5 

.0038 

0,8 

3-15 

13.6466 

1169 

11,6895 

1165 

0.99633 

7,3 

1.0037 

o,7 

.16 

11.7641 

1181 

11.8065 

1176 

.99641 

7,2 

.0036 

o,7 

.17 

11.8827 

1192 

11.9247 

1188 

.99648 

7,o 

.0035 

o,7 

.18 

12.0025 

1204 

12.0442 

1  200 

.99655 

6,9 

•  0035 

o,7 

.19 

I2~  1236 

1216 

12.1648 

1212 

.99662 

6,8 

.0034 

o,7 

3-20 

12.2459 

1229 

12.2866 

1225 

0.99668 

6,6 

1.0033 

0,7 

.21 

12.3694 

1241 

12.4097 

1237 

•99675 

6,5 

.0033 

o,7 

.22 

12.4941 

1253 

12.5340 

1249 

.99681 

6,4 

.0032 

0,6 

•23 

I2.62OO 

1266 

12.6596 

1262 

.99688 

6,2 

.0031 

0,6 

.24 

12.7473 

1279 

12.7864 

1275 

.99694 

6,1 

.0031 

0,6 

3-25 

12.8758 

1291 

12.9146 

1288 

0.99700 

6,0 

1.0030 

0,6 

.26 

13.0056 

1304 

13.0440 

1301 

.99706 

5,9 

.0030 

0,6 

.27 

13-1367 

1317 

13.1747 

1314 

•99712 

5,8 

.0029 

0,6 

.28 

13.2691 

I33i 

13.3067 

1327 

.99717 

5,6 

.0028 

0,6 

.29 

13.4028 

1344 

I3-440I 

1340 

.99723 

5,5 

.0028 

0,6 

3-30 

13-5379 

1357 

13.5748 

1354 

0.09728 

5,4 

1.0027 

o,5 

•31 

13.6743 

1371 

13-7108 

1367 

•99734 

5,3 

.0027 

o,5 

•32 

13.8121 

1385 

13-8483 

1381 

.99739 

5,2 

.0026 

o,5 

•  33 

13.9513 

1399 

13.9871 

1395 

.99744 

5,1 

.0026 

o,5 

•34 

14.0918 

I4U 

14.1273 

1409 

•99749 

5,o 

.0025 

o,5 

3-35 

14.2338 

1427 

14.2689 

1423 

0.99754 

4,9 

1.0025 

o,5 

.36 

14.3772 

1441 

14.4120 

1438 

•99759 

4,8 

.0024 

o,5 

•  37 

14-5221 

1456 

14.5565 

1452 

.99764 

4,7 

.0024 

o,5 

.38 

14.6684 

1470 

14.7024 

1467 

.99768 

4,6 

.0023 

0,5 

•  39 

14.8161 

1485 

14.8498 

1482 

•99773 

4,5 

.0023 

o,5 

3-40 

14.9654 

1500 

14.9987 

1497 

0.99777 

4,4 

I.OO22 

0,4 

.41 

15.1161   1515 

15.1491 

1512 

.99782 

4^4 

.OO22 

0,4 

.42 

IS.2'&\    1530 

J.5.30H 

1527 

.99786 

4,3 

.0021 

0,4 

•43 

I5.422T     1545 

15.4545 

1542 

.99790 

4,2 

.OO2I 

0,4 

.44 

15."      I56l 

15.6095 

1558 

.99795 

4,1 

.O02I 

0,4 

3-45 

15.734-     1577 

1-5.7661 

1573 

0.99799 

4,0 

I.OO20 

0,4 

.46 

15.8928    1592 

15.9242 

1589 

.99803 

3,9 

.002O 

0,4 

•  47 

I6.O528 

1608 

16.0839 

1605 

.99807 

3,9 

.OOI9 

0,4 

.48 

16.2145 

1625 

16.2453 

1621 

.99810 

3,8 

.OOI9 

0,4 

.49 

16.3777 

1641 

16.4082 

1638 

.99814 

3,7 

.OOI9 

0,4 

3.50 

16.5426 

,1657 

16.5728 

1654 

0.99818 

3*6 

I.OOI8 

0,4 

u 

tan  gd  u 

-Fo' 

sec  od  u 

«FO' 

sin  gd  u 

H  F..' 

csc  gd  u 

•  FV 

SMITHSONIAN  TABLES 


166 


Natural  Hyperbolic  Functions. 


u 

sinh  u 

w  Fo' 

cosh  u 

«F0' 

tanh  u 

•  ft 

coth  u 

«F0' 

/  3.50 

16.5426 

1657 

16.5728 

1654 

0.90818 

3,6 

l.OOiS 

0,4 

.51 

16.7092 

1674 

16.7391 

1671 

.99821 

3,6 

.0018 

0,4 

.52 

16.8774 

1691 

16.9070 

1688 

.99825 

3,5 

.0018 

0,4 

.53 

17.0473 

1708 

17.0766 

1705 

.99828 

3,4 

.0017 

0,3 

.54 

17.2190 

1725 

17.2480 

1722 

.99832 

3,4 

.0017 

0,3 

3-55 

17.3923 

1742 

17.4210 

1739 

0.99835 

3,3 

I.OOI7 

0,3 

.56 

17.5674 

I76O 

17.5958 

1757 

.99838 

3,2 

.0016 

o,3 

•  57 

17.7442 

1777 

17.7724 

1774 

.99842 

3,2 

.0016 

0,3 

.58 

17.9228 

1795 

17.9507 

1792 

.99845 

3,1 

.0016 

o,3 

•  59 

I8.I032 

1813 

18.1308 

1810 

.99848 

3,0 

.0015 

o,3 

3-60 

18.2855 

1831 

18.3128 

1829 

0.99851 

3,0 

I.OOI5 

o,3 

.61 

18.4695 

1850 

18.4966 

1847 

.99854 

2,9 

.0015 

0,3 

.62 

18.6554 

1868 

18.6822 

1866 

.99857 

2,9 

.0014 

0,3 

•  63 

18.8432 

1887 

18.8697 

1884 

.99859 

2,8 

.0014 

o,3 

.64 

19.0328 

1906 

19.0590 

1903 

.99862 

2,8 

.0014 

0,3 

3.65 

19.2243 

1925 

19.2503 

1922 

0.99865 

2,7 

I.OOI4 

o,3 

.66 

19.4178 

1944 

19-4435 

1942 

.99868 

2,6 

.0013 

o,3 

.67 

19.6132 

1964 

19-6387 

1961 

.99870 

2,6 

.0013 

o,3 

.68 

19.8106 

1984 

19.8358 

1981 

.99873 

2,5 

.0013 

o,3 

.69 

20.0099 

2003 

20.0349 

200  1 

.99875 

2,5 

.OOI2 

0,2 

3.70 

20.2113 

2024 

20.2360 

2021 

0.99878 

2,4 

I.OOI2 

0,2 

•  71 

20.4U7 

2044 

20.4391 

2041 

.99880 

2,4 

.OOI2 

0,2 

.72 

2O.62OI 

2064 

20.6443 

2O52 

.99883 

2,3 

.OOI2 

0,2 

•  73 

20.8276 

2085 

20.8516 

2083 

.99885 

2,3 

.OOI2 

0,2 

•  74 

21.0371 

2106 

21.0609 

2IO4 

.99887 

2,3 

.OOII 

0,2 

3-75 

21.2488 

,  2127 

21.2723 

2125 

0.99889 

2,2 

I.OOII 

0,2 

.76 

21.4626 

2149 

21.4859 

2146 

.99892 

2,2 

.OOII 

0,2 

•  77 

21.6785 

2170 

21.7016 

2168 

.99894 

2,1 

.0011 

0,2 

.78 

21.8966 

2192 

21.9194 

2190 

.5^896 

2,1 

.0010 

0,2 

•  79 

22.1169 

2214 

22.1395 

2212 

.99898 

2,0 

.0010 

0,2 

3-80 

22.3394 

2236 

22.3618 

2234 

0.99900 

2,0 

I.  0010 

0,2 

.81 

22.5641 

2259 

22.5863 

2256 

.99902 

2,0 

.0010 

0,2 

.82 

22./9II 

2281 

22.8131 

2279 

.99004 

1,9 

.0010 

0,2 

.83 

23.0204 

2304 

23.0421 

2302 

.99905 

i,9 

.0009 

0,2 

.84 

23.2520 

2327 

23.2735 

2325 

.99908 

1,8 

.0009 

0,2 

3.85 

23.4859 

2351 

23.5072 

2349 

0.99909 

1,8 

1.0009 

0,2 

.86 

23.7221 

2374 

23.7432 

2372 

.99911 

1,8 

.0009 

0,2 

.87 

23.9608 

2398 

23.9816 

2396 

.99913 

i,7 

.0009 

0,2 

.88 

24.2018 

2422 

24.2224 

24'20 

•99915 

i,7 

.0009 

0,2 

.89 

24.4452 

2447 

24.4657 

2445 

.99916 

i,7 

.0008 

0,2 

3-90 

24.6911 

2471 

24.7H3 

2469 

0.09918 

1,6 

1.0008 

0,2 

.91 

24.9395 

2496 

24.9595 

2494 

.99920 

1,6 

.0008 

O,2 

.92 

25.1903 

2521 

25.2101 

2519 

.99921 

1,6 

.0008 

0,2 

•93 

25.4437 

2546 

25-4633 

2544 

.90923 

,5 

.0008 

O,2 

•94 

25.6906 

2572 

25.7190 

2570 

.99924 

,5 

.0008 

0,2 

3.95 

25.9581 

2598 

25-9773 

2596 

0.99926 

,5 

1.0007 

0,1 

.96 

26.2191 

2624 

26.2382 

2622 

.90927 

,5 

.0007 

0,1 

.97 

26.4828 

2650 

26.5017 

2648 

.99929 

,4 

.0007 

0,1 

.98 

26.7492 

2677 

26.7679 

2675 

.99930 

1,4 

.0007 

0,1 

.99 

27.0182 

2704 

27.0367 

27O2 

.99932 

1,4 

.0007 

0,1 

4.00 

27.2899 

2731 

27.3082 

2729 

0.99933 

1,3 

1.0007 

0,1 

u 

tan  gd  u 

«FO' 

sec  gd  u 

<-Fo' 

sin  gd  u 

wF0' 

csc  gd  u 

«FO' 

SMITHSONIAN  TABLES 


167 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

«FO' 

tanh  u 

-  Fo' 

coth  u 

«  Fo' 

4.00 

27.2899 

2731 

27.3082 

2729 

0.99933 

1-3 

I.OOO7 

0,1 

.01 

27.5644 

2758 

27.5825 

2756 

.95934 

i,3 

.0007 

.02 

27.8416 

2786 

27.8595 

2784 

.99936 

1,3 

.0006 

•03 

28.1216 

2814 

28.1393 

2812 

•99937 

1,3 

.0006 

.04 

28.4044 

2842 

28.4220 

2840 

.99938 

1,2 

.0006 

4.05 

28.6900 

2871 

28.7074 

2869 

0.99939 

,2 

I.  0006 

0,1 

.06 

28.9785 

2900 

28.9958 

2898 

.99941 

,2 

.0006 

.07 

29.2699 

2929 

29.2870 

2927 

.95942 

,2 

.0006 

.08 

2958 

29.5812 

2956 

•99943 

f 

.0006 

.09 

29.8616 

2088 

29.8783 

2986 

.99944 

j 

.0006 

4.10 

30.1619 

3018 

30.1784 

3016 

0.99945 

I, 

I.OOO5 

0,1 

.u 

30.4652 

3048 

30.4816 

3047 

.99946 

I, 

.0005 

.12 

30.7715 

3079 

30.7877 

3077 

•99947 

I, 

.0005 

.13 

31.0809 

3110 

31.0970 

3108 

.99948 

1,0 

.0005 

.14 

31.3934, 

3141 

31.4094 

3i39 

•99949 

1,0 

.0005 

4-lS 

3L709I 

3172 

31.7249 

3171 

0.09950 

I,O 

1.0005 

0,1 

.16 

32.0280 

3204 

32.0436 

3203 

•99951 

I,O 

.0005 

.17 

32.3500 

3237 

32.3655 

3235 

.99952 

1,0 

.0005 

.18 

32.6753 

3269 

32.6906 

3268 

•99953 

0,9 

.0005 

.19 

33.0038 

3302 

33.0190 

3300 

•99954 

0,9 

.0005 

4.20 

33-3357 

3335 

33.3507 

3334 

0.99955 

0,9 

1.0004 

0,1 

.21 

33.6708 

3369 

33.6857 

3367 

.99956 

0,9 

.0004 

.22 

34.0094 

3402 

34.0241 

3401 

.99957 

o,9 

.0004 

•23 

34.3513 

3437 

34.3659 

3435 

.99958 

0,8 

.0004 

.24 

34.6967 

3471 

34.7IH 

3470 

.99958 

0,8 

.0004 

4-25 

35.0456 

3506 

35.0598 

3505 

0.99959 

0,8 

I.OOO4 

0,1 

.26 

35-3979 

354  1 

35.4121 

3540 

.99060 

0,8 

.0004 

.27 

35.7538 

3577 

35.7678 

3575 

.99061 

0,8 

.0004 

.28 

36.1133 

3613 

36.1271 

3611 

.99962 

0,8 

.0004 

.29 

36.4764 

3649 

36.4901 

3648 

.99962 

0,8 

.0004 

4-30 

36.8431 

3686 

36.8567 

3684 

0.90963 

o,7 

1.0004 

0,1 

•31 

37.2135 

3723 

37.2270 

3721 

•99964 

o,7 

.0004 

•32 

37.5877 

376o 

37.6010 

3759 

•99965 

o,7 

.0004 

•  33 

37.9656 

3798 

37.9787 

3797 

.99965 

o,7 

.0003 

•34 

38.3473 

3836 

38.3603 

3835 

.99966 

o,7 

.0003 

4-35 

38.7328 

3875 

38.7457 

3873 

0.99967 

o,7 

1.0003 

0,1 

.36 

39.1222 

3913 

39.1350 

3912 

.99967 

o,7 

.0003 

•  37 

39.5155 

3953 

39.5281 

3952 

.99968 

0,6 

.0003 

•  38 

39.9128 

3993 

39.9253 

3991 

.99969 

0,6 

.0003 

•  39 

40.3UO 

4033 

40.3264 

4031 

.99969 

0,6 

.0003 

4.40 

40.7193 

4073 

40.7316 

4072 

0.99970 

0,6 

1.0003 

0,1 

.41 

41.1287 

4114 

41.1408 

4H3 

•99970 

0,6 

.0003 

.42 

41.5421 

4155 

41.5542 

4154 

.99971 

0,6 

.0003 

•  43 

41.9598 

4197 

41.9717 

4196 

.99972 

0,6 

.0003 

.44 

42.3816 

4239 

4-'-  3934 

4238 

•99972 

0,6 

.0003 

4-45 

42.8076 

4282 

42.8193 

4281 

0.99973 

o,5 

1.0003 

0,1 

.46 

43-2380 

432-5 

43.2495 

4324 

•99973 

o,5 

.0003 

•  47 

43.6726 

4368 

43-6841 

4367 

•99974 

o,5 

.0003 

.48 

44.IH7 

4412 

44.1230 

44" 

•99974 

o,5 

.0003 

.49 

44o55I 

4457 

44.5663 

4456 

.Q997S 

0,5 

.0003 

4-50 

45.0030 

4501 

4S.OI4I 

4500 

0.99975 

0,5 

I.OOO2 

0,0 

u 

tan  gd  u 

«F0' 

sec  ad  u 

«F0' 

sin  gd  u 

•  Fo' 

csc  gd  u 

-Fo' 

SMITHSONIAN  TABUS 


168 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«Fo' 

cosh  u 

uiFu' 

tanh  u 

«Fo' 

cothu 

wF0' 

,4.50 

45.0030 

4501 

45.0141 

4500 

0.99975 

0,5 

I.OOO2 

0,0 

-51 

45.4554 

4547 

45.4664 

4546 

.99976 

0,5 

.0002 

'  .52 

45.9124 

4592 

45.9232 

459i 

.99976 

o,5 

.OOO2 

•  53 

46.3739 

4638 

46.3847 

4637 

.99977 

o,5 

.O002 

•  54 

46.8401 

4685 

46.8507 

4684 

•99977 

o,5 

.OOO2 

4-55 

47.3109 

4732 

47.3215 

473i 

0.99978 

0,4 

1.0002 

0,0 

.56 

47.7865 

478o 

47-7970 

4779 

.99978 

0,4 

.OOO2 

.57 

48.2669 

4828 

48.2772 

4827 

.99979 

0,4 

.OOO2 

.58 

48.7521 

4876 

48.7623 

4875 

.99979 

0,4 

.O002 

•  59 

49.2421 

4925 

49.2523 

4924 

.99979 

0,4 

.OOO2 

4.60 

49.7371 

4975 

49.7472 

4974 

0.99080 

0,4 

I.OOO2 

0,0 

.61 

50.2371 

5025 

50.2471 

5024 

.99980 

0,4 

.OOO2 

.62 

50.7421 

5075 

50.7519 

5074 

.99981 

0,4 

.OOO2 

•  63 

51.2522 

5126 

51.2619 

5125 

.99981 

0,4 

.OOO2 

.64 

51.7673 

5178 

51.7770 

5177 

.99981 

0,4 

.OOO2 

4.65 

52.2877 

5230 

52.2973 

5229 

0.99982 

0,4 

I.OOO2 

0,0 

.66 

52.8133 

5282 

52.8228 

5281 

.99982 

0,4 

.OOO2 

.67 

53-3442 

5335 

53.3536 

5334 

.99982 

0,4 

.OOO2 

.68 

53.8804 

5389 

53.8897 

5388 

.99983 

o,3 

.O002 

.69 

54.4220 

5443 

54.4312 

5442 

.99983 

0,3 

.OOO2 

4.70 

54-9690 

5498 

54.9781 

5497 

0.99983 

0,3 

I.OOO2 

0,0 

•  71 

55.5216 

5553 

55-5306 

5552 

.99984 

0,3 

.OOO2 

.72 

56.0797 

5609 

56.0886 

5608 

.99984 

o,3 

.OOO2 

•  73 

56.6434 

5665 

56.6522 

5664 

.99984 

o,3 

.OOO2 

•  74 

57.2127 

5722 

57.2215 

5721 

.99985 

0,3 

.OOO2 

4-75 

57.7878 

578o 

57.7965 

5779 

0.99985 

0,3 

I.OOOI 

0,0 

.76 

58.3687 

5838 

58.3772 

5837 

.99985 

0,3 

.OOOI 

•  77 

58.9554 

5896 

58.9639 

5896 

.99986 

0,3 

.OOOI 

•  78 

59.5480 

5956 

59.5564 

5955 

.99986 

o,3 

.OOOI 

•  79 

60.  1465 

6015 

60.1548 

6015 

.99986 

0,3 

.OOOI 

4.80 

60.7511 

6076 

60.7593 

6075 

0.99986 

0,3 

I.OOOI 

0,0 

.81 

61.3617 

6i37 

61.3699 

6136 

.99987 

0,3 

.OOOI 

.82 

61.9785 

6199 

61.9866 

6198 

.99987 

0,3 

.OOOI 

.83 

62.6015 

6261 

62.6095 

6260 

.99987 

0,3 

.OOOI 

.84 

63.2307 

6324 

63.2386 

6323 

.99987 

o,3 

.OOOI 

4-85 

63.8663 

6387 

63.8741 

6387 

0.99988 

0,2 

I.OOOI 

0,0 

.86 

64.5082 

6452 

64.5160 

6451 

.99988 

0,2 

.OOOI 

.87 

65.1566 

6516 

65.1643 

6516 

.99988 

0,2 

.OOOI 

.88 

65.8115 

6582 

65.8191 

6581 

.99988 

0,2 

.OOOI 

.89 

66.4730 

6648 

66.4805 

6647 

.99989 

0,2 

.OOOI 

4.90 

67.1412 

6715 

67.1486 

6714 

0.99989 

0,2 

I.OOOI 

0,0 

.91 

67.8160 

6782 

67.8234 

6782 

.99989 

0,2 

.0001 

.92 

68.4977 

6850 

68.5050 

6850 

.99989 

0,2 

.OOOI 

•93 

69.1861 

6919 

.69.1934 

6919 

•99990 

0,2 

.OOOI 

•  94 

69.8815 

6989 

69.8887 

6988 

.99990 

0,2 

.OOOI 

4-95 

70.5839 

7059 

70.5910 

7058 

0.09090 

0,2 

I.OOOI 

0,0 

.96 

71.2934 

7130 

7L3004 

7129 

.99990 

0,2 

.0001 

•  97 

72.0100 

7202 

72.0169 

7201 

.99090 

0,2 

.OOOI 

.98 

72.7338 

7274 

72.7406 

7273 

.99991 

0,2 

.OOOI 

.99 

73.4648 

7347 

73.4716 

7346 

.99991 

0,2 

.OOOI 

5-00 

74.2032 

7421 

74.2099 

7420 

0.99991 

0,2 

I.OOOI 

0,0 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

sin  gd  u 

<oFu' 

csc  gd  u 

«F0' 

SMITHSONIAN  TABLES 


169 


Natural  Hyperbolic  Functions. 


u 

sinhu 

«F0' 

cosh  u 

•  IV 

tanh  u 

«FO' 

cothu 

•  IV 

5.00 

74.2032 

7421 

74.2099 

7420 

0.99991 

0,2 

I.  0001 

0,0 

.01 

74.9490 

7496 

74.9557 

7495 

.99991 

0,2 

.0001 

.02 

75.7023 

7571 

75.7000 

7570 

.99991 

0,2 

.0001 

•  03 

76.4632 

7647 

76.4698 

7646 

.99991 

0,2 

.0001 

.04 

77-.23I8 

7724 

77.2382 

7723- 

.99992 

0,2 

.0001 

5-05 

78.0080 

7801 

78.0144 

7801 

0.99992 

0,2 

I.  0001 

0,0 

.06 

78.7921 

7880 

78.7984 

7879 

.99992 

0,2 

.0001 

.07 

79.5840 

7959 

79.5903 

7958 

.99992 

0,2 

.0001 

.08 

80.3839 

8039 

80.3901 

8038 

.99992 

0,2 

.0001 

.09 

81.1918 

8120 

81.1980 

8119 

.99992 

0,2 

.0001 

S.io 

82.0079 

8201 

82.0140 

8201 

0.99993 

0,1 

I.OOOI 

0,0 

.11 

82.8322 

8284 

82.8382 

8283 

•  99993 

0,1 

.0001 

.12 

83-6647 

8367 

83.6707 

8366 

•99993 

0,1 

.0001 

.13 

84.5056 

8451 

84.5115 

8451 

•99993 

0,1 

.0001 

.14 

85.3550 

8536 

85.3608 

8535 

•99993 

0,1 

.0001 

5.15 

86.2128 

8622 

86.2186 

8621 

0.99993 

0,1 

I.OOOI 

0,0 

.16 

87.0794 

8709 

87.0851 

8708 

•99993 

0,1 

.0001 

.17 

87.9546 

8796 

87-9603 

8795 

.99994 

0,1 

.0001 

.18 

88.8386 

8884 

88.8442 

8884 

•99994 

0,1 

.0001 

.19 

89.7315 

8974 

89.7371 

8973 

.99994 

0,1 

.0001 

5-20 

90.6334 

0064 

90.6389 

9063 

0.99994 

0,1 

I.OOOI 

0,0 

.21 

91.5443 

9155 

91.5498 

9154 

•99994 

0,1 

.0001 

.22 

92.4644 

9247 

92.4698 

9246 

.99994 

0,1 

.0001 

.23 

93.3937 

9340 

93.3991 

9339 

.99994 

0,1 

.0001 

.24 

94-3324 

9434 

94-3377 

9433 

.99994 

0,1 

.0001 

5-25 

95.2805 

9529 

95.2858 

9528 

0.00994 

0,1 

I.OOOI 

0,0 

.26 

96.2381 

9624 

96.2433 

9624 

•99995 

0,1 

.0001 

.27 

97.2054 

9721 

97.2106 

9721 

•99995 

0,1 

.0001 

.28 

98.  1824 

9819 

98.1875 

9818 

•99995 

0,1 

.0001 

.29 

99.1692 

9917 

99.1742 

9917 

•99995 

0,1 

.0001 

5.30 

100.  1659 

10017 

IOO.I7O9 

10017 

0.99995 

0,1 

I.  0000 

0,0 

-31 

101.1726 

10118 

101  .  1776 

10117 

.99995 

0,1 

.0000 

•32 

102.1895 

10219 

IO2.I944 

10219 

•99995 

0,1 

.0000 

.33 

103.2166 

10322 

103.2214 

10322 

•99995 

0,1 

.0000 

•  34 

104.2540 

10426 

104.2588 

10425 

•99995 

0,1 

.0000 

5-35 

105.3018 

I053I 

105.3065 

10530 

0.99995 

0,1 

I.OOOO 

0,0 

.36 

106.3601 

10636 

106.3648 

10636 

.99996 

0,1 

.0000 

.37 

107.4291 

10743 

107.4338 

10743 

.99996 

0,1 

.0000 

.38 

108.5088 

10851 

I08.5I34 

10851 

.99996 

0,1 

.0000 

•  39 

109.5994 

10960 

109.6040 

10960 

.99996 

0,1 

.0000 

5.40 

110.7009 

11071 

110.7055 

11070 

0.99906 

0,1 

I.OOOO 

0,0 

.41 

111.8136 

11182 

III.8l8o 

11181 

.99996 

0,1 

.0000 

.42 

H2.9375 

11294 

112.9418 

11294 

.99996 

0,1 

.0000 

•43 

114.0724 

11408 

114.0768 

11407 

.99996 

0,1 

.0000 

.44 

115.2189 

11522 

115.2233 

11522 

•99096 

0,1 

.0000 

5-45 

116.3769 

11638 

Il6.38l2 

11638 

0.99996 

0,1 

I.OOOO 

0,0 

.46 

117-5466 

H755 

117.5508 

II755 

.99006 

0,1 

.0000 

•47 

118.7280 

n873 

118.7322 

n873 

.99996 

0,1 

.0000 

.48 

119.9213 

1  1993 

119.9254 

11092 

.99997 

0,1 

.0000 

.49 

121.1265 

12113 

I2I.I307 

12113 

.99997 

0,1 

.0000 

5.50 

122.3439 

12235 

122.3480 

12234 

0.99997 

0,1 

I.OOOO 

0,0 

u 

tan  gd  u 

•  Fo' 

sec  gd  u 

-Fo' 

•in  od  u 

-Fo' 

csc  gd  u 

•*r 

SMITHSONIAN  TABLES 


170 


Natural  Hyperbolic  Functions. 


llx- 

sinh  u 

«F0' 

cosh  u 

«F0' 

tanhu 

«FO' 

coth  u 

«Fo' 

3.50 

122.3439 

12235 

122.3480 

12234 

0.90997 

0,1 

I.  0000 

0,0 

'.51 

123-5735 

12358 

123.5776 

12357 

.99997 

0,1 

.0000 

.52 

124.8155 

12482 

124.8195 

12482 

•99997 

0,1 

.0000 

.53 

I26.O7OO 

12007 

126.0739 

12607 

.99997 

0,1 

.0000 

•  54 

127.3370 

12734 

127.3410 

12734 

.99997 

0,1 

.0000 

S.S5 

I28.6l68 

12862 

128.6207 

12862 

0.99997 

0,1 

I.OOOO 

0,0 

•  56 

129.9095 

12991 

129.9133 

12991 

•99997 

0,1 

.0000 

.57 

I3I.2I5I 

13122 

131.2190 

13122 

•99997 

0,1 

.0000 

.58 

132.5339 

13254 

132.5377 

13253 

•99997 

0,1 

.0000 

•  59 

133.8659 

13387 

133.8697 

13387 

•99997 

0,1 

.0000 

5.6o 

I35.2II4 

13522 

135.2150 

13521 

0.99997 

0,1 

I.OOOO 

0,0 

.61 

136.5703 

13657 

136.5739 

13657 

•99997 

0,1 

.0000 

.62 

137.9429 

13795 

137.9465 

13794 

.99997 

0,1 

.0000 

.63 

139.3293 

13933 

I39-3329 

13933 

.99997 

0,1 

.0000 

.64 

140.7296 

14073 

140.7331 

14073 

•  99997 

0,1 

.0000 

5.65 

142.1440 

14215 

142.1475 

14214 

0.99998 

0,0 

I.OOOO 

0,0 

.66 

143.5726 

14358 

143.5761 

14357 

•99998 

0,0 

.0000 

.67 

145.0155 

14502 

145.0190 

14502 

.99998 

0,0 

.0000 

.68 

146.4730 

14648 

146.4764 

14647 

.99998 

0,0 

.0000 

.69 

147-9451 

14795 

147.9485 

14795 

.99998 

0,0 

.0000 

5.70 

149.4320 

14944 

149.4354 

14943 

0.99998 

0,0 

I.OOOO 

0,0 

•  71 

150.9339 

15094 

150.9372 

15093 

.99998 

0,0 

.0000 

.72 

152.4508 

15245 

152.4541 

15245 

.99998 

0,0 

.0000 

•  73 

153.9830 

15399 

153.9863 

15398 

.99998 

0,0 

.0000 

.74 

155.5306 

15553 

155.5338 

15553 

.99998 

0,0 

.0000 

5-75 

157.0938 

I57IO 

157.0969 

15709 

0.99998 

0,0 

I.OOOO 

0,0 

.76 

158.6726 

15868 

r58.6757 

15867 

.99998 

0,0 

.0000 

•  77 

160.2673 

16027 

160.2704 

16027 

.99998 

0,0 

.0000 

•  78 

161.8781 

16188 

161.881  I 

16188 

•99998 

0,0 

.0000 

•  79 

163  .  5O5O 

16351 

163.5080 

16350 

.99998 

0,0 

.0000 

5.8o 

165.1483 

16515 

165.1513 

16515 

0.99998 

0,0 

I.OOOO 

0,0 

.81 

166.8081 

16681 

166.8111 

16681 

.99998 

0,0 

.0000 

.82 

168.4845 

16849 

168.4875 

16848 

.99998 

0,0 

.0000 

.83 

170.1779 

17018 

170.1808 

17018 

.99998 

0,0 

.0000 

.84 

171.8882 

17189 

171.8911 

17189 

.99998 

0,0 

.0000 

5.85 

173.6158 

17362 

173-6186 

17362 

0.99998 

0,0 

I.OOOO 

0,0 

.86 

175.3006 

17536 

175.3635 

17536 

.99998 

0,0 

.0000 

.87 

I77.I23I 

I77I3 

177.1259 

17712 

.99998 

0,0 

.0000 

.88 

178.9032 

17891 

178.9060 

17890 

.99998 

0,0 

.0000 

.89 

180.7013 

18070 

180  .  7040 

18070 

.99998 

0,0 

.0000 

5-90 

182.5174 

18252 

182.5201 

18252 

0.99998 

0,0 

I.OOOO 

0,0 

.91 

184.3517 

18435 

184.3544 

18435 

•99999 

0,0 

.0000 

.92 

186.2045 

18621 

186.2072 

18620 

•99999 

0,0 

.0000 

•93 

188.0759 

18808 

188.0786 

18808 

•99999 

0,0 

.0000 

•  94 

189.9661 

18997 

189.9688 

18997 

•99999 

0,0 

.0000 

5-95 

191.8754 

19188 

191.8780 

19188 

0-99999 

0,0 

I.OOOO 

0,0 

.96 

193.8038 

I938i 

193-8064 

19380 

•99999 

0,0 

.0000 

1   .97 

195.7516 

19575 

I95.754I 

19575 

•99999 

0,0 

.0000 

.98 

197.7189 

19772 

197-7214 

19772 

.99999 

0,0 

.0000 

.99 

199.7061 

19971 

199-7086 

19971 

•99999 

0,0 

.0000 

6.00 

201.7132 

20172 

201.7156 

20171 

0.99999 

0,0 

I.OOOO 

0,0 

u 

tan  gd  u 

«FO' 

sec  gd  u 

«FO' 

sin  gd  u 

«F0' 

csc  gd  u 

«F</ 

SMITHSONIAN  TABLES 


171 


TABLE  III 


NATURAL  AND  LOGARITHMIC  CIRCULAR  FUNCTIONS 


173 


Circular  Functions. 


u 

sin  u 

wF0' 

COS  U 

«F0' 

log  sin  u 

«F0' 

log  cos  u 

«F0' 

u 

o.oooo 

O.OOOOO 

10,0 

I.OOOOO 

0,0 

CO 

-foo 

0.00000 

0,0 

0            4             tl 

O  00  OO.OO 

.0001 

.OOOIO 

.00000 

6.00000 

43429,4 

.00000 

o  oo  20.63 

.0002 

.00020 

.00000 

.30103 

21714,7 

.00000 

o  oo  41.25 

.0003 

.00030 

.00000 

.47712 

14476,5 

.00000 

o  01  01.88 

.0004 

.00040 

.00000 

.60206 

10857,4 

.00000 

o  01  22.51 

0.0005 

0.00050 

IO,O 

I.OOOOO 

0,0 

6.69897 

8685,9 

O.OOOOO 

0,0 

0  01   43-13 

.0006 

.00060 

.00000 

.77815 

7238,2 

.00000 

o  02  03.76 

.0007 

.00070 

.00000 

.84510 

6204,2 

.00000 

0  02  24.39 

.0008 

.00080 

.00000 

.90309 

5428,7 

.00000 

0  02  45.01 

.0009 

.00090 

.00000 

.95424 

4825,5 

.00000 

o  03  05.64 

0.0010 

O.OOIOO 

10,0 

I.OOOOO 

0,0 

7.00000 

4342,9 

O.OOOOO 

0,0 

o  03  26.26 

.OOII 

.OOIIO 

.00000 

.04139 

3948,1 

.00000 

o  03  46.89 

.0012 

.00120 

.00000 

.07918 

3619,1 

.00000 

o  04  07.52 

.0013 

.00130 

.00000 

.11304 

3340,7 

.00000 

o  04  28.14 

.0014 

.00140 

.00000 

.  14613 

3102,1 

.00000 

0  04  48.77 

0.0015 

0.00150 

IO,O 

I.OOOOO 

0,0 

7.17609 

2895,3 

O.OOOOO 

0,0 

o  05  09.40 

.0016 

.00160 

.00000 

.20412 

2714,3 

.00000 

o  05  30.02 

.0017 

.00170 

.00000 

.23045 

2554,7 

.00000 

o  05  50.65 

.0018 

.00180 

.00000 

.25527 

2412,7 

.00000 

o  06  11.28 

.0019 

.00190 

.00000 

.27875 

2285,8 

.00000 

o  06  31.90 

O.OO2O 

0.00200 

IO,O 

I.OOOOO 

0,0 

7.30103 

2171,5 

O.OOOOO 

0,0 

o  06  52.53 

.0021 

.00210 

.00000 

.32222 

2068,1 

.00000 

o  07  13.16 

.0022 

.00220 

.00000 

.34242 

1974,1 

.00000 

o  07  33-78 

.0023 

.00230 

.00000 

.36173 

1888,2 

.00000 

o  07  54.41 

.0024 

.00240 

.00000 

.38021 

1809,6 

.00000 

o  08  15.04 

0.0025 

0.00250 

IO,O 

I.OOOOO 

0,0 

7-39794 

1737,2 

O.OOOOO 

0,0 

o  08  35.66 

.0026 

.00260 

.00000 

.41497 

1670,4 

.00000 

o  08  56.29 

.0027 

.O027O 

.00000 

.43136 

1608,5 

.00000 

o  09  16.91 

.0028 

.O0280 

.00000 

.44716 

I55i,o 

.00000 

o  09  37-54 

.0029 

.O02OO 

.00000 

.46240 

1497,6 

.00000 

o  09  58.17 

0.0030 

0.00300 

IO,O 

I.OOOOO 

0,0 

7.47712 

1447,6 

0.00000 

0,0 

o  10  18.79 

.0031 

.00310 

.00000 

.49136 

1400,9 

.00000 

o  10  39.42 

.0032 

.00320 

0.99999 

.50515 

1357,2 

.00000 

0   II   00.05 

.0033 

.00330 

.99999 

.51851 

1316,0 

.00000 

on  20.67 

.0034 

.00340 

•99999 

.53148 

1277,3 

.00000 

o  ii  41.30 

0.0035 

0.00350 

10,0 

0.99999 

0,0 

7.54407 

1240,8 

0.00000 

0,0 

O    12  01.93 

.0036 

.00360 

.99999 

.55630 

1206,4 

.00000 

O    12   22.55 

.0037       .00370 

•99999 

.56820 

ii73,8 

.00000 

0   12  43.18 

.0038 

.00380 

•99999 

.57978 

1142,9 

.00000 

o  13  03.81 

.0039 

.00390 

•99999 

.59106 

1113,6 

.00000 

o  13  24.43 

0.0040 

O.OO4OO 

10,0 

0.99999 

0,0 

7.60206 

1085,7 

O.OOOOO 

0,0 

o  13  45-06 

.0041 

.OO4IO 

•  99999 

.61278 

1059,2 

.00000 

0  14  05.69 

.0042 

.OO42O 

.99999 

.62325 

1034,0 

.00000 

o  14  26.31 

.0043 

.00430 

.99999 

.63347 

1010,0 

.00000 

o  14  46.94 

.0044 

.00440 

.99999 

.64345 

087,0 

.00000 

o  15  07.57 

0.0045 

O.O045O 

10,0 

0.99999 

0,0 

7.65321 

965,1 

O.OOOOO 

0,0 

o  15  28.19 

.0046 

.OO40O 

.99999 

.66276 

944,1 

.00000 

o  15  48.82 

.0047 

.00470 

.99999 

.67210 

9^4,0 

.00000 

o  16  09.44 

.0048 

.00480 

•99999 

.68124 

904,8 

.00000 

o  16  30.07 

.0049 

.00490 

•  99999 

.69019 

886,3 

9.99999 

o  16  50.70 

0.0050 

0.00500 

10,0 

0.99999 

0,0 

7.69897 

868,6 

9.99999 

0,0 

o  17  11.32 

u 

isinhiu 

-FO' 

cosh  iu 

-FO' 

i««,'inh  iu 

«FO' 

log  cosh  iu 

«F0' 

u 

log      . 

SMITHSONIAN  TABLES 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«F0' 

u 

0.0056 

0.00500 

IO,0 

0.99999 

0,0 

7.09897 

868,6 

9.99999 

0,0 

0    /     // 

o  17  11.32 

.0051 

.00510 

.99999 

0,1 

.70757 

851,6 

.99999 

o  17  31.95 

.0052 

.OO52O 

.99999 

.71600 

835,2 

.99999 

o  17  52.58 

•  0053 

.00530 

•99999 

.72427 

819,4 

•99999 

o  18  13.20 

.0054 

.00540 

.99999 

.73239 

804,2 

.99999 

o  18  33.83 

0.0055 

0.00550 

10,0 

0.09998 

0,1 

7.74036 

789,6 

9.99999 

0,0 

o  18  54.46 

.0056 

.00560 

.99998 

.74819 

775,5 

•99999 

o  19  15.08 

.0057 

.00570 

.99998 

.75587 

76i,9 

•99999 

o  19  35-71 

.0058 

.00580 

.99998 

.76343 

748,8 

•99999 

o  19  56.34 

.0059 

.00590 

.99998 

•77085 

736,1 

•99999 

o  20  16.96 

0.0060 

0.00600 

IO,0 

0.99998 

0,1 

7.77815 

723,8 

9.99999 

0,0 

0  20  37-59 

.0061 

.00610 

.99998 

•78533 

7ii,9 

.99999 

0  20  58.22 

.0062 

.00620 

.99998 

•79239 

7oo,5 

•99999 

0  21  18.84 

.0063 

.00630 

.99998 

689,3 

.99999 

0  21  39.47 

.0064 

.00640 

.99998 

.80618 

678,6 

•99999 

O  22  OO.O9 

0.0065 

0.00650 

10,0 

0.09998 

0,1 

7.81291 

668,1 

9.99999 

0,0 

O  22  2O.72 

.0066 

.00660 

.99998 

.81954 

658,0 

.99999 

0  22  41.35 

.0067 

.00670 

.99998 

.82607 

6148,2 

•99999 

o  23  01.97 

.0068 

.00680 

.09998 

.83251 

638,7 

•99999 

o  23  22.60 

.0069 

.00690 

.99998 

.83885 

629,4 

•99999 

o  23  43-23 

0.0070 

0.00700 

10,0 

0.09998 

0,1 

7.84509 

620,4 

9.99999 

0,0 

o  24  03.85 

.0071 

.00710 

.99997 

.85125 

611,7 

.99999 

o  24  24.48 

.0072 

.00720 

.99997 

•85733 

603,2 

•99999 

o  24  45  .  i  i 

.0073 

.00730 

.99997 

.86332 

594,9 

.99909 

o  25  05.73 

.0074 

.00740 

.99997 

.86923 

586,9 

•99999 

o  25  26.36 

0.0075 

0.00750 

10,0 

0.99997 

0,1 

7.87506 

579,0 

9.99909 

0,0 

o  25  46.99 

.0076 

.00760 

.99997 

.88081 

571,4 

.99999 

o  26  07.61 

.0077 

.00770 

.99997 

.88649 

564,0 

•99999 

o  26  28.24 

.0078 

.00780 

.99997 

.89209 

556,8 

.99999 

o  26  48.87 

.0079 

.00790 

.99997 

.89762 

549,7 

•99999 

o  27  09-49 

0.0080 

0.00800 

10,0 

0.99997 

0,1 

7.90309 

542,9 

9.90999 

0,0 

o  27  30.12 

.0081 

.00810 

.99997 

.908148 

536,2 

•99999 

o  27  50.74 

.0082 

.00820 

.99997 

.91381 

529,6 

•99999 

o  28  11.37 

.0083 

.00830 

.99997 

.91907 

523,2 

•99999 

o  28  32.00 

.0084 

.00840 

.09996 

.92427 

517,0 

.99998 

o  28  52.62 

0.0085 

0.00850 

IO,O 

0.99996 

0,1 

7.92041 

510,9 

9.99998 

0,0 

o  29  13.25 

.0086 

.00860 

.99996 

•93449 

505,0 

.99998 

o  29  33.88 

.0087 

.00870 

.99996 

•93951 

499,1 

.99998 

o  29  54-50 

.0088 

.00880 

.99996 

.94448 

493,5 

.99998 

o  30  15.13 

.0089 

.00890 

.99996 

.94938 

488,0 

•99998 

o  30  35.76 

0.0090 

0.00000 

10,0 

0.99996 

0,1 

7.95424 

482,5 

9.99998 

0,0 

o  30  56.38 

.0091 

.00910 

.99996 

•95904 

477,2 

.99998 

o  31  17.01 

.0092 

.00920 

.99996 

.96378 

472,0 

.99998 

o  31  37.64 

.0093 

.00930 

.99996 

.96848 

467,0 

.99998 

o  31  58.26 

.0094 

.00940 

.99996 

.97312 

462,0 

.99998 

o  32  18.89 

0.0095 

0.00950 

10,0 

0.99995 

0,1 

7.97772 

457,1 

9.99998 

0,0 

o  32  39-52 

.0096 

.00960 

•99995 

.98226 

452,4 

.99998 

o  33  00.14 

.0097 

.00970 

•99995 

.98676 

447,7 

.99998 

o  33  20.77 

.0098 

.00980 

•99995 

.99122 

443,1 

.99998 

o  33  41.40 

.0099 

.00990 

•99995 

.99563 

438,7 

.99998 

o  34  02.02 

O.OIOO 

0.01000 

10,0 

0.99995 

0,1 

7.99999 

434,3 

9.99998 

0,0 

0  34  22.65 

u 

-isinhiu 

«F0' 

cosh  iu 

-FO' 

,__sinh  iu 

«F0' 

log  cosh  iu 

«FO' 

u 

log   . 

SMITHSONIAN  TABLES 


175 


Circular  Functions. 


u 

sin  u 

•  IV 

COS  U 

w  Fo'       log  sin  u 

«  Fo' 

log  cos  u 

-Fo' 

U 

O.OIOO 

O.OIOOO 

10,0 

0.99995 

0,1 

7.99999 

434,3 

9.99998 

0,0 

o°34'  22"65 

.OIOI 

.OIOIO 

•  99995 

8.00431 

430,0 

.99998 

o  34  43-27 

.0102 

.OIO2O 

.99995 

.00859 

425,8 

.99998 

o  35  03.00 

.0103 

.OI03O 

.99995 

.01283 

421,6 

•99998 

o  35  24.53 

.0104 

.OI040 

.99995 

.01703 

417,6 

.99998 

0  35  45-15 

0.0105 

0.01050 

10,0 

0.99994 

0,1 

8.02II8 

413,6 

9.99998 

0,0 

o  36  05.78 

.0106 

.01000 

.99994 

.02530 

409,7 

.99998 

o  36  26.41 

.0107 

.OIO/O 

.99994 

.02938 

405,9 

.99998 

G  ^6  47.03 

.0108 

.OIOSO 

.99994 

.03342 

402,1 

•99997 

o  37  07.66 

.0109 

.OIOQO 

.99994 

.03742 

398,4 

.99997 

0  37  28.29 

O.OIIO 

O.OIIOO 

10,0 

0.99994 

0,1 

8.04138 

394,8 

9.99997 

0,0 

o  37  48.91 

.OIII 

.OHIO 

•99994 

•04531 

39i,2 

•99997 

o  38  09.54 

.0112 

.OI  120 

.99994 

.04921 

387,7 

.99997 

o  38  30.17 

.0113 

.01130 

.99994 

•05307 

384,3 

•99997 

o  38  50.79 

.0114 

.OII4O 

.99994 

.05690 

380,9 

•99997 

o  39  11.42 

0.0115 

O.OII5O 

IO,O 

0.99993 

0,1 

8.06069 

377,6 

9-99997 

0,0 

o  39  32.05 

.0116 

.OII60 

•99993 

.06445 

374,4 

•99997 

0,1 

o  39  52.67 

.0117 

.OII7O 

•99993 

.05818 

371,2 

•99997 

o  40  13.30 

.0118 

.OIlSo 

•99993 

.07187 

368,0 

.99997 

o  40  33.92 

.0119 

.OIIOO 

•99993 

.07554 

364,9 

,99997 

o  40  54-55 

O.OI20 

O.OI2OO 

IO,0 

0.99993 

O,I 

8.07917 

36i,9 

9.99997 

0,1 

o  41  15.18 

.OI2I 

.OI2IO 

•99993 

.08277 

358,9 

•99997 

o  41  35.80 

.0122 

.OI22O 

.99993 

.08635 

356,0 

•99997 

o  41  56.43 

.0123 

.01230 

.99992 

.08989 

353,1 

•99997 

o  42  17.06 

.OI24 

.01240 

.99992 

.09341 

350,2 

•99997 

o  42  37-68 

0.012-5 

O.OI25O 

10,0 

0.99992 

0,1 

8.09690 

347,4 

9.99997 

0,1 

o  42  58.31 

.0126 

.OI2OO 

.99992 

.10036 

344,7 

•99997 

o  43  i8.94 

.OI27 

.OI27O 

•99992 

•  10379 

342,0 

.9999^ 

o  43  39.56 

.0128 

.OI28O 

.99992 

.  10720 

339,3 

.95996 

o  44  00.19 

.OI29 

.01290 

.99992 

.11058 

336,6 

•99996 

o  44  20.82 

0.0130 

O.OI3OO 

10,0 

0.99992 

0,1 

8.  i  1393 

334,1 

9-99996 

0,1 

o  44  41.44 

.0131 

.01310 

.99991 

.11726 

331,5 

.99996 

o  45  02.07 

.OI32 

.OI32O 

.99991 

.  12056 

329,0 

.99996 

0  45  22.70 

•0133 

.01330 

.99991 

.12384 

326,5 

.99996 

0  45  43-32 

.0134 

.01340 

.99991 

.12709 

324,1 

.99996 

0  46  03-95 

0.0135 

O.OI35O 

10,0 

0.09991 

0,1 

8.  13032 

321,7 

9.99996 

0,1 

o  46  24.57 

.0136 

.01360 

.99991 

•  13353 

319,3 

.99996 

o  46  45.20 

.0137 

.01370 

•99991 

.  13671 

317,0 

.99996 

0  47  05.83 

.0138 

.01380 

•99990 

.13987 

314,7 

.99996 

o  47  26.45 

.0139 

.01390 

.99990 

.14300 

312,4 

•99996 

0  47  47.08 

0.0140 

O.OI4OO 

10,0 

0.99990 

0,1 

8.14611 

310,2 

9.99996 

0,1 

o  48  07.71 

.0141 

.01410 

•99990 

.14920 

308,0 

.99996 

0  48  28.33 

.0142 

.01420 

.99990 

.  15227 

305,8 

.90996 

0  48  48.96 

.0143 

.01430 

.99090 

.15532 

303,7 

.99096 

0  49  09-59 

.0144 

.01440 

.99990 

•15835 

301,6 

•99995 

0  49  30.21 

0.0145 

0.01450 

10,0 

0.99089 

0,1 

8.16135 

299,5 

9-99995 

0,1 

©  49  50.84 

.0146 

.01460 

.99989 

.  16434 

297,4 

•99995 

0  50  11-47 

.0147 

.01470 

.99989 

.16730 

295,4 

•99995 

o  50  32.09 

.0148 

.OI48O 

.90089 

.  17025 

2934 

•99995 

o  50  52.72 

.0149 

.01490 

.99989 

.17317 

291,5 

•99995 

0  51   13-35 

0.0150 

O.OI5OO 

10,0 

0.90989 

0,1 

8.17608 

289,5 

9-99995 

0,1 

o  51  33-97 

u 

-isinhiu 

«F0' 

cosh  iu 

-Fo' 

|og«inh  Iu 

-Fo' 

log  cosh  iu 

-Fo' 

j 

SMITHSONIAN  TABLES 


17" 


Circular  Functions. 


u 

sin  u 

«FO' 

COS  U 

«Fo' 

log  sin  u 

«    Fo' 

log  cos  u 

-FO' 

u 

0.0150 

O.OI5OO 

IO,O 

0.99989 

0,1 

8.17608 

289,5 

9-99995 

0,1 

o°5i'33"97 

.0151 

.OI5IO 

0,2 

.17896 

287,6 

.99995 

o  51  54.6o 

.0152 

.OI52O 

.99988 

.18183 

285,7 

•99995 

o  52  15.23 

.0153 

.01530 

.99988 

.18467 

283,8 

.99995 

o  52  35.85 

.0154 

.01540 

.99988 

.18750 

282,0 

•99995 

o  52  56.48 

0.0155 

0.01550 

IO,O 

0.99988 

0,2 

8.19031 

280,2 

9-99995 

0,1 

o  53  17-10 

.0156 

.01500 

.99988 

.19311 

278,4 

.99995 

o  53  37.73 

.0157 

.01570 

.99988 

.19588 

276,6 

•99995 

o  53  58.36 

.0158 

.01580 

.99988 

.19864 

274,9 

•99995 

o  54  18.98 

.0159 

.01590 

.99987 

.20138 

273,1 

.99995 

o  54  39.6i 

0.0160 

O.OIOOO 

IO,O 

0.99987 

0,2 

8.20410 

271,4 

9.99994 

0,1 

o  55  00.24 

.0161 

.Ol6lO 

.99987 

.20681 

269,7 

•9999* 

o  55  20.86 

.0162 

.Ol62O 

.99987 

.20950 

268,1 

.99994 

o  55  41-49 

.0163 

.01630 

.99987 

.21217 

266,4 

•99994 

O  56  O2.  12 

.0164 

.01640 

.99987 

.21482 

264,8 

•99994 

o  56  22.74 

0.0165 

O.OI65O 

IO,O 

0.99985 

0,2 

8.21746 

263,2 

9.99994 

0,1 

o  56"  43-37 

.0166 

.Ol66o 

.99986 

.22009 

261,6 

.99994 

o  57  04.00 

.0167 

.01670 

.99986 

.22270 

260,0 

.99994 

o  57  24.62 

.0168 

.01680 

.09986 

.22529 

258,5 

•99994 

o  57  45.25 

.0169 

.01690 

.99986 

.22787 

257,0 

•99994 

o  58  05.88 

0.0170 

0.01700 

10,0 

0.99986 

0,2 

8.23043 

255,4 

9.99904 

0,1 

o  58  26.50 

.0171 

.OI7IO 

.99985 

.23298 

253,9 

•99994 

o  58  47.13 

.0172 

.OI72O 

.95985 

•23551 

252,5 

•99994 

o  59  07.75 

.0173 

.01730 

.99985 

.23802 

251,0 

•99994 

o  59  28.38 

.0174 

.01740 

.99985 

.24053 

249,6 

•99993 

o  59  49.01 

0.0175 

0.01750 

10,0 

0.99985 

0,2 

8.24302 

248,1 

9-99993 

0,1 

oo  09.63 

.0176 

.01760 

.99985 

.24549 

246,7 

•  99993 

oo  30.26 

.0177 

.01770 

.99984 

.24795 

245,3 

•  99993 

oo  50.89 

.0178 

.01780 

.99984 

.25040 

244,0 

•99993 

01  11.51 

.0179 

.OI79O 

.99984 

.25283 

242,6 

•99993 

01  32.14 

0.0180 

O.OlSoO 

IO,O 

0.99984 

0,2 

8.25525 

241,2 

9-99993 

0,1 

oi  52.77 

.0181 

.OlSlO 

.99984 

.25766 

239,9 

.99993 

02    13-39 

.0182 

.01820 

.99983 

.26005 

238,6 

•99993 

02   34.02 

.0183 

.01830 

.99983 

.26243 

237,3 

•99993 

02   54.65 

.0184 

.01840 

.99983 

.26479 

236,0 

•99993 

03  15-27 

0.0185 

O.Ol85O 

IO,O 

0.09983 

0,2 

8.26715 

234,7 

9-99993 

0,1 

03  35.00 

.0186 

.01860 

.99983 

.26949 

233,5 

.99992 

03  56.53 

.0187 

.01870 

.99983 

.27182 

232,2 

.99992 

04  17.15 

.0188 

.01880 

.99982 

.27413 

231,0 

.99992 

04  37.78 

.0189 

.01890 

.99982 

.27644 

229,8 

.99992 

04  58.40 

0.0190 

O.OI90O 

IO,O 

0.99982 

0,2 

8.27873 

228,5 

9.99992 

0,1 

05  19-03 

.0191 

.01910 

.99982 

.28101 

227,4 

.99992 

05  39.66 

.0192 

.OI92O 

.99982 

.28327 

226,2 

.99992 

06  00.28 

.0193 

.01930 

.09981 

.28553 

225,0 

.99992 

06  20.91 

.0194 

.01940 

.99981 

.28777 

223,8 

.99992 

06  41.54 

0.0195 

O.OI950 

IO,O 

0.99981 

0,2 

8.29001 

222,7 

9.99992 

0,1 

O7  Q2.l6 

.0196 

.01960 

.99981 

.29223 

221,6 

.99992 

07  22.79 

.0197 

.OI97O 

.99981 

.29444 

220,4 

.99992 

07  43.42 

.0198 

.01980 

.99980 

.20664 

219,3 

.99991 

08  04.04 

.0199 

.01990 

.99980 

.29882 

218,2 

.99991 

08  24.67 

0.020O 

O.O2OOO 

IO,O 

0.99980 

0,2 

8.30100 

217,1 

9.99991 

0,1 

I  08  45.30 

. 
i  sinn  iu 

CO   Fn' 

cosh  iu 

'    (ll    Fn' 

.     sinh  iu 

Cl>    Pn' 

01    FA' 

"»  TO 

*•  TO 

log      . 

w  FO 

IOQ  cosh  iu 

<•»  TO 

11 

SMITHSONIAN  TABLES 


177 


Circular  Functions. 


u 

sin  u 

«FO' 

COS  U 

«F0' 

log  sin  u 

«FO' 

loo  cos  u 

-FO' 

U 

O.Q200 

O.O2OOO 

IO,O 

0.99980 

0,2 

8.30100 

217,1 

9.99991 

0,1 

I   0645.30 

.O2OI 

.O20IO 

.99980 

•30317 

216,0 

.99991 

09  05.02 

.O2O2 

.O2O2O 

.99980 

.30532 

2I'5,0 

.99991 

09  26.55 

.0203 

.02030 

.99979 

.30747 

213,9 

.99991 

09  47.18 

.O2O4 

.02040 

.99979 

.30960 

212,9 

.99991 

10  07.80 

O.0205 

O.O2O5O 

IO,O 

0.99979 

0,2 

8.31172 

211,8 

9.99991 

0,1 

10  28.43 

.0206 

.02060 

.99979 

•31384 

210,8 

.99991 

10  49.06 

.0207 

.O2O7O 

.99979 

•31594 

209,8 

.99991 

II  09.68 

.0208 

.02080 

.99978 

•31803 

208,8 

.99991 

II  30.31 

.0209 

.02090 

•99978 

.32012 

207,8 

.99991 

II  50.93 

O.O2IO 

0.02100 

10,0 

0.99978 

0,2 

8.32219 

1206,8 

9.99990 

0,1 

12   11.56 

.O2I  I 

.O2IIO 

.99978 

.32425 

205,8 

.99990 

12  32.19 

.O2I2 

.02120 

.99978 

.32630 

204,8 

.99990 

12   52.8l 

.0213 

.02130 

.99977 

•32835 

203,9 

.99990 

13    13-44 

.O2I4 

.O2I4O 

.99977 

.33038 

202,9 

.99990 

13   34.07 

O.O2I5 

O.O2I50 

10,0 

0.99977 

0,2 

8.  33*241 

202,0 

9.99990 

0,1 

13   54.69 

.O2l6 

.02IOO 

•99977 

•33442 

201,0 

.99990 

H    15.32 

.O2I7 

.O2I7O 

.99976 

•33643 

200,1 

.99990 

14  35-95 

.0218 

.02l8o 

•99976 

•  33842 

199,2 

.99990 

H  56.57 

.O2I9 

.02190 

.99976 

.34041 

198,3 

.99990 

IS  17.20 

O.O22O 

0.02200 

10,0 

0.99976 

0,2 

8.34239 

197,4 

9.99989 

0,1 

15  37-& 

.O22I 

.02210 

.99976 

•34436 

196,5 

.99989 

15  58.45 

.O222 

.O2220 

-99975 

.34632 

195,6 

.99989 

16  19.08 

.O223 

.O223O 

•99975 

-34827 

194,7 

.99989 

16  39.71 

.0224 

.O224O 

•99975 

•35021 

193,8 

.99989 

17  00.33 

0.0225 

O.O225O 

IO,O 

0.99975 

0,2 

8.35215 

193,0 

9.99989 

0,1 

17  20.96 

.O226 

.O2260 

.99974 

•35407 

192,1 

.99989 

17  41.58 

.0227 

.O2270 

.99974 

•35599 

191,3 

.99989 

18  02.  21 

.0228 

.02280 

.99974 

•35790 

190,4 

.99989 

18  22.84 

.0229 

.02200 

.99974 

.35980 

189,6 

.99989 

18  43-46 

O.023O 

0.02300 

10,0 

0.99974 

0,2 

8.36169 

188,8 

9.99989 

0,1 

19  04.09 

.0231 

.02310 

•99973 

.36357 

188,0 

.99988 

19  24.72 

.0232 

.O232O 

•99973 

•  36545 

187,2 

.99988 

19  45-34 

.0233 

.02330 

•99973 

•36732 

186,4 

.99988 

20  05.97 

.0234 

.02340 

•99973 

•36918 

185,6 

.99988 

2O  26.60 

0.0235 

0.02350 

10,0 

0.99972 

0,2 

8.37103 

184,8 

9.99988 

0,1 

2O  47.22 

.0236 

.02360 

.99972 

•37287 

184,0 

.99988 

21   O7.85 

.0237 

.02370 

.99972 

•37471 

183,2 

.99988 

21   28.48 

.0238 

.O238O 

•99972 

.37654 

182,4 

.99988 

21   49.IO 

.0239 

.02390 

.99971 

.37836 

181,7 

.99988 

22  09.73 

0.0240 

0.02400 

10,0 

0.99971 

0,2 

8.38017 

180,9 

9.99987 

0,1 

22   30.36 

.0241 

.O24IO 

.99971 

.38198 

180,2 

.99987 

22   50.98 

.0242 

.0242O 

.99971 

.38377 

179,4 

.99987 

23    II.6I 

.0243 

.02430 

.99970 

.3-S556 

178,7 

.99987 

23  32.23 

.0244 

.02440 

•99970 

.38735 

178,0 

.99987 

23  52.86 

0.0245 

O.O245O 

IO,O 

0.99970 

0,2 

8.38912 

177,2 

9.99987 

0,1 

24    13.49 

.0246 

.02460 

.99970 

.39089 

176,5 

.99987 

24  34.ii 

.0247 

.02470 

.99969 

•  39265 

175,8 

.99987 

24  54.74 

.0248 

.02480 

.99969 

.30441 

I75,i 

.99987 

25  15.37 

.0249 

.02490 

.09969 

.39615 

174,4 

.99987 

25   35-99 

0.0250 

0.02500 

10,0 

0.99969 

0,2 

8.39789 

173,7 

9.99986 

0,1 

I  25  56.62 

1  •Ink  III 

fa>  p  ' 

r>n*ti    in 

id  fn' 

|0«slnh  lu 

Id   f   ' 

u  F  ' 

u 

1  1  sinn  lu 

w  TO 

cosn  iu 

*»  TO 

100     , 

<•»  ro 

00  cosh  iu 

*»  TO 

u 

SMITHSONIAN  TABLCS 


178 


Circular  Functions. 


u 

sin  u 

O.FO' 

cos  u 

«F0' 

log  sin  u 

«    Fo' 

log  cos  u 

«FO' 

u 

O.O25^> 

O.O25OO 

IO,O 

0.99969 

0,2 

8.39780 

173,7 

9.99986 

0,1 

°25/56'/62 

.0251 

.02510 

.99969 

o,3 

.39963 

I73,o 

.99986 

26  17.25 

.0252 

.02520 

.99968 

.40135 

172,3 

.99986 

26  37.87 

.0253 

.02530 

.99968 

.40307 

171,6 

.99986 

26  58.50 

.0254 

.02540 

.99968 

.40479 

170,9 

.99986 

27  19.13 

0.0255 

O.O2550 

10,0 

0.99967 

0,3 

8.40649 

170,3 

9.99986 

0,1 

27  39-75 

.0256 

.02560 

.99967 

.40819 

169,6 

.99986 

28  00.38 

.0257 

.02570 

.99967 

.40989 

168,9 

.99986 

28  21.01 

.0258 

.02580 

.99967 

.4H57 

168,3 

.99986 

28  41.63 

.0259 

.02590 

.99966 

.41325 

167,6 

.99985 

29  O2.26 

0.0260 

0.02600 

IO,O 

0.99966 

0,3 

8.41492 

167,0 

9.99985 

0,1 

29  22.88 

.0261 

.02610 

.99966 

.41659 

166,4 

.99985 

29  43.51 

.0262 

.02620 

.99966 

.41825 

165,7 

.99985 

30  04.14 

.0263 

.02630 

.99965 

.41991 

165,1 

.99985 

30  24.76 

.0264 

.02640 

.99965 

.42155 

164,5 

.99985 

30  45.39 

0.0265 

0.02650 

IO,O 

0.99965 

0,3 

8.42320 

163,8 

9.99985 

0,1 

31  06.02 

.0266 

.02660 

.99965 

.42483 

163,2 

.99985 

31  26.64 

.0267 

.02670 

•99964 

.42646 

162,6 

.99985 

31  47.27 

.0268 

.02680 

•  99964 

.42808 

162,0 

•99984 

32  07-90 

.0269 

.02690 

.99964 

.42970 

161,4 

•99984 

32  28.52 

0.0270 

O.027OO 

10,0 

0.99964 

o,3 

8.43I3I 

160,8 

9.99984 

0,1 

32  49.15 

.0271 

.O27IO 

.99963 

.43292 

160,2 

.99984 

33  09.78 

.0272 

.02720 

.99963 

•43452 

159,6 

.99984 

33  30.40 

.0273 

.02730 

.99963 

.43611 

I59,o 

•99984 

33  51.03 

.0274 

.02740 

.99962 

.43770 

158,5 

.99984 

34  11.66 

0.0275 

0.02750 

10,0 

0.99962 

0,3 

8.43928 

157,9 

9.99984 

0,1 

34  32.28 

.0276 

.02760 

.99962 

.44085 

157,3 

.99983 

34  52.91 

.0277 

.02770 

.99962 

.44242 

156,7 

.99983' 

35  13.54 

.0278 

.02780 

.99961 

•44399 

156,2 

•99983 

35  34.i6 

.0279 

.02790 

.99961 

•44555 

155,6 

.99983 

35  54-79 

0.0280 

0.02800 

10,0 

0.99961 

0,3 

8.44710 

I55,i 

9.99983 

0,1 

36  15.41 

.0281 

.02810 

.99961 

.44865 

154,5 

.99983 

36  36.04 

.0282 

.02820 

.99960 

.45019 

I54,o 

.99983 

36  56.67 

.0283 

.02830 

.99960 

.45173 

153,4 

.99983 

37  17.29 

.0284 

.02840 

.99960 

.45326 

152,9 

.99982 

37  37-92 

0.0285 

0.02850 

10,0 

0-99959 

0,3 

8.45479 

152,3 

9.99982 

0,1 

37  58.55 

.0286 

.02860 

•99959 

.45631 

151,8 

.99982 

38  IQ.I7 

.0287 

.02870 

•99959 

.45782 

I5i,3 

.99982 

38  39.8o 

.0288 

.02880 

.99959 

•45933 

150,8 

.99982 

39  00.43 

.0289 

.02890 

.99958 

.46084 

150,2 

.99982 

39  21.05 

O.O20O 

0.02900 

IO,O 

0.99958 

o,3 

8.46234 

149,7 

9.99982 

0,1 

39  41.68 

.O29I 

.02910 

.99958 

.46383 

149,2 

.99982 

40  02.31 

.0292 

.02920 

•99957 

•46532 

148,7 

.99981 

40  22.93 

•0293 

.02930 

.99957 

.46681 

148,2 

.99981 

40  43.56 

.0294 

.02940 

•99957 

.46828 

147,7 

.99981 

41  04.19 

0.0295 

O.O295O 

IO,O 

0.99956 

o,3 

8.46976 

147,2 

9-99981 

0,1 

41  24.81 

.0296 

.02960 

.99956 

.47123 

146,7 

.99981 

41  45.44 

.0297 

.02970 

.99956 

.47269 

146,2 

.99981 

42  06.06 

.0298 

.02080 

.99956 

.47415 

145,7 

.99981 

42  26.69 

.0299 

.02990 

•99955 

.47561 

H'5,2 

.99981 

42  47.32 

0.0300 

0.03000 

10,0 

0.99955 

0,3 

8.47706 

144,7 

9.09980 

0,1 

I  43  07.94 

:  -.:  —  u  ;,. 

£.)    P    ' 

rn*h  in 

ii>  F  ' 

sinh  iu 

0    P    ' 

. 

F  ' 

U 

—  i  sinn  iti 

w  ro 

cosn  lu 

*»  ro 

lOfl       . 

«•>  ro 

log  cosh  iu 

*>  TO 

u 

SMITHSONIAN  TABLES 


179 


Circular  Functions. 


u 

sin  u 

O.FO' 

COS  U 

.« 

log  sin  u 

w  F(j' 

log  cos  u 

-W- 

u 

0.0300 

0.03000 

10,0 

0.99955 

0,3 

8.47706 

144,7 

9.90980 

0,1 

I  43  O7'.'o4 

.0301 

.03010 

.99955 

.47850 

144,2 

.99980 

43  28.57 

.0302 

.03020 

.99954 

-47994 

143.8 

43  49.20 

.0303 

.03030 

.99954 

.48138 

143,3 

.99980 

44  09.82 

.0304 

.03040 

.99954 

.48281 

142,8 

.99980 

44  30-45 

0.0305 

0.03050 

IO,O 

0.99953 

0,3 

8.48423 

142,3 

9.99980 

0,1 

44  Si.oS 

.0306 

.03060 

•99953 

.48565 

141,9 

.99980 

45  H-70 

.0307 

.030/0 

•99953 

.48707 

141,4 

.99980 

45  32-33 

.0308 

.03080 

.99953 

.48848 

141,0 

.99979 

45  52.06 

.0309 

.03090 

.99952 

.48989 

140,5 

.99979 

46  13-58 

0.0310 

O.O3IOO 

10,0 

0.99952 

o,3 

8.49129 

140,1 

9-99979 

0,1 

46  34-21 

.0311 

.03109 

•99952 

.49269 

139,6 

.99979 

46  54-84 

.0312 

.03119 

•99951 

.49408 

139,2 

•99979 

47  15.46 

•0313 

.03129 

•99951 

.49547 

138,7 

.99979 

47  36.09 

.0314 

.03139 

•99951 

.49686 

138,3 

-99979 

47  56.71 

0.0315 

0.03149 

10,0 

0-99950 

0,3 

8.49824 

137,8 

9.99978 

0,1 

48  17.34 

.0316 

.03159 

.99950 

.49961 

137,4 

.99978 

48  37.97 

.0317 

.03169 

.99950 

.50099 

I37,o 

.99978 

48  58.59 

.0318 

.03179 

•99949 

•50235 

136,5 

.99978 

49  19.22 

.0319 

.03189 

•99949 

.50372 

136,1 

.99978 

49  39.85 

0.0320 

0.03109 

10,0 

0.99949 

0,3 

8.50508 

135,7 

9.99978 

0,1 

50  00.47 

.0321 

.03209 

.99948 

.50643 

135,2 

.99978 

50  21.  10 

.0322 

.03219 

.59948 

00778 

134,8 

.99977 

50  41-73 

.0323 

.03229 

.99948 

.50913 

134,4 

.99977 

5i  02.35 

.0324 

.03239 

.95948 

.51047 

134,0 

•99977 

51  22.98 

0.0325 

0.03249 

10,0 

0.99947 

0,3 

8.51181 

133,6 

9-99977 

0,1 

51  43.6i 

.0326 

.03259 

.99947 

.51314 

133,2 

.99977 

52  04-23 

.0327 

.03269 

.99947 

-51447 

132,8 

.99977 

52  24.86 

.0328 

.03279 

.99946 

.51580 

132,4 

•99977 

52  45-49 

.0329 

.03289 

.99946 

.51712 

132,0  t 

.99976 

53  06.  II 

0.0330 

0.03299 

IO,0 

0.99946 

0,3 

8.51844 

131,6 

9-99976 

0,1 

53  26.74 

.0331 

.03309 

.99945 

.51975 

131,2 

.99976 

53  47-37 

.0332 

.03319 

.99945 

.52106 

130,8 

.99976 

54  07-99 

.0333 

.03329 

•99945 

.52236 

130,4 

.99976 

54  28.62 

.0334 

.03339 

•99944 

.52367 

130,0 

•99976 

54  49.24 

0.0335 

0.03349 

10,0 

0.99944 

0,3 

8.52496 

129,6 

9.99976 

0,1 

55  09.87 

•  0336 

•03359 

.99944 

.52626 

129,2 

•99975 

55  30.50 

•  0337 

.03369 

•99943 

.52755 

'  128,8 

.99975 

55  51.12 

.0338 

.03379 

•99943 

.52883 

128,4 

.99975 

56  n.75 

•  0339 

.03389 

•99943 

.53012 

128,1 

.99975 

56  32.38 

0.0340 

0.03399 

IO,O 

0.99942 

o,3 

8.53-140 

127,7 

9-99975 

0,1 

56  53-00 

.0341 

.03409 

.99942 

'53267 

127,3 

•99975 

57  13-63 

•  0342 

.03419 

•99942 

.53394 

126,9 

•99975 

57  34-26 

.0343 
.0344 

•03429 
•03439 

.99941 
.99941 

•53521 
.53647 

126,6 
126,2 

•99974 
.99974 

57  54-88 
58  I5.5I 

0.0345 

0.03449 

IO,O 

0.99940 

o,3 

8.53773 

125,8 

9.99974 

0,1 

58  36.14 

r»    s    £ 

.0346 

.03459 

.99940 

.53899 

125,5 

•99974 

0,2 

58  56.76 

.0347 

.03469 

•99940 

.54024 

125,1 

•99974 

59  17-39 

.0348 

.03479 

•99939 

.54149 

124,7 

•99974 

I  59  38.02 

.0349 

.03489 

•99939 

.54274 

124,4 

•99974 

I  59  58-64 

0.0350 

0.03499 

10,0 

0.99939 

0,3 

8.54398 

124,0 

9-99973 

0,2 

2  00  19.27 

r-  / 

C  ' 

sinh  iu 

Hi  F  ' 

Inn  roth  iu 

«  F  ' 

u 

-isinhiu 

w  Fo 

cosh  iu 

••  TO 

«•»  To 

toy  co»n  iu 

SMITHSONIAN  TABLES 


180 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«Fo' 

log  sin  u 

«-  Fo' 

log  cos  u 

<oF0' 

U 

v 

o.0350\ 

0.03499 

IO,0 

0.99939 

0,3 

8.54398 

124,0 

9-99973 

0,2 

o   /   // 
2  00  19.27 

.0351 

.03509 

.99938 

0,4 

.54522 

123,7 

.99973 

2  00  39.89 

.0352 

.03519 

.99938 

.54645 

123,3 

•99973 

2  01  00.52 

.03-53 

.03-529 

.99938 

.54768 

123,0 

•99973 

2  OI  21.15 

.0354 

.03539 

•99937 

.54891 

122,6 

•99973 

2  01  41.77 

0.0355 

0.03549 

10,0 

0.99937 

0,4 

8.55014 

122,3 

9-99973 

0,2 

2  O2  O2.4O 

.0356 

.03559 

.99937 

.55136 

121,9 

.99972 

2  02  23.03 

.0357 

.03569 

.99936 

.552>58 

121,6 

.99972 

2  02  43.65 

.0358 

.03579 

.99936 

•55379 

121,3 

.99972 

2  O3  04.28 

•  0359 

.03589 

.99936 

.55500 

1  20,9 

.99972 

2  O3  24.91 

0.0360 

0.03'599 

10,0 

0.99935 

0,4 

8.55621 

120,6 

9.99972 

0,2 

2  03  45-53 

.0361 

.03609 

.99935 

.55741 

120,3 

.99972 

2  04  06.  16 

.0362 

.03619 

•99934 

.55861 

119,9 

.99972 

2  04  26.79 

.0363 

.03629 

•99934 

.55981 

119,6 

.99971 

2  04  47.41 

.0364 

.03639 

•99934 

.56101 

119,3 

.99971 

2  O5  O8.O4 

0.0365 

0.03649 

IO,O 

0.99933 

0,4 

8.56220 

118,9 

9.99971 

0,2 

2  05  28.67 

.0366 

.03659 

•99933 

.56338 

118,6 

.99971 

2  05  49-29 

.0367 

.03669 

.99933 

.56457 

118,3 

.99971 

2  06  09.92 

.0368 

.03679 

.99932 

.56575 

118,0 

.99971 

2  O6  3O.54 

.0369 

.03689 

.99932 

06693 

117,6 

.99970 

2  O6  51.17 

0.0370 

0.03699 

10,0 

0.99932 

0,4 

8.56810 

H7,3 

9.99970 

0,2 

2,O7  II.SO 

.0371 

.03709 

.99931 

.56927 

117,0 

.99970 

2  07  32.42 

.0372 

.03719 

•99931 

.57044 

116,7 

.99970 

2  07  53.05 

.0373 

.03729 

.99930 

.57i6i 

116,4 

•99970 

2  08  13.68 

.0374 

.03739 

•99930 

.57277 

116,1 

.99970 

2  08  34.30 

0.0375 

0.03749 

10,0 

0.99930 

0,4 

8.57393 

H5,8 

9.99969 

0,2 

2  OS  54.93 

.0376 

.03759 

.99929 

.57509 

H5,4 

.99969 

2  09  15.56 

.0377 

.03769 

.99929 

.57624 

H5,i 

.99969 

2  O9  36.18 

.0378 

.03779 

.99929 

•57739 

114,8 

.99969 

2  O9  56.8l 

.0379 

.03789 

.99928 

.57854 

H4,5 

.99969 

2  10  17-44 

0.0380 

0.03799 

IO,O 

0.99928 

0,4 

8.57968 

114,2 

9.99969 

0,2 

2  IO  38.06 

.0381 

.03809 

.99927 

.58082 

H3,9 

.99968 

2  10  58.69 

.0382 

.03819 

.99927 

.58196 

113,6" 

.99968 

2  II  19.32 

.0383 

.03829 

.99927 

.58309 

H3,3 

.90968 

2  II  39-94 

.0384 

.03839 

.99926 

.58422 

H3,o 

.99968 

2  12  OO.57 

0.0385 

0.03849 

10,0 

0.99926 

0,4 

8.58535 

112,7 

9.99968 

0,2 

2  12  21.  2O 

.0386 

.03859 

.99926 

.58648 

112,5 

.99968 

2  12  41.82 

.0387 

.03869 

.99925 

.58760 

112,2 

.99967 

2  13  02.45 

.0388 

.03879 

.99925 

.58872 

111,9 

.99967 

2  13  23.07 

.0389 

.03889 

.99924 

.58984 

111,6 

•99967 

2  13  43.70 

0.0390 

0.03899 

IO,O 

0.99924 

0,4 

8.59095 

in,3 

9.99967 

0,2 

2  14  04.33 

.0391 

.03909 

.99924 

.59207 

III,O 

.99967 

2  14  24.95 

.0392 

.03919 

.99923 

.59317 

110,7 

.99967 

2  14  45.58 

.0393 

.03929 

.99923 

.59428 

no,  5 

.99966 

2  15  06.  21 

.0394 

.03939 

.99922 

.59538 

IIO,2 

.99966 

2  15  26.83 

0.0395 

0.03949 

10,0 

0.99922 

0,4 

8.59648 

109,9 

9.99966 

0,2 

2  15  47.46 

.0396 

•03959 

.99922 

.59758 

109,6 

.99966 

2  16  08.09 

.0397 

.03969 

.99921 

.59868 

109,3 

.99966 

2  16  28.71 

.0398 

.03979 

.99921 

•59977 

109,1 

.99966 

2  l6  49-34 

.0399 

.03989 

.99920 

.60086 

108,8 

•99965 

2  17  09.97 

0.0400 

0.03999 

IO,O 

0.99920 

0,4 

8.60194 

108,5 

9.9996"5 

0,2 

2  17  30.59 

u 

-isinhiu 

»F0' 

cosh  iu 

«F0' 

.  sinh  iu 

«F0' 

log  cosh  iu 

«F0' 

U 

log   . 

SMITHSONIAN  TABLES 


181 


Circular  Functions. 


u 

sin  u 

-FO' 

COS  u 

-  Fo'       log  sin  u 

«    Fo' 

log  cos  u 

-FO' 

u 

0.0400 

0.03999 

10,0 

0.99920 

0,4 

8.60194 

108,5 

9.99965 

0,2 

2°i7/3o'./59 

.0401 

.04009 

.99920 

.60303 

108,2 

•99965 

2   17  51.22 

.0402 

.04019 

.99919 

.60411 

108,0 

.99965 

2  18  11.85 

.0403 

.04029 

.99919 

.60519 

107,7 

.99965 

2  18  32.47 

.0404 

.04039 

.99918 

.60626 

107,4 

•99965 

2  18  53-10 

0.0405 

0.04049 

IO,O 

0.99918 

0,4 

8.60734 

107,2 

9.99964 

0,2 

2   19   13.72 

.0406 

.04059 

.99918 

.60841 

106,9 

.99964 

2    19  34-35 

.0407 

.04069 

.99917 

.00947 

106,6 

•99964 

2    19  54.98 

.0408 

.04079 

.99917 

.61054 

106,4 

.99964 

2  2O   15.60 

.0409 

.04089 

.99916 

.61160 

106,1 

.99964 

2   20  36.23 

0.0410 

0.04099 

10,0 

0.99916 

0,4 

8.61266 

105,9 

9.99963 

0,2 

2  20  56.86 

.0411 

.04109 

.99916 

.61372 

•   105,6 

•99963 

2  21    17.48 

.0412 

.04119 

.99915 

.61477 

105,4 

•99963 

2  21    38.11 

.0413 

.04129 

.99915 

.61583 

105,1 

.90963 

2  21    58.74 

.0411 

.04139 

.99914 

.61688 

104,8 

.99963 

2  22    19.36 

0.0415 

0.04149 

IO,O 

0.90914 

0,4 

8.61792 

104,6 

9.99963 

0,2 

2  22  39.99 

.0416 

.04159 

.99913 

.61897 

104,3 

.99962 

2  23  OO.62 

.0417 

.04169 

.99913 

.62OOI 

104,1 

.99962 

2   23   21.24 

.0418 

.04179 

.99913 

.6210*5 

103,8 

.99062 

2   23  41.87 

.0419 

.04189 

.99912 

.62209 

103,6 

.99962 

2  24  O2.5O 

0.0420 

0.04199 

IO,O 

0.99912 

0,4 

8.62312 

103,3 

9.99962 

0,2 

2  24  23.12 

.0421 

.04209 

.99911 

.62415 

103,1 

.99962 

2  24  43-75 

.0422 

.04219 

.99911 

.62518 

102,9 

.99961 

2   25  04.37 

.0423 

.04229 

.99911 

.62621 

102,6 

.99961 

2  25  25.0O 

.0424 

.04239 

.99910 

.62724 

102,4 

.99961 

2  25   45.63 

0.0425 

o  .  04249 

IO,O 

0.99910 

0,4 

8.62826 

102,1 

9.99961 

0,2 

2  26  06.25 

.0426 

.04259 

.99909 

.62928 

101,9 

.99961 

2   26  26.88 

.0427 

.04269 

.99909 

.63030 

101,6 

.99960 

2  26  47.51 

.0428 

.04279 

.99908 

.63131 

101,4 

.99960 

2  27  08.I3 

.0429 

.04289 

.99908 

.63232 

101,2 

.99960 

2   27  28.76 

0.0430 

0.04299 

10,0 

0.99908 

0,4 

8.6J333 

100,9 

9.99960 

0,2 

2  27  49-39 

.0431 

.04309 

.99907 

.63434 

100,7 

.99960 

2   28    10.01 

.0432 

.04319 

.99907 

.63535 

100,5 

•99959 

2  28  30.64 

.0433 

.04329 

.99906 

•63635 

100,2 

•99959 

2  28   51.27 

.0434 

•04339 

.99906 

.63735 

100,0 

•99959 

2  29    11.  90 

0.0433 

0.04349 

IO,O 

0.99905 

0,4 

8.63835 

99,8 

9-99959 

0,2 

2   29  32.52 

.0436 

.04359 

.99905 

.63935 

99,5 

.99959 

2  29  53-15 

•  0437 

.04369 

.99905 

.64034 

99,3 

.99959 

2  30    13.77 

.0438 

.04379 

.99904 

.64134 

99,i 

.99958 

2   30  34.40 

•0439 

.04389 

.99904 

•64233 

98,9 

.99958 

2  30  55-02 

0.0440 

.0441 

0.04399 
.04409 

10,0 

0.09903 
.99903 

0,4 

8.64331 
.64430 

98,6 
98,4 

9.99958 
.99958 

0,2 

2  31    15.65 
2   31    36.28 

.0442 

.04419 

.09902 

.64528 

98,2 

.99958 

2  31    56.OO 

•  0443 
.0444 

.04429 
.04439 

.09902 
.99901 

.64626 
.64724 

98,0 
97,7 

.99957 
•99957 

2  32    17-53 

2  32  38.  16 

0.0445 

0.04449 

IO,O 

0.99901 

0,4 

8.64822 

97,5 

9-99957 

0,2 

2  32   58.78 

.0446 

.04459 

.99901 

.64919 

97,3 

•99957 

2  33  19-41 

•  O447 

.04469 

.99900 

.65016 

97,i 

.99957 

2  33  40.04 

.0448 

.04479 

.99900 

.65H3 

06,9 

.99956 

2  34  00.66 

.0449 

.04488 

.99899 

.65210 

96,7 

.99956 

2  34  21.29 

0.0450 

0.04498 

10,0 

0.99899 

0,4 

8.65307 

96,4 

9.99956 

0,2 

2  34  41.92 

u 

isinhiu 

-Fo' 

cosh  iu 

-Fo' 

,0fl«inhju 

-Fo' 

log  cosh  iu 

-Fo' 

u 

SMITHSONIAN  TABLE* 


182 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

wFo' 

log  sin  u 

W  Fo' 

log  cos  u 

wF0' 

U 

0.0450 

o\  04498 

IO,O 

0.99899 

0,4 

8.65307 

96,4 

9.99956 

O,2 

2°34/4i'.'92 

.0451 

.04508 

.99898 

o,5 

.65403 

96,2 

.99956 

2  35  02.54 

.0452 

.04518 

.99898 

.65499 

96,0 

.99956 

2  35  23.17 

.0453 

.04528 

.99897 

.65595 

95,8 

•99955 

2  35  43.8o 

.0454 

.04538 

.99897 

.65691 

95,6 

.99955 

2  36  04.42 

0.0455 

0.04548 

IO,O 

0.99897 

o,5 

8.65786 

95,4 

9-99955 

0,2 

2  36  25.05 

.0456 

.04558 

.99896 

.65881 

95,2 

.99955 

2  36  45-68 

•  0457 

.04568 

.99896 

.65976 

95,0 

.99955 

2  37  06.30 

.04158 

.04578 

.99895 

.66071 

94,8 

•99954 

2  37  26.93 

.0459 

.04588 

.99895 

.66166 

94,6 

•99954 

2  37  47.55 

0.0460 

0.04598 

10,0 

0.99894 

o,5 

8.66260 

94,3 

9-99954 

0,2 

2  38  08.  18 

.0461 

.04608 

.99894 

.66355 

94,1 

•99954 

2  38  28.81 

.0462 

.04618 

.99893 

.66449 

93,9 

•99954 

2  38  49-43 

.0463 

.04628 

.99893 

.66543 

93,7 

•99953 

2  39  10.06 

.0464 

.04638 

.99892 

.66636 

93,5 

•99953 

2  39  30.69 

0.0465 

0.04648 

10,0 

0.99892 

o,5 

8.66730 

93,3 

9-99953' 

0,2 

2  39  5I.3I 

.0466 

.04658 

.99891 

.66823 

93,1 

.99953 

2  40  11.94 

.0467 

.04668 

.99891 

.66916 

92,9 

•99953 

2  40  32.57 

.0468 

.04678 

.99891 

.67009 

92,7 

•99952 

2  40  53.19 

.0469 

.04688 

.99890 

.67101 

92,5 

.99952 

2  41  13.82 

0.0470 

0.04698 

IO,O 

0.99890 

o,5 

8.67194 

92,3 

9.99952 

0,2 

2  41  34.45 

.0471 

.04708 

.99889 

.67286 

92,1 

.99952 

2  41  55-07 

.0472 

.04718 

.99889 

.67378 

91,9 

.99952 

2  42  I5.70 

.0473 

.04728 

.99888 

.67470 

9i,7 

•99951 

2  42  36.33 

.0474 

.04738 

.99888 

.67562 

91*6 

•99951 

2  42  56.95 

0.0475 

O.O4748 

IO,0 

0.99887 

o,5 

8.67653 

91,4 

9-99951 

0,2 

2  43  17.58 

.0476 

.04758 

.99887 

.67744 

91,2 

.99951 

2  43  38.20 

.0477 

.04768 

.99886 

.67835 

91,0 

.99951 

2  43  58.83 

.0478 

.04778 

.99886 

.67926 

90,8 

.99950 

2  44  19-46 

.0479 

.04788 

.99885 

.68017 

90,6 

•99950 

2  44  40.08 

0.0480 

0.04798 

IO,O 

0.99885 

0,5 

8.68107 

90,4 

9.99950 

0,2 

2  45  00.71 

.0481 

.04808 

.99884 

.68198 

90,2 

.99950 

2  45  21.34 

.0482 

.04818 

.99884 

.68288 

90,0 

•99950 

2  45  41.96 

.0483 

.04828 

.99883 

.68378 

89,8 

•99949 

2  46  02.59 

.0484 

.04838 

.99883 

.68468 

89,7 

.99949 

2  46  23.22 

0.0485 

0.04848 

IO,O 

0.99882 

o,5 

8.68557 

89,5 

9.99949 

0,2 

2  46  43.84 

.0486 

.04858 

.99882 

.68647 

89,3 

.99949 

2  47  04.47 

.0487 

.04868 

.99881 

.68736 

89,1 

.99948 

2  47  25.10 

.0488 

.04878 

.99881 

.68825 

88,9 

.99948 

2  47  45.72 

.0489 

.04888 

.99880 

.68914 

88,7 

.99948 

2  48  06.35 

0.0490 

0.04898 

10,0 

0.99880 

o,5 

8.69002 

88,6 

9.99948 

0,2 

2  48  26.98 

.0491 

.04908 

.99879 

.69091 

88,4 

.99948 

2  48  47.60 

.  .0492 

.04918 

.99879 

.69179 

88,2 

•99947 

2  49  08.23 

.0493 

.04928 

.99879 

.69267 

88,0 

.99947 

2  49  28.85 

.0494 

.04938 

.99878 

.69355 

87,8 

.99947 

2  49  49.48 

0.0495 

0.04948 

10,0 

0.99878 

o,5 

8.69443 

87,7 

9-99947 

0,2 

2  50  10.  II 

.0496 
.0497 

.04958 
.04968 

.99877 
.99877 

.69530 
.69618 

87,5 
87,3 

•99947 
.99946 

2  50  30.73 
2  50  51.36 

.0498 

.04978 

.99876 

.69705 

87,1 

.99946 

2  51  11-99 

.0499 

.04988 

.99876 

.69792 

87,0 

.99946 

2  51  32.6l 

0.0500 

0.04998 

IO,O 

0.99875 

o,5 

8.69879 

86,8 

9.99946 

0,2 

2  51  53-24 

u 

-isinhiu 

«F0' 

cosh  iu 

«FO' 

sinh  iu 

«Fo' 

ogcoshiu 

«F0' 

U 

log  . 

SMITHSONIAN  TABLES 


183 


Circular  Functions. 


I 

sin  u 

»F0' 

cos  u 

w  F    log  sin  u 

«  Fo' 

log  cos  u 

"Fo' 

u 

0.0500 

0.04098 

10,0 

0.99875 

o,5 

8.69879 

86,8 

9.99946 

0,2 

2  51  53.24 

.0501 

.05008 

.99875 

.69966 

86,6 

•99945 

2  52  13.87 

.0502 

.05018 

.99874 

.70052 

86,4 

•99945 

2  52  34.49 

.0503 

.05028 

.99874 

.70138 

86,3 

•99945 

2  52  55.12 

.0504 

.05038 

.99873 

.70225 

86,1 

•99945 

2  53  15-75 

0.0505 

0.05048 

IO,O 

0.99873 

o,5 

8.703II 

85,9 

9-99945 

0,2 

2  53  36.37 

.0506 

.05058 

.99872 

.70397 

85,8 

-99944 

2  53  57-00 

.0507 

.05068 

.99872 

.70482 

85,6 

.99944 

2  54  17.63 

.0508 

.05078 

.99871 

.70568 

85,4 

•99944 

2  54.38.25 

.0509 

.05088 

.99870 

.70653 

85,2 

•99944 

2  54  58.88 

0.0510 

0.05098 

IO,0 

0.99870 

o,5 

8.70738 

85,1 

9-99943 

0,2 

2  55  19.51 

.0511 

.05108 

.99869 

.70823 

84,9 

•99943 

2  55  40.13 

.0512 

.05118 

.99869 

.70908 

84,7 

•99943 

2  56  00.76 

.0513 

.05128 

.99868 

.70993 

84,6 

•99943 

2  56  21.38 

.0514 

.05138 

.99868 

.71077 

84,4 

•99943 

2  56  42.01 

0.0515 

0.05148 

10,0 

0.95867 

o,5 

8.71162 

84,3 

9.99942 

0,2 

2  57  02.64 

.0516 

.05158 

.99867 

.71246 

84,1 

•99942 

2  57  23.26 

.0517 

.05168 

.99866 

.71330 

83,9 

.99942 

2  57  43.89 

.0518 

.05178 

.99866 

.71414 

83,8 

•99942 

2  58  04.52 

.0519 

.05188 

.99865 

.71497 

83,6 

•99941 

2  58  25.14 

0.0520 

0.05198 

IO,O 

0.99865 

o,5 

8.7I58I 

83,4 

9.99941 

O,2 

2  58  45-77 

.0521 

.05208 

.99864 

.7l654- 

83,3 

•99941 

2  59  06.40 

.0522 

.05218 

.99864 

.71747 

83,1 

•99941 

2  59  27.02 

.0523 

.05228 

.99363 

.71830 

83,0 

•99941 

2  59  47.65 

-.0524 

.05238 

.99863 

.71913 

82,8 

.99940 

3  oo  08.28 

0.0525 

0.05248 

10,0 

0.99862 

o,5 

8.71996 

82,6 

9-99940 

0,2 

3  oo  28.90 

.0526 

.05258 

.99862 

.72079 

82,5 

•99940 

3  oo  49.53 

.0527 

.05268 

.99861 

.72161 

82,3 

•99940 

3  01  10.16 

.0528 

.05278 

.99861 

.72243 

82,2 

•99939 

3  01  30.78 

.0529 

.05288 

.99860 

.72325 

82,0 

.99939 

3  oi  51.41 

0.0530 

0.05298 

IO,O 

0.99860 

o,5 

8.72407 

81,9 

9-99939 

0,2 

3  02  12.03 

.0531 

.05308 

.99859 

.72489 

8i,7 

•99939 

3  02  32.66 

.0532 

.05317 

.99859 

.72571 

81,6 

•99939 

3  02  53.29 

.0533 

.05327 

.99858 

.72652 

81,4 

•99938 

3  03  13.91 

.0534 

.05337 

.99857 

.72733 

81,3 

.99938 

3  03  34-54 

0.0535 

0.05347 

IO,O 

0.99857 

o,5 

8.72815 

81,1 

9.99938 

0,2 

3  03  55-17 

•  0536 

.05357 

.99856 

.72896 

80,9 

.99938 

3  04  15.79 

•  0537 

•05367 

.99856 

.72977 

80,8 

•99937 

3  04  36.42 

.0538 

•C5377 

.99855 

.73057 

80,6 

•99937 

3  04  57.05 

•0539 

.05387 

.99855 

.73138 

80,5 

•99937 

3  05  17.67 

0.0540 

0.05397 

IO,O 

0.99854 

o,5 

8.73218 

80,3 

9-99937 

0,2 

3  05  38.30 

.0541 

.05407 

.99854 

.73299 

80,2 

.99936 

3  05  58.93 

.0542 

.05417 

.99853 

•73379 

80,0 

.99936 

3  06  19.55 

.0543 

.05427 

.99853 

.73459 

79,9 

.99936 

3  06  40.  18 

•  0544 

.05437 

.99852 

.73538 

79,8 

.99936 

3  07  00.81 

0.0545 

0.05447 

IO,O 

0.99852 

o,5 

8.73618 

79,6 

9-99935 

0,2 

3  07  21.43 

.0546 

.05457 

.99851 

.73698 

79,5 

•99935 

3  07  42.06 

•  0547 

.05467 

.99850 

•73777 

79,3 

•99935 

3  08  02.68 

.0548 

.05477 

.99850 

.73856 

79,2 

•99935 

3  08  23.31 

•  0549 

.05487 

.99849 

•73935 

79,0 

•99935 

3  08  43-94 

0.0550 

0.05497 

10,0 

0.99849 

o,5 

8.74014 

78,9 

9-99934 

0,2 

3  09  04.56 

2* 

-isinhiu 

«F0' 

cosh  iu 

-F,,' 

loa$lnh  lu 

-Fo' 

log  cosh  iu 

wF0' 

u 

log   . 

SMITHSONIAN  TABLES 


184 


Circular  Functions. 


u 

sinu 

«FO' 

COS  U 

«F0'- 

log  sin  u 

«•>  FO' 

log  cos  u 

wF0' 

u 

0.0550 

0.05497 

IO,O 

0.99849 

0,5 

8.74014 

78,9 

9-99934 

0,2 

3°09'o4.'56 

.0551 

.05507 

.99848 

0,6 

.74093 

78,7 

•99934 

3  09  25.19 

.0552 

.05517 

.95848 

.74172 

78,6 

•99934 

3  09  45.82 

.0553 

.05527 

.99847 

.74250 

78,5 

•99934 

3  to  06.44 

.0554 

.05537 

.99847 

.74329 

78,3 

•99933 

3  10  27-07 

0.0555 

O.OS547 

IO,O 

0.99846 

0,6 

8.74407 

78,2 

9-99933 

0,2 

3  10  47.70 

.0556 

•05557 

.99845 

.74485 

78,0 

•99933 

3  II  08.32 

.0557 

.05567 

.99845 

.74563 

77,9 

•99933 

3  II  28.95 

.0558 

.05577 

.99844 

.74641 

77,7 

.99932 

3  ii  49-58 

•0559 

.05587 

.99844 

•74719 

77,6 

•99932 

3  12  10.20 

0.0560 

0.05597 

IO,O 

0.99843 

0,6 

8.74796 

77,5 

9.99932 

0,2 

3  12  30.83 

.0561 

.05607 

.99843 

.74873 

77,3 

•99932 

3  12  51.46 

.0562 

.05617 

.99842 

•74951 

77,2 

•99931 

3  13  12.08 

.0563 

.05627 

.99842 

.75028 

77,1 

•99931 

3  13  32.71 

.0564 

.05637 

.99841 

.75105 

76,9 

•99931 

3  13  53-34 

0.0565 

0.05647 

IO,O 

0.99840 

0,6 

8.75182 

76£ 

9.99931 

0,2 

3  14  13.96 

.0566 

.05657 

.99840 

.75258 

76,6 

•99930 

3  14  34.59 

.0567 

.05667 

.99839 

.75335 

76,5 

•99930 

3  H  55-21 

.0568 

.05677 

.99839 

.754H 

76,4 

•99930 

3  15  15.84 

.0569 

.05687 

.99838 

.75488 

76,2 

•99930 

3  15  36.47 

0.0570 

0.05697 

IO,O 

0.99838 

0,6 

8.75564 

76,1 

9.99929 

0,2 

3  15  57.09 

.0571 

.05707 

.99837 

•75640 

76,0 

.99929 

3  16  17.72 

.0572 

.05717 

.99836 

.75716 

75,8 

.99929 

3  16  38.35 

.0573 

.05727 

.99836 

•75792 

75,7 

.99929 

3  16  58.97 

•  0574 

.05737 

.99835 

.75867 

75,6 

.99928 

3  17  19-60 

0.0575 

0.05747 

10,0 

0.99835 

0,6 

8.75943 

75,4 

9.99928 

O,2 

3  17  40.23 

•  0576 

.05757 

.99834 

.76018 

75,3 

.99928 

0,3 

3  18  00.85 

.0577 

.05767 

.99834 

.76093 

75,2 

.99928 

3  18  21.48 

.0578 

.05777 

.99833 

.76169 

75,1 

.99927 

3  18  42.11 

.0579 

.05787 

.99832 

.76244 

74,9 

•99927 

3  19  02.73 

0.0580 

0.05797 

10,0 

0.99832 

0,6 

8.76318 

74,8 

9.99927 

0,3 

3  19  23.36 

.0581 

.05807 

.99831 

.76393 

74,7 

.99927 

3  19  43-99 

.0582 

.05817 

.99831 

.76468 

74,5 

.99926 

3  20  04.61 

.0583 

.05827 

.99830 

.76542 

74,4 

.99926 

3  20  25.24 

.0584 

.05837 

.99830 

.76617 

74,3 

.99926 

3  20  45.86 

0.0585 

0.05847 

10,0 

0.99829 

0,6 

8.76691 

742 

9.99926 

0,3 

3  21  06.49 

.0586 

.05857 

.99828 

.76765 

74,0 

.99925 

3  21  27.12 

.0587 

.05867 

.99828 

.76839 

73,9 

.99925 

3  21  47.74 

.0588 

.05877 

.99827 

.76913 

73,8 

.99925 

3  22  08.37 

.0589 

.05887 

.99827 

.76986 

73,6 

.99925 

3  22  29.00 

0.0590 

0.05897 

10,0 

0.99826 

0,6 

8.77060 

73,5 

9.99924 

0,3 

3  22  49.62 

.0591 

.05907 

.99825 

.77133 

73,4 

.99924 

3  23  10.25 

.0592 

.05917 

.99825 

.77207 

73,3 

.99924 

3  23  30.88 

•  0593 

.05927 

.99824 

.77280 

73,2 

.99924 

3  23  51.50 

.0594 

.05937 

.99824 

•  77353 

73,0 

•99923 

3  24  12.13 

0.0595 

0.05946 

10,0 

0.99823 

0,6 

8.77426 

72,9 

9.99923 

0,3 

3  24  32.76 

.0596 

.05956 

.99822 

•77499 

72,8 

.99923 

3  24  53.38 

•  0597 

.05966 

.99822 

•77572 

72,7 

.99923 

3  25  14.01 

.0598 

.05976 

.99821 

.77644 

72,5 

.99922 

3  25  34.64 

.0599 

.05986 

.99821 

.77717 

72,4 

.99922 

3  25  55.26 

0.0600 

0.05996 

IO,O 

0.99820 

0,6 

8.77789 

72,3 

9.99922 

o,3 

3  26  15.89 

u 

-isinhiu 

wF0' 

cosh  iu 

«FO' 

sinh  iu 

-Fo' 

ogcoshiu 

«FO' 

u 

log 

SMITHSONIAN  TABLES 


185 


Circular  Functions. 


u 

sin  u 

»F0' 

COS  U 

»F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

0.0600 

0.05996 

IO,O 

0.99820 

0,6 

8.77789 

72,3 

9.99922 

0,3 

3°26'  is'.'89 

.0601 

.06006 

.99819 

.77861 

72,2 

.99922 

3  26  36.51 

.0602 
.0603 

.06016 
.06026 

.99819 
.99818 

.77933 
.78005 

72,1 
71,9 

.99921 
.99921 

3  26  57.14 
3  27  17.77 

.0604 

.06036 

.99818 

.78077 

7i,8 

.99921 

3  27  38.39 

0.0605 

0.06046 

IO,O 

0.99817 

0,6 

8.78149 

7i,7 

9.99920 

0,3 

3  27  59.02 

.0606 

.06056 

.99816 

.  78221 

7i,6 

.99920 

3  28  19.65 

.0607 

.06066 

.99816 

.78292 

7i,5 

.99920 

3  28  40.27 

.0608 

.06076 

.99815 

.78364 

7i,3 

.99920 

3  29  00.90 

.0609 

.06086 

.99815 

. 

.78435 

71,2 

.99919 

3  29  21.53 

0.0610 

0.06096 

IO,O 

0.99814 

0,6 

8.78506 

7U 

9.99919 

o,3 

3  29  42.15 

.0611 

.06106 

.99813 

.78577 

7i,o 

.99919 

3  30  02.78 

.0612 

.06116 

.99813 

.78648 

70,9 

.99919 

3  30  23.41 

.0613 

.06126 

.99812 

.78719 

70,8 

.99918 

3  30  44-03 

.0614 

.06136 

.99812 

.78790 

70,6 

.99918 

3  31  04.66 

0.0615 

0.06146 

10,0 

0.99811 

0,6 

8.78860 

70,5 

9.99918 

o,3 

3  31  25.29 

.0616 

.06156 

.99810 

.78931 

70,4 

.99918 

3  31  45.91 

.0617 

.06166 

.99810 

.79001 

70,3 

.99917 

3  32  06.54 

.0618 

.06176 

.99809 

.70071 

70,2 

.99917 

3  32  27.17 

.0619 

.06186 

.99808 

.79UI 

70,i 

.99917 

3  32  47-79 

0.0620 

0.06196 

IO,O 

0.99808 

0,6 

8.79211 

70,o 

9.99916 

0,3 

3  33  08.42 

.0621 

.06206 

.99807 

.79281 

69,8 

.99916 

3  33  29.04 

.0622 

.06216 

.99807 

•79351 

69,7 

.99916 

3  33  49.67 

.0623 

.06226 

.99806 

.79421 

69,6 

.90916 

3  34  10.30 

.0624 

.06236 

.99805 

.79490 

69,5 

.99915 

3  34  30.92 

0.0625 

0.06246 

IO,O 

0.99805 

0,6 

8.79560 

69,4 

9.99915 

o,3 

3  34  51.55 

.0626 

.06256 

.99804 

.79629 

69,3 

•99915 

3  35  12.  18 

.0627 

.06266 

.99804 

.79698 

69,2 

.99915 

3  35  32.8o 

.0628 

.06276 

.99803 

.79767 

69,1 

.99914 

3  35  53.43 

.0629 

.06286 

.99802 

.79836 

69,0 

.99914 

3  36"  14.06 

0.0630 

0.06296 

IO,0 

0.99802 

0,6 

8.79905 

68,8 

9.99914 

o,3 

3  36  34.68 

.0631 

.06306 

.99801 

•79974 

68,7 

.99913 

3  36  55-31 

.0632 

.06316 

.99800 

•80043 

68,6 

.99913 

3  37  15-94 

.0633 

.06326 

.99800 

.80111 

68,5 

.99913 

3  37  36.56 

.0634 

.06336 

.99799 

.80180 

68,4 

.99913 

3  37  57.19 

0.0635 

0.06346 

IO,O 

0.99798 

0,6 

8.80248 

68,3 

9.99912 

o,3 

3  38  17.82 

.0636 

.06356 

.99798 

.80316 

68,2 

.99912 

3  38  38.44 

.0637 

.06366 

.99797 

•80385 

68,1 

.99912 

3  38  59.07 

.0638 

.06376 

•99797 

.80453 

68,0 

.99912 

3  39  19-69 

.0639 

.06386 

.99796 

.80521 

67,9 

.99911 

3  39  40.32 

0.0640 

0.06396 

IO,O 

0.09795 

0,6 

8.80588 

67,8 

9.999H 

o,3 

3  40  00.95 

.0641 

.06406 

.99795 

.80656 

67,7 

.99911 

3  40  21.57 

.0642 

.06416 

.99794 

.80724 

67,6 

.99910 

3  40  42.20 

.0643 

.06426 

.99793 

.80791 

67,4 

.99910 

3  41  02.83 

.0644 

.06436 

•99793 

.80859 

67,3 

.99910 

3  41  23.45 

0.0645 

0.06446 

IO,O 

0.99792 

0,6 

8.80926 

67,2 

9.99910 

0,3 

3  41  44-08 

.0646 

.06456 

•99791 

.80993 

67,1 

.99909 

3  42  04.71 

.0647 

.06465 

.99791 

.81060 

67,0 

.90909 

3  42  25.33 

.0648 

.06475 

.99790 

.81127 

6fo 

.99909 

3  42  45.96 

.0649 

.06485 

.99789 

.81194 

66,8 

.99908 

3  43  06.59 

0.0650 

0.06495 

1  0,0 

0.99789 

0,6 

8.81261 

65,7 

9.99908 

o,3 

3  43  27.21 

u 

isinhiu 

»Fo' 

cosh  iu 

-FO' 

l«flSinh  iU 

-FO' 

log  cosh  iu 

-FO' 

u 

lOfl   , 

SMITHSONIAN  TABLES 


1 86 


Circular  Functions. 


u 

siriu 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  oos  u 

«F0' 

u 

0.0650 

0.06495 

IO,O 

0.99789 

O,6 

8.81261 

66,7 

9.99908 

0,3 

3°43'27'.'2i 

.0651 

.06505 

.99788 

o,7 

.81327 

66,6 

.99908 

3  43  47.84 

.0652 

.06515 

.99788 

.81394 

66,5 

.99908 

3  44  08.47 

.0653 

.06525 

.99787 

.81460 

66,4 

.99907 

3  44  29.09 

.0654 

.06535 

.99786 

.81527 

66,3 

.99907 

3  44  49.72 

0.0655 

0.06545 

IO,O 

0.99786 

o,7 

8.81593 

66,2 

9.99907 

0,3 

3  45  10.34 

.0656 

•06555 

.99785 

.81659 

66,1 

.99906 

3  45  30.97 

.0657 

.06565 

.99784 

.81725 

66,0 

.99906 

3  45  51.60 

.0658 

•06575 

.99784 

.81791 

65,9 

.99906 

3  46  12.22 

.0659 

.06585 

.99783 

.81857 

65,8 

.99906 

3  46  32.85 

0.0660 

0.06595 

IO,O 

0.99782 

o,7 

8.81923 

65,7 

9.99905 

0,3 

3  46  53.48 

.0661 

.06605 

.99782 

.81989 

65,6 

.99905 

3  47  14.10 

.0662 

.06615 

.99781 

.82054 

65,5 

.99905 

3  47  34.73 

.0663 

.06625 

.99780 

.82120 

65,4 

.99904 

3  47  55.36 

.0664 

.06635 

.99780 

.82185 

65,3 

.99904 

348  15.08 

0.0665 

0.06645 

IO,O 

0.99779 

o,7 

8.82250 

65,2 

9.99904 

0,3 

3  48  36.61 

.0666 

.06655 

.99778 

.82315 

65,1 

.99904 

3  48  57-24 

.0667 

.06665 

.99778- 

.82380 

65,0 

.99903 

3  49  17.86 

.0668 

.06675 

•99777 

.82445 

64,9 

.99903 

3  49  38.49 

.0669 

.06685 

.99776 

.82510 

64,8 

.99903 

3  49  59-12 

0.0670 

0.06695 

IO,O 

0.99776 

o,7 

8.82575 

64,7 

9.99902 

0,3 

3  50  19.74 

.0671 

.06705 

.99775 

.82640 

646 

.99902 

3  50  40.37 

.0672 

.06715 

•99774 

.82704 

64,5 

.99902 

3  51  00.09 

.0673 

.06725 

•99774 

.82769 

64,4 

.09902 

3  51  21.62 

.0674 

.06735 

.99773 

.82833 

64,3 

.99901 

3  51  42.25 

0.0675 

0.06745 

10,0 

0.99772 

o,7 

8.82897 

64,2 

9.99001 

0,3 

3  52  02.87 

.0676 

.06755 

.99772 

.82962 

64,1 

.09901 

3  52  23.50 

.0677 

.06765 

.99771 

.83026 

64,1 

.99900 

3  52  44-13 

.0678 

.06775 

.99770 

.83090 

64,0 

.99900 

3  53  04-75 

.0679 

.06785 

•99770 

.83154 

63,9 

.99900 

3  53  25.38 

0.0680 

0.06795 

IO,O 

0.99769 

o,7 

8.83217 

63,8 

9.99900 

0,3 

3  53  46.01 

.0681 

.06805 

.99768 

.83281 

63,7 

.99899 

3  54  06.63 

.0682 

.06815 

.99768 

.83345 

63,6 

.99899 

3  54  27.26 

.0683 

.06825 

.99767 

.83408 

63,5 

.90899 

3  54  47.89 

.0684 

.06835 

.99766 

.83472 

63,4 

.99898 

3  55  08.51 

0.0685 

0.06845 

IO,O 

0.99765 

o,7 

8.83535 

63,3 

9.99898 

0,3 

3  55  29.14 

.0686 

.06855 

.99765 

.83598 

63,2 

.99898 

3  55  49.77 

.0687 

.06865 

.99764 

.83662 

63,1 

.99897 

3  56  10.39 

.0688 

.06875 

.99763 

.83725 

63,0 

.99897 

3  56  31.02 

.0689 

.06885 

.99763 

.83788 

62,9 

.99897 

3  56  51.65 

0.0600 

0.06895 

IO,O 

0.99762 

o,7 

8.83850 

62,8 

9.99897 

0,3 

3  57  12.27 

.0691 

.06905 

.99761 

.83913 

62,8 

.99896 

3  57  32.90 

.0692 

.06914 

.99761 

.83976 

62,7 

.99896 

3  57  53.52 

.0693 

.06924 

.99760 

.84039 

62,6 

.99896 

3  58  14-15 

.0604 

.06934 

•99759 

.84101 

62,5 

.99895 

3  58  34.78 

0.0695 

0.06944 

IO,O 

0.99759 

o,7 

8.84164 

62,4 

9.99895 

0,3 

3  58  55-40 

.0696 

.00954 

•99758 

.84226 

62,3 

.99895 

3  59  16.03 

.0697 

.06964 

•99757 

.84288 

62,2 

.99894 

3  59  36.66 

.0698 

.06974 

.99756 

.84350 

62,1 

.99894 

3  59  57.28 

.0699 

.06984 

.99756 

.84412 

62,0 

.99894 

4  oo  17.91 

0.0700 

0.06994 

IO,0 

0.99755 

o,7 

8.84474 

6i,9 

9.99894 

0,3 

4  oo  38.54 

u 

-isinhiu 

wF0' 

cosh  iu 

«F0' 

sinh  iu 

«•>  Fo' 

loo  cosh  iu 

«FO' 

u 

log  , 

SMITHSONIAN  TABLES 


187 


Circular  Functions. 


u 

sin  u 

«FO' 

COS  U 

«F0* 

log  sin  u 

•  FO' 

log  cos  u 

«F0' 

U 

0.0700 

0.06994 

10,0 

0.99755 

o,7 

8.84474 

61,9 

9-99894 

0,3 

4°oo  38"  54 

.0701 

.07004 

.99754 

.84536 

6i,9 

.99893 

4  oo  59.16 

.0702 

.07014 

•99754 

.84598 

61,8 

•99893 

4  oi  19.79 

.0703 

.07024 

•99753 

.84660 

61,7 

.99893 

4  01  40.42 

.0704 

.07034 

•99752 

.84721 

61,6 

.99892 

4  02  01.04 

0.0705 

0.07044 

10,0 

0.99752 

o,7 

8.84783 

61,5 

9.99892 

0,3 

4  02  21.67 

.0706 

•07054 

.99751 

.84844 

61,4 

.99892 

4  02  42.30 

.0707 

.07064 

•99750 

.84906 

61,3 

.99891 

4  03  02.92 

.0708 

.07074 

•99749 

.84967 

61,2 

.99891 

4  03  23.55 

.0709 

.07084 

.99749 

.85028 

61,2 

.99891 

4  03  44.17 

0.0710 

0.07094 

10,0 

0.99748 

o,7 

8.85089 

61,1 

9.99890 

0,3 

4  04  04.80 

.0711 

.07104 

.99747 

.85150 

61,0 

.99890 

4  04  25.43 

.0712 

.07114 

.99747 

.85211 

60,9 

.99890 

4  04  46.05 

.0713 

.07124 

.99746 

.85272 

60,8 

.99890 

4  05  06.68 

.0714 

.07134 

.99745 

.85333 

60,7 

•99889 

4  05  27.31 

0.0715 

0.07144 

1  0,0 

0-99744 

o,7 

8.85394 

60,6 

9.99889 

0,3 

4  05  47.93 

.0716 

.07154 

•99744 

•85454 

60,6 

4  06  08.56 

.0717 

.07164 

•99743 

.85515 

60,5 

99888 

4  06  29.19 

.0718 

.07174 

•99742 

•85575 

60,4 

.99888 

4  06  49.81 

.0719 

.07184 

.99742 

.85635 

60,3 

.99888 

4  07  10.44 

0.0720 

0.07194 

IO,0 

0.99741 

0,7 

8.85696 

60,2 

9.99887 

0,3 

4  07  31.07 

.0721 

.07204 

•99740 

.85756 

00,1 

.99887 

4  07  51.69 

.0722 

.07214 

•99739 

.85816 

60,0 

.99887 

4  08  12.32 

.0723 

.07224 

•99739 

.85876 

60,0 

.99886 

4  08  32.95 

.0724 

.07234 

.99738 

.85936 

59,9 

.99886 

4  08  53-57 

0.0725 

0.07244 

IO,O 

0.99737 

o,7 

8.85996 

59,8 

9.99886 

0,3 

4  09  14.20 

.0726 

.07254 

.99737 

.86056 

59,7 

.99885 

4  09  34.82 

.0727 

.07264 

.99736 

.86115 

59,6 

.99885 

4  09  55-45 

.0728 

.07274 

' 

•99735 

•86175 

59,6 

.99885 

4  10  16.08 

.0729 

.07284 

•99734 

.86234 

59,5 

•99884 

4  10  36.70 

0.0730 

0.07294 

IO,O 

0.99734 

o,7 

8.86294 

59,4 

9.99884 

0.3 

4  10  57-33 

.0731 

.07303 

.99733 

•86353 

59,3 

.99884 

4  II  17-96 

.0732 

.07313 

.99732 

.86412 

59,2 

.99884 

4  u  38.58 

•0733 

.07323 

•99731 

.86472 

59,i 

.99883 

4  u  59-21 

•0734 

.07333 

•99731 

•86531 

59,1 

.99883 

4  12  19.84 

0.0735 

0.07343 

IO,O 

0.99730 

o,7 

8.86590 

59,0 

9.99883 

0,3 

4  12  40.46 

.0736 

.07353 

.99729 

.86649 

58,9 

.99882 

4  13  01.09 

.0737 

.07363 

.99729 

.86707 

58,8 

.99882 

4  13  21.72 

.0738 

.07373 

.99728 

.86766 

58,7 

.99882 

4  13  42.34 

.0739 

.07383 

.99727 

.86825 

58,7 

.99881 

4  14  02.97 

0.0740 

0.07393 

10,0 

0.99726 

0,7 

8.86884 

58,6 

9-99881 

0,3 

4  14  23.60 

.0741 

.07403 

.99726 

.86942 

58,5 

.99881 

4  M  44.22 

.0742 

.07413 

.99725 

.87001 

58,4 

.99880 

4  IS  04.85 

.0743 

.07423 

.99724 

.87059 

58,3 

.99880 

4  15  25.48 

.0744 

.07433 

.99723 

.87117 

58,3 

.99880 

4  15  46.10 

0.0745 

0.07443 

10,0 

0.99723 

0,7 

8.87175 

58,2 

9.99879 

0,3 

4  16  06.73 

.0746 

.07453 

.99722 

.87234 

58,1 

.99879 

4  16  27.35 

.0747 

.07463 

•99721 

.87292 

58,0 

•99879 

4  16  47-98 

.0748 

.07473 

•99720 

.87350 

58,0 

.99878 

4  17  08.  61 

.0749 

.07483 

.99720 

.87408 

57,9 

.99878 

4  17  29.23 

0.0750 

0.07493 

10,0 

0.99719 

0,7 

8.87465 

57,8 

9.09878 

0,3 

4  17  49-86 

u 

-isinhiu 

«F0' 

cosh  iu 

«F0' 

|00$inh  iu 

•  IV 

ogcoshiu 

-Fo' 

u 

log  , 

SMITHSONIAN  TABLES 


188 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«-  Fo' 

log  cos  u 

•  Fo' 

u 

O     4     44 

0.0750 

0.07493 

10,0 

0.99719 

o,7 

8.87465 

57,8 

9.99878 

o,3 

4  17  49-86 

.0751 

.07503 

.99718 

0,8 

.87523 

57,7 

.99877 

4  18  10.49 

.0752 

.07513 

.99717 

.87581 

57,6 

.99877 

4  18  31.11 

.0753 

.07523 

.99717 

.87638 

57,6 

.99877 

4  18  51-74 

.0754 

.07533 

.99716 

.87696 

57,5 

.99876 

4  19  12.37 

0.0755 

0.07543 

10,0 

0.99715 

0,8 

8.87753 

57,4 

9.99876 

0,3 

4  19  32.99 

.0756 

.07553 

.99714 

.87811 

57,3 

.99876 

4  19  53.62 

.0757 

.07563 

.99714 

.87868 

57,3 

.99875 

4  20  14.25 

.0758 

.07573 

.99713 

.87925 

57,2 

.99875 

4  20  34.87 

.0759 

.07583 

.99712 

.87982 

57,1 

.99875 

4  20  55.50 

0.0760 

0.07593 

10,0 

0.99711 

0,8 

8.88040 

57,0 

9.99874 

0,3 

4  21  16.13 

.0761 

.07603 

.99711 

.88097 

57,o 

.99874 

4  21  36.75 

.0762 

.07613 

.99710 

.88153 

56,9 

.99874 

4  21  57.38 

.0763 

.07623 

.99709 

.88210 

56,8 

.99873 

4  22  iS.OO 

.0764 

.07633' 

.99708 

.88267 

56,7 

.99873 

4  22  38.63 

0.0765 

0.07643 

10,0 

0.99708 

0,8 

8.88324 

56,7 

9.99873 

0,3 

4  22  59.26 

.0766 

.07653 

.99707 

.88380 

56,6 

.99872 

4  23  19.88 

.0767 

.07662 

.99706 

.88437 

56,5 

.99872 

4  23  40.51 

.0768 

.07672 

.99705 

.88493 

56,4 

.99872 

4  24  01.14 

.0769 

.07682 

.99704 

.88550 

56,4 

.99871 

4  24  21.76 

0.0770 

0.07692 

10,0 

0.99704 

0,8 

8.88606 

56,3 

9.99871 

0,3 

4  24  42.39 

.0771 

.07702 

.99703 

.88562 

56,2 

.99871 

4  25  03.02 

.0772 

.07712 

.99702 

.88719 

56,1 

.99870 

4  25  23.64 

.0773 

.07722 

.99701 

.88775 

56,1 

.09870 

4  25  44.27 

.0774 

.07732 

.99701 

.88831 

56,0 

.99870 

4  26  04.90 

0.0775 

0.07742 

10,0 

0.99700 

0,8 

8.88887 

55,9 

9.99869 

0,3 

4  26  25.52 

.0776 

.07752' 

.99699 

.88943 

55,9 

.99869 

4  26  46.15 

.0777 

.07762 

.99698 

.88998 

55,8 

.99869 

4  27  06.78 

.0778 

.07772 

.99698 

^89054 

55,7 

.99868 

4  27  27.40 

.0779 

.07782 

.99697 

.89110 

55,6 

.99868 

4  27  48.03 

0.0780 

0.07792 

10,0 

0.99696 

0,8 

8.89165 

55,6 

9.99868 

0,3 

4  28  08.65 

.0781 

.07802 

.99695 

.89221 

55,5 

.99867 

4  28  29.28 

.0782 

.07812 

.99694 

.89276 

55,4 

.99867 

4  28  49-91 

.0783 

.07822 

.99694 

.89332 

55,4 

.99867 

4  29  10.53 

.0784 

.07832 

.99693 

.89387 

55,3 

.99866 

4  29  31.16 

0.0785 

0.07842 

10,0 

0.99692 

0,8 

8.89442 

55,2 

9.99866 

0,3 

4  29  51.79 

.0786 

.07852 

.99691 

.89498 

55,i 

.99866 

4  30  12.41 

.0787 

.07862 

.99690 

.89553 

55,1 

.99865 

4  30  33.04 

.0788 

.07872 

.89608 

55,o 

.99865 

4  30  53-67 

.0789 

.07882 

.99689 

.89663 

54,9 

.99865 

4  31  14.29 

0.0700 

0.07892 

IO,O 

0.99688 

0,8 

8.89718 

54,9 

9.99864 

0,3 

4  31  34-92 

.0791 

.07902 

•  .99687 

.89772 

54,8 

.99864 

4  31  55.55 

.0792 

.07912 

.99687 

.89827 

54,7 

.99864 

4  32  16.17 

.0793 

.07922 

.99686 

.89882 

54,7 

.99863 

4  32  36.80 

.0794 

.07932 

.99685 

• 

.89936 

54,6 

.99863 

4  32  57-43 

0.0795 

0.07942 

10,0 

0,99684 

0,8 

8.89991 

54,6 

9.99863 

o,3 

4  33  18.05 

.0706 

.07952 

.99683 

.90045 

54,4 

.99862 

4  33  38.68 

.0797 

.07962 

.99683 

.90100 

54,4 

.99862 

4  33  59.31 

.0798 

.07972 

.99682 

.90154 

54,3 

.99862 

• 

4  34  19.93 

.0799 

.07982 

.99681 

.90208 

54,2 

.99861 

4  34  40.56 

0.0800 

0.07991 

IO,O 

0.99680 

0,8 

8.90263 

54,2 

9.99861 

o,3 

4  35  oi  .  18 

u 

-isinhiu 

«F0' 

cosh  iu 

•  IV 

sinh  iu 

O.FO' 

log  cosh  iu 

«FO' 

u 

log   . 

SMITHSONIAN  TABLES 


189 


Circular  Functions. 


u 

sin  u 

«FO' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«F0' 

u 

0.0800 

0.07991 

10,0 

0.99680 

0,8 

8.90263 

54,2 

9.99861 

o,3 

4°3s'oi'.'i8 

.0801 

.08001 

.99679 

.90317 

54,1 

.99861 

4  35  21.  81 

.0802 

.08011 

.99679 

.90371 

54,o 

.99860 

4  35  42.44 

.0803 

.08021 

.99678 

.90425 

54,0 

.99860 

4  36  03.06 

.0804 

.08031 

.99677 

.90479 

53,9 

.99859 

4  36  23.69 

0.0805 

0.08041 

10,0 

0.99676 

0,8 

8.90533 

'53,8 

9.99859 

0,4 

4  36  44-32 

.0806 

.08051 

.99675 

.90586 

53,8 

.99859 

4  37  04.94 

.0807 

.08061 

.99675 

.90640 

53,7 

.99858 

4  37  25.57 

.0808 

.08071 

.99674 

.90694 

53,6 

.99858 

4  37  46.20 

.0809 

.08081 

.99673 

.90747 

53,6 

.99858 

4  38  06.82 

0.0810 

0.08091 

10,0 

0.99672 

0,8 

8.90801 

53,5 

9.99857 

0,4 

4  38  27-45 

.0811 

.08101 

.99671 

.90854 

53,4 

.99857 

4  38  48.08 

.0812 

.08111 

.99671 

.90908 

53,4 

.99857 

4  39  08.70 

.0813 

.08121 

.99670 

.90961 

53,3 

.99856 

4  39  29.33 

.0814 

.08131 

.99669 

.91014 

53,2 

.99856 

4  39  49.96 

0.0815 

0.08141 

10,0 

0.99668 

0,8 

8.91068 

53,2 

9.99856 

0,4 

4  40  10.58 

.0816 

.08151 

.99667 

.91121 

53>i 

.99855 

4  40  31-21 

.0817 

.08161 

.99666 

.9U74 

53,o 

.99855 

4  40  51.83 

.0818 

.08171 

.99666 

.91227 

53,0 

.99855 

4  41  12.46 

.0819 

.08181 

.99665 

.91280 

52,9 

.99854 

4  41  33.09 

0.0820 

0.08191 

1  0,0 

0.99664 

0,8 

8.91333 

52,8 

9.99854 

0,4 

4  41  53.71 

.0821 

.08201 

.99663 

.91386 

52,8 

.99853 

4  42  14.34 

.0822 

.08211 

.99662 

.91438 

52,7 

.99853 

4  42  34.97 

.0823 

.08221 

.99662 

.91491 

52,7 

.99853 

4  42  55-59 

.0824 

.08231 

.99661 

.91544 

52,6 

.99852 

4  43  16.22 

0.0825 

0.08241 

IO,O 

0.99660 

0,8 

8.91596 

52,5 

9.99852 

0,4 

4  43  36.85 

.0826 

.08251 

.99659 

.91649 

52,5 

.99852 

4  43  57-47 

.0827 

.08261 

.99658 

.91701 

52,4 

.99851 

4  44  18.  10 

.0828 

.08271 

.99657 

.91753 

52,3 

.99851 

4  44  38.73 

.0829 

.08281 

.99657 

.91806 

52,3 

.99851 

4  44  59-35 

0.0830 

0.08290 

IO,O 

0.99656 

0,8 

8.91858 

52,2 

9.99850 

0,4 

4  45  19.98 

'.0831 

.08300 

.99655 

.91910 

52,1 

.99850 

4  45  40.61 

.0832 

.08310 

.99654 

.91962 

52,1 

.99850 

4  46  01.23 

.0833 

.08320 

.99653 

.92014 

52,0 

.99849 

4  46  21.86 

.0834 

.08330 

.99652 

.92066 

52,0 

.99849 

4  46  42.48 

0.0835 

0.08340 

10,0 

0.99652 

0,8 

8.92118 

51,9 

9.99848 

0,4 

4  47  03.11 

.0836 

.083-50 

.99651 

.92170 

5i,8 

.99848 

4  47  23-74 

.0837 

.08360 

.99650 

.92222 

5i,8 

.99848 

4  47  44.36 

.0838 

.08370 

.92274 

5i,7 

.99847 

4  48  04.99 

.0839 

.08380 

.99648 

.92325 

5i,6 

.99847 

4  48  25.62 

0.0840 

0.08390 

10,0 

0.99647 

0,8 

8.92377 

5i,6 

9.99847 

0,4 

4  48  46.24 

.0841 

.08400 

.99647 

.92428 

51,5 

.99846 

4  49  06.87 

.0842 

.08410 

.99646 

.92480 

51,5 

.99846 

4  49  27.50 

.0843 

.08420 

.99645 

.92531 

51,4 

.99846 

4  49  48.12 

.0844 

.08430 

.99644 

.92583 

51,3 

.99845 

4  50  08.75 

0.0845 

0.08440 

10,0 

0.09643 

0,8 

8.92634 

51,3 

9.99845 

0,4 

4  50  29.38 

.0846 

.08450 

.99642 

.92685 

51,2 

.99844 

4  50  50.00 

.0847 

.08460 

.99642 

.92736 

51,2 

.99844 

4  51  10.63 

.0848 

.08470 

.99641 

.92788 

5i,i 

.99844 

4  51  31-26 

.0849 

.08480 

.99640 

.92839 

5i,o 

.99843 

4  51  51.88 

0.0850 

0.08490 

10,0 

0.99639 

0,8 

8.92890 

5i,o 

9.99843 

0,4 

4  52  12.51 

u 

-isinhiu 

•Fo' 

cosh  iu 

«  F' 

lno«inh  JU 

loo  p- 

•  FV 

log  cosh  iu 

-FO' 

u 

SMITHSONIAN  TABLES 


IQO 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

»Fo* 

log  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

0.0850 

0.08490 

10,0 

0.99639 

0,8 

8.92890 

51,0 

9.99843 

0,4 

4°52/i27si 

.0851 

.08500 

.99638 

0,8 

.92941 

50,9 

.99843 

4  52  33  -14 

.0852 

.08510 

.99637 

0,9 

.92991 

50,9 

.99842 

4  52  53.76 

.0853 

.08520 

.99636 

.93042 

50,8 

.99842 

4  53  14.39 

.0854 

.08530 

.99636 

.93093 

50,7 

.99841 

4  53  35-01 

0.0855 

0.08540 

IO,O 

0.99635 

o,9 

8.93144 

50,7 

9.99841 

0,4 

4  53  55.64 

.0856 

.08550 

.99634 

.93194 

50,6 

.99841 

4  54  16.27 

.0857 

.08560 

.99633 

.93245 

50,6 

.99840 

4  54  36.89 

.0858 

.08569 

.99632 

.93295 

50,5 

.99840 

4  54  57.52 

.0859 

.08579 

.99631 

.93346 

50,4 

.99840 

4  55  18.15 

0.0860 

0.08589 

10,0 

0.99630 

o,9 

8.93396 

50,4 

9.99839 

0,4 

4  55  38.77 

.0861 

.08599 

.99630 

•93447 

50,3 

.99839 

4  55  59.40 

.0862 

.08609 

.99629 

•93497 

50,3 

.99838 

4  56  20.03 

.0863 

.08619 

.99628 

.93547 

50,2 

.99838 

4  56  40.65 

.0864 

.08629 

.99627 

•93597 

50,1 

.99838 

4  57  01.28 

0.0865 

0.08639 

10,0 

0.99626 

0,9 

8.93647 

50,i 

9.99837 

0,4 

4  57  21.91 

.0866 

.08649 

.99625 

.93697 

50,0 

•99837 

4  57  42.53 

.0867 

.08659 

.99624 

•93747 

50,0 

.99837 

4  58  03.16 

.0868 

.08669 

.99624 

.93797 

49,9 

.99836 

4  58  23.79 

.0869 

.08679 

.99623 

.93847 

49,9 

.99836 

4  58  44.41 

0.0870 

0.08689 

10,0 

0.99622 

0,9 

8.93897 

49,8 

9.99835 

0,4 

4  59  05.04 

.0871 

.08699 

.99621 

•93947 

49,7 

•99835 

4  59  25.66 

.0872 

.08709 

.99620 

•93997 

49,7 

.99835 

4  59  46.29 

.0873 

.08719 

.99619 

.94046 

49,6 

.99834 

5  oo  06.92 

.0874 

.08729 

.99618 

.94096 

49,6 

.99834 

5  oo  27.54 

0.0875 

0.08739 

10,0 

0.99617 

o,9 

8.04145 

49,5 

9-99834 

0,4 

5  oo  48.17 

.0876 

.08749 

.99617 

.94195 

49,5 

.99833 

5  01  08.80 

.0877 

.08759 

.99616 

.94244 

49,4 

.99833 

5  01  29.42 

.0878 

.08769 

.99615 

.94294 

49,3 

•99832 

5  01  50.05 

.0879 

.08779 

.99614 

•94343 

49,3 

.99832 

5  02  10.68 

0.0880 

0.08789 

IO,O 

0.99613 

0,9 

8.94392 

49,2 

9.99832 

0,4 

5  02  31.30 

.0881 

.08799 

.99612 

.94441 

49,2 

.99831 

5  02  51.93 

.0882 

.08809 

.99611 

.94491 

49,1 

.99831 

5  03  12.56 

.0883 

.08819 

.99610 

.94540 

49,1 

.99830 

5  03  33.i8 

.0884 

.08828 

.99610 

.94589 

49,0 

.99830 

5  03  53.81 

0.0885 

0.08838 

IO,O 

0.99609 

0,9 

8.94638 

48,9 

9.99830 

0,4 

5  04  14.44 

.0886 

.08848 

.99608 

.94687 

48,9 

.99829 

5  04  35.o6 

.0887 

.08858 

.99607 

•94735 

48,8 

.99829 

5  04  55.69 

.0888 

.08868 

.99606 

.94784 

48,8 

.90829 

5  05  16.31 

.0889 

.08878 

.99605 

.94833 

48,7 

.99828 

5  05  36.94 

0.0890 

0.08888 

IO,O 

0.99604 

0,9 

8.94882 

48,7 

9.99828 

0,4 

5  05  57.57 

.0891 

.08898 

.99603 

.94930 

48,6 

.99^27 

5  06  18.19 

.0892 

.08908 

.99602 

.94979 

48,6 

.99827 

5  06  38.82 

.0893 

.08918 

.99602 

.95027 

48,5 

.99827 

5  06  59-45 

.0894 

.08928 

.99601 

.95076 

48,4 

.99826 

5  07  20.07 

0.0895 

0.08938 

10,0 

0.99600 

0,9 

8.95124 

48,4 

9.99826 

0,4 

5  07  40.70 

.0896 

.08948 

•99599 

.95173 

48,3 

.99825 

5  08  01.33 

.0897 

.08958 

.99598 

.95221 

48,3 

.99825 

5  08  21.95 

.0858 

.08968 

•99597 

.95269 

48,2 

.99825 

5  08  42.58 

.0899 

.08978 

.99596 

•95317 

48,2 

.99824 

5  09  03.21 

0.0900 

0.08988 

IO,O 

0.99595 

0,9 

8.95366 

48,1 

9.99824 

0,4 

5  09  23.83 

u 

isinhiu 

«F0' 

cosh  iu 

«F0' 

sinh  iu 

»Fo' 

log  cosh  iu 

«FO' 

u 

tog   . 

SMITHSONIAN  TABLES 


Circular  Functions. 


u 

sin  u 

»F0' 

COS  U 

«  Fo'   log  sin  u 

«  Fo' 

log  cos  u 

-FO' 

u 

0.0900 

0.08988 

IO,O 

0.99595 

0,9 

8.95366 

48,1 

9.99824 

0,4 

5°09'  23'.'83 

.0901 

.08998 

.99594 

.954H 

48,1 

.99823 

5  09  44.46 

.0902 

.00008 

.99593 

.95462 

48,0 

.99823 

5  10  05.09 

.0903 

.09018 

•99593 

•95510 

48,0 

.99823 

5  10  25.71 

.0904 

.09028 

.99592 

.95558 

47,9 

.99822 

5  10  46.34 

0.0905 

0.09038 

10,0 

0.99591 

0,9 

8.95606 

47,9 

9.99822 

0,4 

5  ii  06.96 

.0906 

.09048 

•99590 

.95653 

47,8 

.99822 

5  ii  27.59 

.0907 

.00058 

.99589 

.95701 

47,8 

.99821 

5  ii  48.22 

.0908 

.09068 

.99588 

•95749 

47,7 

.99821 

5  12  08.84 

.0909 

.09077 

.99587 

•95797 

47,6 

.99820 

5  12  29.47 

0.0910 

0.09087 

IO,O 

0.99586 

0,9 

8.95844 

47,6 

9.99820 

0,4 

5  12  50.10 

.0911 

.00097 

.99585 

.95892 

47,5 

.90820 

5  13  10.72 

.0912 

.09107 

.99584 

•95939 

47,5 

.90819 

5  13  31-35 

.0913 

.09117 

.99584 

•95087 

47,4 

.99819 

5  13  51.98 

.0914 

.09127 

.99583 

.96034 

47,4 

.99818 

5  14  12.60 

0.0915 

0.09137 

10,0 

0.99582 

0,9 

8.06081 

47,3 

9.99818 

0,4 

5  14  33.23 

.0916 

.09147 

.99581 

.96129 

47,3 

.99818 

5  14  53-86 

.0917 

.09157 

,99580 

.96176 

47,2 

.99817 

5  15  14.48 

.0918 

.09167 

..99579 

.96223 

47,2 

.99817 

5  15  35.ii 

.0919 

.09177 

.99578 

.96270 

47,1 

.998l6 

5  15  55-74 

0.0920 

0.09187 

IO,O 

0.99577 

0,9 

8.96317 

47,1 

9.998l6 

0,4 

5  16  16.36 

.0921 

.09197 

.99576 

.96365 

47,0 

.99816 

5  16  36.99 

.0922 

.09207 

•99575 

.96412 

47,0 

.99815 

5  16  57.62 

.0923 

.09217 

•99574 

.96458 

46,9 

.99815 

5  17  18.24 

.0924 

.09227 

.99573 

.96505 

46,9 

.99814 

5  17  38.87 

0.0925 

0.09237 

10,0 

0.99572 

0,9 

8.96552 

46,8 

9.09814 

0,4 

5  17  59-49 

.0926 

.09247 

.99572 

.96599 

46,8 

.09814 

5  18  20.12 

.0927 

.09257 

.99571 

.96646 

46,7 

•99813 

5  18  40.75 

.0928 

.09267 

.99570 

.96692 

46,7 

.99813 

5  19  01.37 

.0929 

.09277 

.99569 

.96739 

46,6 

.99812 

5  19  22.00 

!  0.0930 

0.09287 

IO,O 

0.99568 

o,9 

8.96786 

46,6 

9.99812 

0,4 

5  19  42.63 

.0931 

.09297 

.99567 

.96832 

46,5 

.99812 

5  20  03.25 

.0932 

.09307 

.99566 

.96879 

46,5 

.99811 

5  20  23.88 

•  0933 

.09316 

.99565 

.96925 

46,4 

.99811 

5  20  44-51 

•  0934 

.09326 

.99564 

.96972 

46,4 

.99810 

5  21  05.13! 

0.0935 

0.09336 

10,0 

0.99563 

0,9 

8.97018 

46,3 

9.09810 

0,4 

5  21  25.76 

.0936 

.09346 

.99562 

.97064 

46,3 

.99809 

5  21  46.391 

.0937 

.09356 

.99561 

.97110 

46,2 

.99809 

5  22  07.OI  { 

.0938 

.09366 

.99560 

.97157 

46,2 

.90809 

5  22  27.64 

•0939 

.09376 

•99559 

.97203 

46,1 

.00808 

5  22  48.27 

0.0940 

0.09386 

10,0 

0.99559 

0,9 

8.97249 

46,1 

9.99808 

0,4 

5  23  08.89 

.0941 

.09396 

.99558 

.97295 

46,0 

.90807 

5  23  29.52 

.0942 

.09406 

•99557 

•57341 

46,0 

.09807 

5  23  50.14 

.0943 

.00416 

.99556 

.97387 

45,9 

.00807 

5  -24  10.77 

.0944 

.09426 

.99555 

•97433 

45,9 

.99806 

5  24  31-40 

0.0945 

0.09436 

10,0 

0.09554 

o,9 

8.97479 

45,8 

9.99806 

0,4 

5  24  52.02' 

.0946 

.09446 

•99553 

.97524 

45,8 

.99805 

5  25  12.65; 

.0947 

.09456 

.99552 

•97570 

45,7 

.99805 

5  25  33.28 

.0948 

.09466 

•99551 

.97616 

45,7 

.99805 

5  25  53.90 

.0949 

.09476 

.99550 

.97661 

45,6 

.09804 

5  26  14.53 

0.0950 

0.09486 

10,0 

0.99549 

0,9 

8.97707 

45,6 

9.09804 

0,4 

5  26  35-16 

u 

-isinhiu 

-Fo' 

cosh  iu 

-Fo' 

log'-^ 

-FV 

log  cosh  iu 

«F0' 

u 

SMITHSONIAN  TABLES 


192 


Circular  Functions. 


u 

.in  u  V 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  oos  u 

«Fo' 

u 

0.0950 

0.09486 

IO,O 

0.99549 

0,9 

8.97707 

45,6 

9.99804 

0,4 

5°26'35'.'i6 

.0951 

.09496 

.99548 

0,9 

.97753 

45,5 

.99803 

5  26  55.78 

.0952 

.09506 

•99547 

1,0 

.97798 

45,5 

•99803 

5  27  16.41 

.0953 

.09516 

.99546 

.97844 

45,4 

.99802 

S  27  37.04 

.0954 

.09526 

•99545 

.97889 

45,4 

.99802 

5  27  57-66 

0.0955 

0.09535 

IO,0 

0.99544 

1,0 

8.97934 

45,3 

9.99802 

0,4 

5  28  18.29 

.0950 

-09545 

•99543 

.97980 

45,3 

.99801 

5  28  38.92 

.0957 

.09555 

•99542 

.98025 

45,2 

.99801 

5  28  59-54 

.0958 

.09565 

.99541 

.98070 

45,2 

.99800 

5  29  20.17 

.0959 

.09575 

•99541 

98115 

45,1 

.99800 

5  29  40.79 

0.0960 

0.09585 

10,0 

0.99540 

1,0 

8.98160 

45,1 

9.99800 

0,4 

5  30  01.42 

.0961 

.09595 

•99539 

.98205 

45,1 

•99799 

5  30  22.05 

.0962 

.09605 

.99538 

.98251 

45,0 

•99799 

5  30  42.67 

.0963 

.09615 

•99537 

.98295 

45,0 

.99798 

5  3i  03.30 

.0964 

.09625 

.99536 

.98340 

44,9 

.99798 

5  31  23.93 

0.0965 

0.09635 

IO,O 

0.99535 

1,0 

8.98385 

44,9 

9-99797 

0,4 

5  3i  44-55 

.0966 

.09645 

.99534 

.98430 

44,8 

.99797 

5  32  05.18 

.0967 

-09655 

.99533 

.98475 

44,8 

.99797 

5  32  25.81 

.0968 

.09665 

.99532 

.98520 

44,7 

.99796 

5  32  46.43 

.0969 

.09675 

•99531 

.98564 

44,7 

.99796 

5  33  07.06 

0.0970 

0.09685 

IO,O 

0.99530 

1,0 

8.98609 

44,6 

9-99795 

0,4 

5  33  27.69 

.0971 

.09695 

•99529 

.98554 

44,6 

•99795 

5  33  48-31 

.0972 

.09705 

.99528 

.98698 

445 

•99795 

5  34  08.94 

.0973 

.09715 

.99527 

.98743 

44,5 

•99794 

5  34  29-57 

.0974 

.09725 

.99526 

.98787 

44,4 

•99794 

5  34  50.19 

0.0975 

0.09735 

IO,O 

0.99525 

1,0 

8.98832 

44,4 

9-99793 

0,4 

5  35  10.82 

.0976 

.09745 

.99524 

.98876 

44,4 

•99793 

5  35  31-45 

.0977 

.09754 

•99523 

.98920 

44,3 

•99792 

5  35  52.07 

.0978 

.09764 

.99522 

.98965 

44,3 

•99792 

5  36  12.70 

.0979 

.09774 

•99521 

.99009 

44,2 

•99792 

5  36  33.32 

0.0980 

0.09784 

IO,O 

0.99520 

1,0 

8.99053 

44,2 

9.99791 

0,4 

5  36  53-95 

.0981 

.09794 

.99519 

.99097 

44,1 

.99791 

5  37  14.58 

.0982 

.09804 

.99518 

.99141 

44,1 

.99790 

5  37  35-20 

.0983 

.09814 

.99517 

.99185 

44,0 

.99790 

5  37  55.83 

.0984 

.09824 

.99516 

.99229 

44,0 

.99789 

5  38  16.46 

0.0985 

0.09834 

10,0 

0.99515 

I,O 

8.99273 

43,9 

9.99789 

0,4 

5  38  37.o8 

.0986 

.09844 

.99514 

.99317 

43,9 

.99789 

5  38  57-71 

.0987 

.09854 

.99513 

.99361 

43,9 

.99788 

5  39  i8.34 

.0988 

.09864 

.99512 

.90405 

43,8 

.99788 

5  39  38.96 

.0989 

.09874 

•995II 

•99449 

43,8 

.99787 

5  39  59-59 

0.0990 

0.09884 

IO,O 

0.99510 

1,0 

8.99493 

43,7 

9.99787 

0,4 

5  40  20.22 

.0991 

.09894 

.99509 

•99536 

43,7 

.99786 

5  40  40.84 

.0992 

.09904 

.99508 

.99580 

43,6 

.99786 

5  4i  01.47 

.0993 

.09914 

.99507 

.99624 

43,6 

.99786 

5  41  22.  IO 

.0994 

.09924 

.99506 

.99667 

43,5 

.99785 

5  41  42.72 

0.0995 

0.09934 

IO,O 

0.99505 

I,O 

8.997H 

43,5 

9.99785 

0,4 

5  42  03.35 

.0996 

.09944 

•99504 

•99754 

43,5 

.99784 

5  42  23.97 

.0997 

.09953 

.99503 

.99798 

43,4 

.99784 

5  42  44.60 

.0998 

.09963 

.99502 

.99841 

43,4 

.99783 

5  43  05.23 

.0999 

.09973 

•99501 

.99884 

43,3 

.99783 

5  43  25.85 

O.IOOO 

0.09983 

IO,O 

0.99500 

I,O 

8.99928 

43,3 

9.99782 

0,4 

5  43  46.48 

u 

-isinhiu 

«F0' 

cosh  iu 

O.FO' 

sinh  iu 

-Fo' 

log  cosh  iu 

«FO' 

u 

tog  . 

SMITHSONIAN  TABLES 


193 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«F0* 

log  sin  u 

«   Fo' 

log  cos  u 

<-F0' 

u 

0.100 

0.09983 

99,5 

0.99500 

IO,O 

8.99928 

432,8 

9.99782 

4,4 

5°43'46'.'48 

.101 

.10083 

99,5 

.99490 

10,1 

9.00358 

428,5 

.99778 

4,4 

5  47  12.75 

.102 

.  10182 

99,5 

.99480 

10,2 

.00785 

424,3 

.99774 

4,4 

5  50  39-01 

.103 

.  10282 

99,5 

.99470 

10,3 

.01207 

420,2 

.99769 

4,5 

5  54  05.28 

.104 

.  10381 

99,5 

.99460 

10,4 

.01625 

416,1 

.99765 

4,5 

5  57  31.54 

0.105 

0.10481 

99,4 

0.99449 

io,5 

9.02039 

412,1 

9.99760 

4,6 

6  oo  57.80 

.106 

.10580 

99,4 

•99439 

10,6 

.02449 

408,2 

.99756 

4,6 

6  04  24.07 

.107 

.10680 

99,4 

.99428 

10,7 

.02855 

404,3 

•99751 

4,7 

6  07  50.33 

.108 

.  10779 

99,4 

.99417 

10,8 

.03258 

400,6 

.99746 

4,7 

6  ii  16.60 

.109 

.10878 

99,4 

.99407 

10,9 

.03657 

396,9 

•99741 

4,8 

6  14  42.86 

O.IIO 

0.10978 

99,4 

0.99396 

11,0 

9.04052 

393,2 

9-99737 

4,8 

6  18  09.13 

.III 

.11077 

99,4 

.99385 

ii,  i 

.04443 

389,6 

•99732 

4,8 

6  21  35.39 

.112 

.11177 

99,4 

•99373 

11,2 

.04831 

386,1 

.99727 

4,9 

6  25  01.66 

•113 

.11276 

99,4 

.99362 

ii,3 

.05215 

382,7 

.99722 

4,9 

6  28  27.92 

.114 

.11375 

99,4 

•99351 

11,4 

.05596 

379,3 

.99717 

5,o 

6  31  54-19 

0.115 

O.I  1475 

99,3 

0.99339 

ii,5 

9.05974 

376,0 

9.99712 

5,o 

6  35  20.45 

.116 

-II574 

99,3 

.99328 

11,6 

.06348 

372,7 

•99707 

5,i 

6  38  46.72 

.117 

.11673 

99,3 

.99316 

n,7 

.06719 

369,5 

•99702 

5,1 

6  42  12.98 

.118 

•II773 

99,3 

.99305 

11,8 

.07087 

366,3 

.99697 

5,1 

6  45  39.25 

.119 

.11872 

99,3 

.99293 

11,9 

.07452 

363,2 

.99692 

5,2 

6  49  05.51 

0.120 

0.11971 

99,3 

0.99281 

12,0 

9.07814 

360,2 

9.99687 

5,2 

6  52  31.78 

.121 

.12070 

99,3 

.99269 

12,1 

.08173 

357,2 

.99681 

5,3 

6  55  58.04 

.122 

.12170 

99,3 

.99257 

12,2 

.08528 

354,2 

.99676 

5,3 

6  59  24.31 

.123 

.12269 

99,2 

.99245 

12,3 

.08881 

351,3 

•99671 

5,4 

7  02  50.57 

.124 

.12368 

99,2 

.99232 

12,4 

.09231 

348,4 

.99665 

5,4 

7  06  16.84 

0.125 

0.12467 

99,2 

0.99220 

12,5 

9.09578 

345,6 

9.99660 

5,5 

7  09  43.10 

.126 

.  12567 

99,2 

.99207 

12,6 

.09922 

342,9 

.99654 

5,5 

7  13  09.37 

.127 

.12666 

99,2 

.99195 

12,7 

.10264 

340,1 

.99649 

5,5 

7  16  35.63 

.128 
.129 

.  12765 
.12864 

99,2 
99,2 

.99182 
.99169 

12,8 

12,9 

.10602 
.10938 

337,4 
334,8 

.99638 

5,6 
5,6 

7  20  01.90 
7  23  28.16 

0.130 
.131 

0.12963 
.13063 

99,2 
99,1 

0.99156 
.99143 

13,0 
13,1 

9.11272 
.11603 

33^,2 
329,6 

9.99632 
.99626 

5,7 
5,7 

7  26  54-42 
7  30  20.69 

.132 

.13162 

99,1 

.09130 

13,2 

.11931 

327,1 

.99621 

5,8 

7  33  46.95 

•133 

.13261 

99,1 

.99117 

13,3 

.  12257 

324,6 

.99615 

5,8 

7  37  13-22 

•134 

.13300 

99,1 

.99104 

13,4 

.12580 

322,2 

.99609 

5,9 

7  40  39.48 

0.135 

0.  13459 

99,1 

0.99090 

13,5 

9.12901 

319,7 

9.99603 

5,9 

7  44  05.75 

.136 

.13558 

99,1 

.99077 

13,6 

.  13220 

317,4 

•99597 

5,9 

7  47  32.01 

•137 

.  13657 

99,1 

.99063 

13,7 

.  13536 

315,0 

.99591 

6,0 

7  50  58.28 

.138 

.13756 

99,0 

.99049 

13,8 

.13850 

312,7 

.99585 

6,0 

7  54  24.54 

•139 

.13855 

99,0 

.99036 

13,9 

.14162 

310,4 

.99579 

6,1 

7  57  5o.8i 

O.I40 

0.13954 

99,0 

0.99022 

14,0 

9.  14471 

308,2 

9-99573 

6,1 

8  01  17.07 

.141 

.  14053 

99,o 

.99008 

14,1 

.  14778 

306,0 

.99567 

6,2 

8  04  43.34 

.142 

.14152 

99,o 

.08993 

14,2 

.15083 

303,8 

.99561 

6,2 

8  08  09.60 

•143 

.14251 

99,0 

.98979 

14,3 

.15385 

301,6 

•99554 

6,3 

8  ii  35.87 

•144 

.  14350 

99,0 

.98965 

14,4 

.15686 

299,5 

.99548 

6,3 

8  15  02.13 

0.145 

0.14449 

99,0 

0.08951 

14,4 

9.15985 

297,4 

9-99542 

6,3 

8  18  28.40 

.146 

.14548 

98,9 

.98936 

14,5 

.16281 

295,3 

•99535 

6,4 

8  21  54-66 

.147 

.  14647 

98,9 

.98921 

14,6 

•  16575 

293,3 

.99529 

6,4 

8  25  20.93 

.148 

.14746 

98,9 

•  9-S007 

M,7 

.16868 

291,3 

.99523 

6,5 

8  28  47.19 

.149 

.14845 

98,9 

.98892 

14,8 

.17158 

289,3 

.09516 

6,5 

8  32  13.46 

0.150 

0.14944 

98,9 

0.98877 

14,9 

9.  17446 

287,4 

9-99510 

6,6 

8  35  39.72 

u 

-isinhiu 

-Fo' 

cosh  iu 

-FO' 

lootinh  iu 

t  uy 

«F0' 

log  cosh  iu 

«FO' 

u 

SMITHSONIAN  TABLES 


(94 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«Fo* 

log  sin  u 

«-  Fo' 

log  cos  u 

-Fo' 

u 

0.150 

0.14944 

98,9 

0.98877 

14,9 

9.17446 

287,4 

9.99510 

6,6 

8°  35'  39''72 

.151 

•  15043 

98,9 

.98862 

I5,o 

.  17733 

285,4 

.99503 

6,6 

8  39  05-99 

.152 

.15142 

98,8 

.98847 

*5,i 

.18017 

283,5 

.99496 

6,7 

8  42  32.25 

.153 

.15240 

98,8 

.98832 

15,2 

.18300 

28l,6 

.99490 

6,7 

8  45  58.52 

.154 

.15339 

98,8 

.98817 

15,3 

.18580 

279,8 

.99483 

6,7 

8  49  24.78 

0.155 

0.15438 

98,8 

0.98801 

15,4 

9.18859 

277,9 

9.99476 

6,8 

8  52  51.04 

.156 

•  15537 

98,8 

.98786 

15,5 

.  19136 

276,1 

.99469 

6,8 

8  56  17.31 

•  157 

.15636 

98,8 

.98770 

15,6 

.19411 

274,3 

.99463 

6,9 

8  59  43-57 

.158 
.159 

.  15734 
.15833 

98,8 
98,7 

.98754 
.98739 

15,7 
15,8 

.19685 
.19957 

272,6 
270,8 

.99456 
.99449 

6,9 
7,0 

9  03  09.84 
9  06  36.  10 

0.160 

0.15932 

98,7 

0.98723 

15,9 

9.20227 

269,1 

9-99442 

7,o 

9  10  02.37 

.161 

^/-T-W 

.16031 

98,7 

.98707 

16,0 

.20495 

267,4 

•99435 

7,i 

9  13  28.63 

.162 

.  16129 

98,7 

.98691 

16,1 

.20761 

265,7 

.99428 

7,i 

9  16  54-90 

.163 

.16228 

98,7 

.98674 

16,2 

.21026 

264,1 

.99420 

7,i 

9  20  21.  16 

.164 

.  16327 

98,7 

.98658 

16,3 

.21290 

202,4 

•99413 

7,2 

9  23  47-43 

0.165 

0.16425 

98,6 

0.98642 

16,4 

9.2I55I 

200,8 

9.99406 

7,2 

9  27  13.69 

.166 

.  16524 

98,6 

.98625 

16,5 

.21811 

259,2 

•99399 

7,3 

9  30  39.96 

.167 

.16622 

98,6 

.98609 

16,6 

.22070 

257,6 

.99392 

7,3 

9  34  06.22 

.168 

.  16721 

98,6 

.98592 

16,7 

.22326 

256,1 

.99384 

7,4 

9  37  32.49 

.169 

.16820 

98,6 

.98575 

16,8 

.22582 

254,5 

•99377 

7,4 

9  40  58.75 

0.170 

0.16918 

98,6 

0.98558 

16,9 

9.22836 

253,0 

9.99369 

7,5 

9  44  25.02 

.171 

.17017 

98,5 

.98542 

17,0 

.23088 

251,5 

.99362 

7,5 

9  47  51.28 

.172 

.17115 

98,5 

.98524 

I7,i 

.23338 

250,0 

•99354 

7,5 

9  51  17-55 

•  173 

.17214 

98,5 

.98507 

17,2 

.23588 

248,5 

•99347 

7,6 

9  54  43.81 

.174 

.17312 

98,5 

.98490 

17,3 

.23836 

247,i 

•99339 

7,6 

9  58  10.08 

0.175 

O.I74H 

98,5 

0.98473 

17,4 

9.24082 

245,6 

9.99332 

7,7 

10  01  36.34 

.176 

.17509 

98,5 

.98455 

17,5 

.24327 

244,2 

.99324 

7,7 

10  05  02.61 

.177 

.17608 

98,4 

.98438 

17,6 

.24570 

242,8 

.99316 

7,8 

10  08  28.87 

.178 

.17706 

98,4 

.98420 

17,7 

.24812 

241,4 

.99308 

7,8 

10  ii  55.14 

.179 

.17805 

98,4 

.98402 

17,8 

.25053 

240,0 

.99300 

7,9 

10  15  21.40 

0.180 

0.17903 

98,4 

0.98384 

17,9 

9-25292 

238,7 

9.99293 

7,9 

10  18  47.67 

.181 

.18001 

98,4 

.98366 

18,0 

.25530 

237,3 

.99285 

7,9 

10  22   13.93 

.182 

.18100 

98,3 

.98348 

18,1 

.25767 

236,0 

.99277 

8,0 

10  25  40.19 

.183 

.18198 

98,3 

.98330 

18,2 

.26002 

234,7 

.99269 

8,0 

10  29  06.46 

.184 

.18296 

98,3 

.98312 

18,3 

.26236 

233,4 

.99261 

8,1 

10  32  32.72 

.0185 

0.18395 

98,3 

0.98294 

18,4 

9.26469 

232,1 

9.99253 

8,1 

10  35  58.99 

.186 

.  18493 

98,3 

.98275 

18,5 

.26701 

230,8 

.99244 

8,2 

10  39  25.25 

.187 

.18591 

98,3 

.98257 

18,6 

.26931 

229,5 

.99236 

8,2 

10  42  51.52 

.188 

.18689 

98,2 

.98238 

18,7 

.27160 

228,3 

.99228 

8,3 

10  46  17.78 

.189 

.18788 

98,2 

.98219 

18,8 

.27387 

227,0 

.99220 

8,3 

10  49  44.05 

0.190 

0.18886 

98,2 

0.98200 

18,9 

9.27614 

225,8 

9.992II 

8,4 

10  53  10.31 

.191 

.18984 

98,2 

.98181 

19,0 

.27839 

224,6 

.99203 

8,4 

10  56  36.58 

.192 

.10082 

98,2 

.98162 

19,1 

.28063. 

223,4 

.99195 

8,4 

ii  oo  02.84 

•  193 

.19180 

98,1 

.98143 

19,2 

.28286 

222,2 

.99186 

8,5 

ii  03  29.11 

.194 

.  19279 

98,1 

.98124 

19,3 

.28507 

221,0 

.99178 

8,5 

ii  06  55-37 

0.195 

0.19377 

98,1 

0.98105 

19,4 

9.28728 

219,9 

9.99169 

8,6 

ii  10  21.64 

.196 

.  19475 

98,1 

.98085 

19,5 

.28947 

218,7 

.99160 

8,6 

II  13  47.90 

.197 

.19573 

98,1 

.98066 

19,6 

.29165 

217,6 

.9915-2 

8,7 

II  17  14.17 

.198 

.19671 

08,0 

.98046 

19,7 

.29382 

216,5 

.99143 

8,7 

II   20  40.43 

.199 

.19769 

98,0 

.98026 

19,8 

.29598 

215,3 

.99134 

8,8 

II   24  06.70 

0.200 

o.  1986.7 

98,0 

0.98007 

19,9 

9-29813 

214,2 

9.99126 

8,8 

II   27  32.96 

U 

-isinhiu 

«F0' 

cosh  iu 

«FO' 

sinh  iu 

«Fo' 

log  cosh  iu 

«FO' 

u 

loo      - 

SMITHSONIAN  TABLES 


195 


Circular  Functions. 


u 

sin  u 

«FO' 

COS  U 

•  Fo' 

log  sin  u 

«   Fo' 

log  oos  u 

•  FO' 

u 

O.2OO 

0.19867 

98,0 

0.98007 

19,9 

9.29813 

214,2 

9.99126 

8,8 

ii°27/32.'o6 

.2OI 

.19965 

98,0 

.97987 

20,O 

.30027 

213,1 

.99117 

8,8 

ii  30  59.23 

.2C2 

.20063 

98,0 

.97967 

20,1 

.30239 

212,1 

.99108 

8,9 

II  34  25.49 

.203 

.20161 

97,9 

.97947 

20,2 

.30451 

2II,O 

.99099 

8,9 

ii  37  51.76 

.204 

.20259 

97,9 

.97926 

20,3 

.30661 

209,9 

.99090 

9,o 

II  41   18.02 

O.205 

0.20357 

97,9 

0.97906 

20,4 

9-30871 

208,9 

9.99081 

9,0 

II  44  44.29 

.206 

.20455 

97,9 

.97886 

20,5 

.31079 

207,8 

.99072 

9,i 

ii  48  10.55 

.207 

.20552 

97,9 

.97865 

2O,6 

.31286 

206,8 

.99063 

9,i 

ii  51  36.81 

.208 

.20650 

97,8 

.97845 

20,7 

.31493 

205,8 

.99054 

9,2 

ii  55  03.08 

.209 

.20748 

97,8 

.97824 

20,7 

.31698 

204,8 

.99044 

9,2 

ii  58  29.34 

0.210 

0.20846 

97,8 

0.97803 

20,8 

9.31902 

203,8 

9.99035 

9,3 

12  01    55-6l 

.211 

.20944 

97,8 

.97782 

20,9 

.32106 

202,8 

.99026 

9,3 

12  05  21.87 

.212 

.21042 

97,8 

.97761 

2I,O 

.32308 

201,8 

.99017 

9,3 

12   08   48.14 

.213 

.21139 

97,7 

.97740 

21,1 

.32509 

200,8 

.99007 

9,4 

12    12    14.40 

.214 

*  .21237 

97,7 

.97719 

21,2 

.32709 

199,8 

.98998 

9,4 

12    15  40.67 

O.2I5 

0.21335 

97,7 

0.97698 

21,3 

9.32909 

198,9 

9.98988 

9,5 

12    19  O6.93 

.216 

.21432 

97,7 

.97676 

21,4 

.33107 

197,9 

.98979 

9,5 

12   22   33.2O 

.217 

.21530 

97,7 

.97655 

21,5 

.33305 

197,0 

.98969 

9,6 

12  25   59.46 

.218 

.21628 

97,6 

.97633 

21,6 

•33501 

196,0 

.98960 

9,6 

12   29  25.73 

.219 

.21725 

97,6 

.97612 

21,7 

.33697 

I95,i 

.98950 

9,7 

12  32   51-99 

0.220 

0.21823 

97,6 

0.97590 

21,8 

9.33891 

194,2 

9.98940 

9,7 

12   36    18.26 

.221 

.21921 

97,6 

.97568 

21,9 

.34085 

193,3 

.98931 

9,8 

12  39  44.52 

.222 

.22018 

97,5 

.97546 

22,0 

.34278 

192,4 

.98921 

9,8 

12  43  10.79 

.223 

.22116 

97,5 

.97524 

22,1 

•34470 

I9i,5 

.98911 

9,8 

12  46  37-05 

.224 

.22213 

97,5 

.97502 

22,2 

.34661 

190,6 

.98901 

9,9 

12   5O  03.32 

0.225 

0.22311 

97,5 

0.97479 

22,3 

9.34851 

189,8 

9.98891 

9,9 

12  53  29.58 

.226 

.22408 

97,5 

•97457 

22,4 

.35041 

188,9 

.98881 

10,0 

12   56   55.85 

.227 

.22506 

97,4 

•97435 

22,5 

.35229 

188,0 

.98871 

10,0 

13  OO  22.11 

.228 

.22603 

97,4 

.97412 

22,6 

.35417 

187,2 

.98861 

10,1 

13  03  48.38 

.229 

.22700 

97,4 

.97389 

22,7 

.35603 

186,3 

.08851 

10,1 

13  07  14-64 

O.23O 

0.22798 

97,4 

0.97367 

22,8 

9.35789 

i85,5 

9.98841 

10,2 

13  10  40.91 

.231 

.22895 

97,3 

•97344 

22,9 

•35974 

184,7 

.98831 

IO,2 

13    14  07.17 

.232 

.22992 

97,3 

.97321 

23,0 

.36158 

183,8 

.98821 

10,3 

13  17  33.44 

•233 

.23000 

97,3 

.97298 

23,1 

.36342 

183,0 

.98810 

10,3 

13   20   59-70 

•234 

.23187 

97,3 

•97275 

23,2 

.36525 

182,2 

.98800 

10,4 

13  24  25.96 

0.235 

0.23284 

97,3 

0.97251 

23,3 

9-36706 

181,4 

9.98790 

10,4 

13  27  52.23 

.236 

.23382 

97,2 

.97228 

23,4 

.36887 

180,6 

.98779 

10,4 

13  31  18.49 

.237 

•23479 

97,2 

.97205 

23,5 

.37068 

179,8 

.98769 

10,5 

13  34  44.76 

.238 

.23576 

97,2 

.97181 

23,6 

.37247 

179,0 

.98758 

10,5 

13  38  I  i.  02 

•239 

.23673 

97,2 

.97158 

23,7 

.37426 

178,2 

.98748 

10,6 

13  41  37-29 

0.240 

0.23770 

97,1 

0.97134 

23,8 

9.37603 

177,5 

9.98737 

10,6 

13  45  03.55 

.241 

.23867 

97,1 

.97110 

23,9 

.37780 

176,7 

.98726 

10,7 

13  48  29.82 

.242 

.23964 

97,i 

.97086 

24,0 

•37957 

175,9 

.98716 

10,7 

13  51  56.08 

.243 

.24062 

97,1 

.97062 

24,1 

.38132 

175,2 

.98705 

10,8 

13  55  22.35 

.244 

.24159 

97,0 

.9/038 

24,2 

•38307 

174,4 

.98694 

10,8 

13  58  48.61 

0.245 

0.24256 

97,0 

0.97014 

24,3 

9.38481 

173,7 

9.98683' 

10,9 

14  02  14.88 

.246 

•24353 

97,0 

.96989 

24,4 

.38655 

I73,o 

.9867J 

10,9 

14  05  41.14, 

.247 

.24450 

97,0 

.96965 

24,4 

.38827 

172,2 

.98669 

11,0 

14  09  07.41 

.248 

•24547 

po0 

.96941 

24,5 

.38999 

I7i,5 

.98651 

11,0 

14    12  33.67 

.249 

.24643 

96,9 

.96916 

24,6 

.39170 

170,8 

.98640 

11,0 

14  15  59-94 

0.250 

0.24740 

96,9 

0.96891 

24,7 

9.39341 

170,1 

9.08628 

lit! 

14  19  26.20 

u 

-isinhiu 

«F0' 

cosh  iu 

•Fo' 

I008inh  iu 

•  Fo' 

log  cosh  iu 

-Fo' 

u 

log     , 

SMITHSONIAN  TABLES 


196 


Circular  Functions. 


u 

sin  u 

«F0' 

•OS  U 

«Fo' 

log  sin  u 

«  Fo' 

log  cos  u 

«F0' 

u 

0.250 

0.2474» 

96,9 

0.96891 

24,7 

9.39341 

170,1 

9.98628 

11,1 

14  19  26.20 

.251 

.24837 

96,9 

.96866 

24,8 

.39510 

169,4 

.98617 

11,1 

14  22   52.47 

.252 

.24934 

96,8 

.96842 

24,9 

.39679 

168,7 

.98606 

11,2 

14  26    18.73 

.253 

.25031 

96,8 

.96817 

25,0 

.39848 

168,0 

.98595 

11,2 

14  29  45.00 

.254 

.25128 

96,8 

.96792 

25,1 

.40015 

167,3 

.98584 

11,3 

14  33  11.26 

0.255 

0.25225 

96,8 

0.96766 

25,2 

9.40182 

166,6 

9.98572 

li,3 

H  36  37-53 

.256 

.25321 

96,7 

.96741 

25,3 

.40349 

165,9 

.98561 

11,4 

14  40  03.79 

.257 

.25418 

96,7 

.96716 

25,4 

.40514 

165,2 

.98550 

11,4 

14  43  30.06 

.258 

.25515 

96,7 

.96690 

25,5 

.40679 

164,6 

.98538 

n,5 

14  46  56.3:2 

.259 

.25611 

96,7 

.96665 

25,6 

.40843 

163,9 

.98527 

11,5 

14  50  22.58 

0.260 

0.25708 

96,6 

0.96639 

25,7 

9.41007 

163,3 

9.98515 

n,6 

14  53  48.85 

.261 

.25805 

96,6 

.96613 

25,8 

.41170 

162,6 

.98504 

11,6 

14  57  iS.ii 

.262 

.25901 

96,6 

.96587 

25,9 

•41332 

162,0 

.08492 

11,6 

15  oo  41.38 

.263 

.25908 

96,6 

.96561 

26,0 

.41494 

161,3 

.98480 

n,7 

15  04  07.64 

.264 

.26094 

96,5 

.96535 

26,1 

.41655 

160,7 

.98469 

.     I  L7 

15  07  33.91 

0.265 

0.26191 

96,5 

0.96509 

26,2 

9.4l8l5 

160,0 

9.98457 

n,8 

15  ii  00.17 

.266 

.26287 

96,5 

.96483 

26,3 

.41975 

!59»4 

.98445 

n,8 

15  14  26.44 

.267 

.26384 

96,5 

.96457 

26,4 

.42134 

158,8 

.98433 

n,9 

15  17  52.70 

.268 

.26480 

96,4 

.96430 

26,5 

.42292 

158,2 

.98421 

n,9 

15  21    l8.97 

.269 

.26577 

96,4 

.96404 

26,6 

.42450 

157,5 

.98409 

12,0 

15  24  45.23 

0.270 

0.26673 

96,4 

0.96377 

26,7 

9.42607 

156,9 

9.98397 

12,0 

15  28  11.50 

.271 

.26770 

96,4 

.96350 

26,8 

.42764 

156,3 

.98385 

12,1 

15  3i  37.76 

.272 

.26866 

96,3 

.96324 

26,9 

.42920 

155,7 

.98373 

12,1 

15  35  04.03 

.273 

.26962 

96,3 

.96297 

27,0 

.43075 

I55,i 

.98361 

12,2 

15  38  30.29 

.274 

.27058 

96,3 

.96270 

27,1 

.43230 

154,5 

.98349 

12,2 

15  41  56.56 

0.275 

0.27155 

96,2 

0.96243 

27,2 

9.43384 

153,9 

9.98337 

12,3 

15  45  22.82 

.276 

.27251 

96,2 

.96215 

27,3 

.43538 

153,3 

.98324 

12,3 

15  48  49-09 

.277 

.27347 

96,2 

.96188 

27,3 

.43691 

'    1:52,8 

.98312 

12,3 

15  52  15.35 

.278 

.27443 

96,2 

.96161 

27,4 

•43844 

152,2 

.08300 

12,4 

15  55  41.62 

.279 

.27539 

96,1 

.96133 

27,5 

•43996 

151,6 

.98287 

12,4 

15  59  07.88 

0.280 

0.27636 

96,1 

0.96106 

27,6 

9.44147 

151,0 

9.98275 

12,5 

16  02  34.15 

.281 

.27732 

96,1 

.96078 

27,7 

.44298 

150,5 

.98262 

12,5 

16  06  00.41 

.282 

.27828 

96,1 

.96050 

27,8 

.44448 

149,9 

.98250 

12,6 

16  09  26.68 

.283 

.27924 

96,0 

.96022 

27,9 

•44597 

149,3 

.98237 

12,6 

16  12  52.94 

.284 

.28020 

96,0 

.95994 

28,0 

.44746 

148,8 

.98225 

12,7 

16  16  19.20 

0.285 

0.28116 

96,0 

0.95966 

28,1 

9.44895 

148,2 

9.98212 

12,7 

16  19  45.47 

.286 

.28212 

95,9 

.95938 

28,2 

.45043 

147,7 

.98199 

12,8 

16  23  11.73 

.287 

.28308 

95,9 

.95910 

28,3 

.45190 

147,1 

.98186 

12,8 

16  26  38.00 

.288 

.28404 

95,9 

.95881 

28,4 

•45337 

146,6 

.98173 

12,9 

16  30  04.26 

.289 

.28499 

95,9 

.95853 

28,5 

.45484 

146,1 

.98161 

12,9 

16  33  30.53 

O.2OO 

0.28595 

95,8 

0.95824 

28,6 

9.45629 

145,5 

9.98148 

13,0 

16  36  56.79 

.291 

.28691 

95,8 

.95796 

28,7 

•45775 

145,0 

.98135 

13,0 

16  40  23.06 

.292 

.28787 

95,8 

.95767 

28,8 

.45919 

144,5 

.98122 

13,1 

16  43  49.32 

•293 

.28883. 

95,7 

.95738 

28,9 

.46064 

144,0 

.98109 

13,1 

16  47  15-59 

•294 

.28978 

95,7 

.95709 

29,0 

.46207 

143,4 

.98095 

13,1 

16  50  41.85 

0.295 

0.29074 

95,7 

0.95680 

29,1 

9.46350 

142,9 

9.98082 

13,2 

16  54  08.12 

.296 

.29170 

95,7 

.95651 

29,2 

.46493 

142,4 

.98069 

13,2 

16  57  34.38 

.297 

.29265 

95,6 

.95622 

29,3 

.46633 

141,9 

.98056 

13,3 

17  01  00.65 

.298 

.29361 

95,6 

•95593 

29,4 

.46777 

141,4 

.980421 

13,3 

17  04  26.91 

.299 

.29456 

95,6 

.95563 

29,5 

.46918 

140,9 

.98029 

13,4 

17  07  53.i8 

0.300 

0.29552 

95,5 

0.95534 

29,6 

9.47059 

140,4 

9.98016 

13,4 

17  ii  19.44 

u 

-i  sinh  iu 

*>Fo' 

cosh  iu 

«F0' 

sinh  iu 

wF0' 

log  cosh  iu 

«F0' 

u 

log      . 

SMITHSONIAN  TABLES 


197 


Circular  Functions. 


u 

sin  u 

-Fo' 

cos  u 

«Fo' 

log  sin  u 

«    Fo' 

log  oos  u 

»F0' 

u 

0.300 

0.29552 

95,5 

0.95534 

29,6 

9.47059 

140,4 

9.98016 

13,4 

17  II   19  '44 

.301 

.29648 

95,5 

.95504 

29,6 

.47199 

139,9 

.08002 

13,5 

17  14  45.71 

.302 

.29743 

95,5 

.95474 

29,7 

•47339 

139,4 

.97989 

13,5 

17  18  11.97 

.303 

.29838 

95,4 

•95445 

29,8 

.47478 

138,9 

•97975 

13,6 

17  21    38.24 

.304 

•29934 

95,4 

.95415 

29,9 

.47616 

138,4 

.97962 

13,6 

17  25  04.50 

0.305 

0.30029 

95,4 

0.95385 

30,0 

9-47755 

137,9 

9.97948 

i3,7 

17  28  30.77 

.306 

.30125 

95,4 

•95355 

30,1 

.47892 

137,5 

•97934 

i3,7 

17  31    57.03 

.307 

.30220 

95,3 

.95324 

30,2 

.48029 

137,0 

.97920 

13,8 

17  35  23.30 

.308 

.30315 

95,3 

.95294 

30,3 

.48166 

136,5 

.97907 

13,8 

17  38  49.56 

.309 

.304H 

95,3 

.95264 

30,4 

.48303 

136,0 

.97893 

13,9 

17  42  15-83 

0.310 

0.30506 

95,2 

0.95233 

30,5 

9.48438 

135,6 

9.97879 

13,9 

17  45  42.09 

.311 

.30601 

95,2 

.95203 

30,6 

.48574 

I35,i 

.97865 

14,0 

17  49  08.35 

.312 

.30696 

95,2 

.95172 

30,7 

.48709 

134,7 

.97851 

14,0 

17  52  34.62 

.313 

.30791 

95,1 

.95141 

30,8 

.48843 

134,2 

.97837 

14,1 

17  56  00.88 

.314 

.30887 

95,1 

.95HI 

30,9 

.48977 

133,7 

.97823 

14,1 

17  59  27.15 

0.315 

0.30982 

95,1 

0.95080 

31,0 

9.49HO 

133,3 

9.97809 

142 

18  02  53.41 

.316 

.31077 

95,o 

.95049 

3i,i 

•49244 

132,8 

•  97795 

14,2 

18  06  19.68 

.317 

.31172 

95,0 

.95017 

31,2 

.49376 

132,4 

.97780' 

14,2 

18  09  45.94 

.318 

.31267 

95,0 

.94986 

3i,3 

.49508 

I3i,9 

.97766 

14,3 

l8    13    12.21 

.319 

.31362 

95,0 

•94955 

31,4 

.49640 

131,5 

•97752 

14,3 

18  16  38.47 

0.320 

0.31457 

94,9 

0.94924 

31,5 

9.49771 

131,1 

9-97737 

14,4 

18  20  04.74 

.321 

.31552 

94,9 

.04892 

3i,6 

.49902 

130,6 

.97723 

14,4 

18  23  31.00 

.322 

.31646 

94,9 

.04860 

3i,6 

.50032 

130,2 

.97709 

H,5 

18  26  57.27 

.323 

.31741 

94,8 

.94829 

3i,7 

.50162 

129,7 

.97694 

14,5 

18  30  23.53 

.324 

.31836 

94,8 

•94797 

31,8 

.50292 

129,3 

.97679 

14,6 

18  33  49.8o 

0.325 

0.3I93I 

94,8 

0.94765 

31,9 

9.50421 

128,9 

9.97665 

14,6 

18  37  16.06 

.326 

.32026 

94,7 

•94733 

32,0 

.50550 

128,5 

.97650 

14,7 

18  40  42.33 

.327 

.32120 

94,7 

.94701 

32,1 

.50678 

128,0 

.97635 

14,7 

18  44  08.59 

.328 

.32215 

94,7 

.94669 

32,2 

.50806 

127,6 

.97621 

14,8 

18  47  34-86 

.329 

.32310 

94,6 

.94637 

32,3 

•50933 

127,2 

.97606 

14,8 

18  51  01.12 

0.330 

0.32404 

94,6 

0.94604 

32,4 

9.51060 

126,8 

9.97591 

14,9 

18  54  27.39 

.331 

.32499 

94,6 

•94572 

32,5 

.5H87 

126,4 

.97576 

14,9 

18  57  53.65 

.332 

•  3'2593 

94,5 

.94539 

32,6 

.51313 

126,0 

.97561 

I5,o 

19  01  19.92 

•333 

.32688 

94,5 

.94507 

32,7 

.51439 

125,6 

.97546 

I5,o 

19  04  46.18 

•  334 

.32782 

94,5 

•94474 

32,8 

.51564 

125,2 

•97531 

I5,i 

19  08  12.45 

0-335 

0.32877 

94,4 

0.04441 

32,9 

9-51689 

124,8 

9.97516 

I5,i 

19  u  38.71 

•  336 

.32971 

94,4 

.94408 

33,o 

.51814 

124,4 

•  97501 

15,2 

19  15  04.97 

•  337 

.33066 

94,4 

•94375 

33,1 

.51938 

124,0 

.97486 

15,2 

19  18  31-24 

.338 

.33160 

94,3 

•  94342 

33,2 

.52062 

123,6 

•97470 

15,3 

19  21  57.50 

•  339 

.33254 

94,3 

.94309 

33,3 

.52185 

123,2 

•97455 

15,3 

19  25  23.77' 

0.340 

0.33349 

94,3 

0.94275 

33,3 

9.52308 

122,8 

9-97440 

15,4 

19  28  50.03 

•  341 

•33443 

94,2 

.94242 

33,4 

.52430 

122,4 

.97424 

15,4 

19  32  16.30! 

•  342 

.33537 

94,2 

.94209 

33,5 

.52553 

1  22,O 

.97409 

15,5 

19  35  42.56! 

•  343 

.33631 

94,2 

.94175 

33,6 

.52674 

121,6 

•97394 

15,5 

19  39  08.83 

•  344 

.33726 

94,1 

.94141 

33,7 

.52796 

121,2 

.97378 

15,6 

19  42  35.09 

0.345 

0.33820 

94,1 

0.94108 

33,8 

9.52917 

120,8 

9.97362 

15,6 

19  46  01.36 

•  346 

.33914 

94,1 

.94074 

'  33,9 

.53038 

120,5 

•97347 

15,7 

19  49  27.62 

•  347 

.34008 

94,0 

.04040 

34,0 

.53158 

120,1 

.97331 

15,7 

19  52  53.89 

.348 

.34102 

94,0 

.04006 

34,1 

.53278 

H9,7 

.97315 

15,8 

19  56  20.15 

•  349 

.34196 

94,0 

•93972 

34,2 

•  53397 

119,3 

•97300 

15,8 

19  59  46.42 

0.350 

0.34290 

93,9 

0.93937 

34,3 

9.53516 

119,0 

9.97284 

15,9 

20  03  12.68 

u 

-Isinhiu 

•  F«f 

cosh  iu 

«Fo' 

.     sinh  iu 

-Fo' 

log  cosh  iu 

«F0' 

u 

log     , 

SMITHSONIAN  TABLES 


198 


Circular  Functions. 


u 

sin  u 

•  Fo' 

cos  u 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«F0' 

u 

0.350 

0.34290 

93,9 

0.93937 

34,3 

9.53516 

119,0 

9.97284 

15,9 

20  °03'  12768 

.351 

.34384 

93,9 

.93903 

34,4 

.53635 

118,6 

.97268 

15,9 

20  06  38.95 

.352 

•34478 

93,9 

.93869 

34,5 

•53754 

118,2 

.97252 

16,0 

20  10  05.21 

•  353 

•34571 

93,8 

.93834 

34,6 

.53872 

117,9 

.97236 

16,0 

20  13  31.48 

•  354 

.34665 

93,8 

.93799 

34,7 

.53989 

H7,5 

.97220 

16,1 

20  16  57-74 

0-355 

0.34759 

93,8 

0.93765 

34,8 

9.54107 

117,2 

9.97204 

16,1 

2O  20  24.OI 

.356 

.34853 

93,7 

•93730 

34,9 

.54224 

116,8 

.97188 

16,1 

20  23  50.27 

•  357 

.34946 

93,7 

.93695 

34,9 

•54340 

116,4 

.97172 

16,2 

2O  27  16.54 

.353 

.35040 

93,7 

.93660 

35,0 

.54457 

116,1 

.97155 

16,2 

2O  3O  42.80 

•  359 

.35134 

93,6 

.93625 

35,1 

•54573 

115,7 

.97139 

16,3 

20  34  09.07 

0.360 

0.35227 

93,6 

0.93590 

35,2 

9.54688 

H5,4 

9.97123 

16,3 

20  37  35-33 

.361 

.35321 

93,6 

.93554 

35,3 

.54803 

H5,o 

.97106 

16,4 

20  41  01.  60 

.362 

.35415 

93,5 

.93519 

35,4 

.54918 

H4,7 

.97000 

16,4 

20  44  27.86 

.363 

.35508 

93,5 

.93484 

35,5 

.55033 

H4,3 

.97074 

16,5 

20  47  54.12 

.364 

.35601 

93,4 

•93448 

35,6 

.55147 

114,0 

•97057 

16,5 

20  51  20.39 

0.365 

0.35095 

93,4 

0.93412 

35,7 

9.55261 

H3,7 

9.97040 

16,6 

20  54  46.65 

.366 

.35788 

93,4 

•93377 

35,8 

.55374 

H3,3 

.97024 

16,6 

20  58  12.92 

.367 

.35882 

93,3 

.93341 

35,9 

.55487 

H3,o 

.97007 

16,7 

21  01  39.18 

.368 

•35975 

93,3 

.93305 

36,0 

.55600 

112,6 

.96990 

16,7 

21  05  05.45 

.369 

.36068 

93,3 

.93269 

36,1 

.55713 

112,3 

.96974 

16,8 

21  08  3L7I 

0.370 

0.36162 

93,2 

0.93233 

36,2 

9.55825 

1  1  2,0 

9.96957 

16,8 

21  II  57.98 

•  371 

.36255 

93,2 

.93197 

36,3 

•55937 

111,6 

.96940 

16,9 

21  15  24.24 

•  372 

.36348 

93,2 

.93i6o 

36,3 

.56048 

in,3 

.06923 

16,9 

21  18  50.51 

•  373 

.36441 

93,1 

.93124 

36,4 

.56159 

III.O 

.96906 

17,0 

21  22  16.77 

•  374 

.36534 

93,1 

.93087 

36,5 

.56270 

110,7 

.96889 

17,0 

21  25  43.04 

0.375 

0.36627 

93,1 

0.93051 

36,6 

9-56380 

110,3 

9.96872 

-17,1 

21  29  09.30 

.376 

.36720 

93,0 

.93014 

36,7 

.56491 

110,0 

•95855 

i7,i 

21  32  35-57 

•  377 

.36813 

93,0 

.92977 

36,8 

.56600 

109,7 

.96838 

17,2 

21  36  01.83 

.378 

.36906 

92,9 

.92940 

36,9 

.56710 

109,4 

.96820 

17,2 

21  39  28.10 

•  379 

.36999 

92,9 

.92904 

37,0 

.56819 

109,0 

.96803 

17,3 

21  42  54.36 

0.380 

0.37092 

92,9 

0.92866 

37,1 

9.56928 

108,7 

9.96786 

17,3 

21  46  20.63 

.381 

.37185 

92,8 

.92829 

37,2 

.57037 

108,4 

.96769 

17,4 

21  49  46.89 

.382 

.37278 

92,8 

.92792 

37,3 

.57145 

108,1 

.96751 

i7;4 

21  53  13.16 

.383 

•37370 

92,8 

.92755 

37,4 

.57253 

107,8 

.96734 

17,5 

21  56  39-42 

.384 

.37463 

92,7 

.92717 

37,5 

.57361 

107,5 

.96716 

17,5 

22  OO  05.69 

0.385 

0.37556 

92,7 

0.92680 

37,6 

9.57468 

107,2 

9.96699 

17,6 

22  03  3L95 

.386 

.37649 

92,6 

.92642 

37,6 

•57575 

106,9 

.96681 

17,6 

22  06  58.22 

.387 

•37741 

92,6 

.92605 

37,7 

.57682 

106,6 

.96663 

17,7 

22  IO  24.48 

.388 

.37834 

92,6 

.92567 

37,8 

.57788 

106,3 

.96646 

17,8 

22  13  50-74 

.389 

.37926 

.92,5 

.92529 

37,9 

.57894 

106,0 

.96628 

17,8 

22  17  17.01 

0.390 

0.38019 

92,5 

0.92491 

38,0 

9.58000 

105,7 

9.96610 

17,9 

22  20  43.27 

•  391 

.38111 

92,5 

.92453 

38,1 

.58105 

105,4 

.06592 

17,9 

22  24  09.54 

•  392 

.38204 

92,4 

.92415 

38,2 

.58211 

105,1 

.96574 

18,0 

22  27  35.80 

•393 

.38206 

92,4 

.92376 

38,3 

.58316 

104,8 

.96556 

18,0 

22  31  02.O7 

•  394 

.38389 

92,3 

•92338 

38,4 

.58420 

104,5 

.96538 

18,1 

22  34  28.33 

0.395 

0.38481 

92,3 

0.92300 

38,5 

9-58524 

104,2 

9-96520 

18,1 

22  37  54.60 

.396 

.38573 

92,3 

.92261 

38,6 

.58628 

103,9 

.06502 

18,2 

22  41  2O.86 

•  397 

.38665 

92,2 

.92223 

38,7 

.58732 

103,6 

.96484 

18,2 

•22  44  47.13 

-398 

.38758 

92,2 

.92184 

38,8 

.58836 

103,3 

.96465 

18,3 

22  48  13.39 

•  399 

.38850 

92,1 

.92145 

38,8 

.58939 

103,0 

.96447 

18,3 

22  51  39.66 

0.400 

0.38942 

92,1 

0.92106 

38,9 

9.59042 

102,7 

9.96429 

18,4 

22  55  05.92 

u 

-isinhiu 

-Fo' 

cosh  iu 

•  Fo' 

sinh  iu 

co  Fo' 

log  cosh  iu 

•  FO' 

u 

loo   . 

SMITHSONIAN  TABLES 


199 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

"Fo' 

u 

0.400 

0.38942 

92,1 

0.92106 

38,9 

9.59042 

102,7 

9.96429 

18,4 

22°55/05/./92 

.401 

.39034 

92,1 

.92067 

39,0 

.59144 

102,4 

.96410 

18,4 

22  58  32.19 

.402 

.39126 

92,0 

.92028 

39,1 

.59247 

IO2,2 

.96392 

18,5 

23  oi  58.45 

.403 

.39218 

92,0 

.91989 

39,2 

•59349 

101,9 

.96374 

18,5 

23  05  24.72 

.404 

.39310 

9i,9 

.91950 

39,3 

.59450 

101,6 

.96355 

18,6 

23  08  50.98 

0.405 

0.30402 

9i,9 

0.91910 

39,4 

9.59552 

101,3 

9.96336 

18,6 

23  12  17.25 

.406 

.39494 

9i,9 

.91871 

39,5 

.59653 

101,0 

.96318 

18,7 

23  15  43.51 

.407 

•  39586 

91,8 

.91831 

39,6 

•59754 

100,7 

.96299 

18,7 

23  19  09.78 

.408 

.39677 

91,8 

.91792 

39,7 

.59854 

100,5 

.96280 

18,8 

23  22  36.04 

.409 

.39769 

91,8 

.91752 

39,8 

•55955 

100,2 

.96262 

18,8 

23  26  O2.3I 

0.410 

0.30861 

91,7 

0.91712 

39,9 

9.60055 

99,9 

9.96243 

18,9 

23  29  28.57 

.411 

•39953 

9i,7 

.91672 

40,0 

.60155 

99,6 

.96224 

18,9 

23  32  54.84 

.412 

.40044 

91,6 

.91632 

40,0 

.60254 

99,4 

.96205 

I9,o 

23  36  21.10 

.413 

.40136 

91,6 

.91592 

40,1 

.60353 

99,i 

.96186 

19,0 

23  39  47.36 

.414 

.40227 

91,6 

.91552 

40,2 

.60452 

98,8 

.96167 

19,1 

23  43  13.63 

0.415 

0.40319 

9i,5 

0.91512 

40,3 

9.60551 

98,6 

9.96148 

19,1 

23  46  39.89 

.416 

.40410 

9i,5 

.91471 

40,4 

.60649 

98,3 

.96128 

19,2 

23  50  06.  16 

.417 

.40502 

91,4 

.91431 

40,5 

.60748 

98,0 

.96109 

19,2 

23  53  32.42 

.418 

•40593 

9i,4 

.91390 

40,6 

.60845 

97,8 

.96090 

19,3 

23  56  58.69 

.419 

.40685 

9i,3 

.91350 

40,7 

.60943 

97,5 

.96071 

19,3 

24  oo  24-95 

0.420 

0.40776 

9i,3 

0.91309 

40,8 

9.61041 

97,3 

9.90051 

19,4 

24  03  51.22 

.421 

.40867 

9i,3 

.91268 

40,9 

.61138 

97,o 

.96032 

19,4 

24  07  17-48 

.422 

.40959 

91,2 

.91227 

41,0 

.61234 

96,7 

.96012 

19,5 

24  10  43-75 

.423 

.41050 

91,2 

.91186 

41,0 

.61331 

96,5 

.95993 

19,6 

24  14  10.01 

.424 

.41141 

91,1 

.91145 

41,1 

.61427 

96,2 

•95973 

19,6 

24  17  36.28 

0.425 

0.41232 

91,1 

0.91104 

41,2 

9.61524 

96,0 

9.95954 

19,7 

24  21  02.54 

.426 

.41323 

91,1 

.91063 

41,3 

.61619 

95,7 

•95934 

19,7 

24  24  28.8l 

.427 

.41414 

91,0 

.91021 

41,4 

.61715 

95,5 

.95914 

19,8 

24  27  55.07 

.428 

.41505 

91,0 

.90980 

41,5 

.61810 

95,2 

.95894 

19,8 

24  31  21.34 

.429 

•41596 

90,9 

.90938 

41,6 

.61905 

94,9 

.95875 

19,9 

24  34  47.60 

0.430 

0.41687 

90,9 

0.00897 

41,7 

9.62000 

947 

9.95855 

19,9 

24  38  13.87 

.431 

.41778 

90,9 

.90855 

41,8 

.62095 

94,4 

.95835 

20,0 

24  41  40.  13 

.432 

.41869 

90,8 

.90813 

4i,9 

.62189 

94,2 

.95815 

20,0 

24  45  06.40 

•433 

.41960 

90,8 

.00771 

42,0 

.62283 

94,0 

•95795 

20,1 

24  48  32.66 

•  434 

.42050 

90,7 

.90729 

42,1 

.62377 

93,7 

•95775 

20,1 

24  51  58.93 

0.435 

0.42141 

90,7 

0.90687 

42,1 

9.62471 

93,5 

9-95755 

20,2 

24  55  25.19 

.436 

.42232 

90,6 

.90645 

42,2 

.62564 

93,2 

•95734 

20,2 

24  58  51.46 

•  437 

.42322 

90,6 

.00603 

42,3 

.62657 

93,0 

•95714 

20,3 

25  02  17.72 

.438 

.42413 

90,6 

.90560 

42,4 

.62750 

92,8 

.95094 

20,3 

25  05  43-99 

•439 

.42503 

90,5 

.90518 

42,5 

.62842 

92,5 

.95673 

.20,4 

25  09  10.25 

0.440 

0.42594 

90,5 

0.90475 

42,6 

9-62935 

92,2 

9.95653 

20,4 

25  12  36.51 

.441 

.42684 

90,4 

.90433 

42,7 

.63027 

92,0 

.95632 

20,5 

25  16  02.78 

.442 

.42775 

90,4 

.00390 

42,8 

.63119 

9i,8 

.95612 

20,6 

25  19  29.04 

•  443 

.42865 

90,3 

.90347 

42,9 

.63210 

9i,5 

•  95591 

20,6 

25  22  55.31 

.444 

.42956 

90,3 

.90304 

43,0 

.63302 

9i,3 

•95571 

20,7 

25  26  21.57 

0.445 

0.43046 

90,3 

0.90261 

43,0 

9.63393 

91,1 

9.95550 

20,7 

25  29  47.84 

.446 

.43136 

90,2 

.90218 

43,1 

.63484 

90,8 

.95529 

20,8 

25  33  14.10 

•  447 

.43226 

90,2 

.90175 

43,2 

.6^575 

00,6 

•95509 

20,8 

25  36  40.37 

.448 

.43316 

00,1 

.90132 

43,3 

.63665 

90,4 

.65488 

20,9 

25  40  06.63 

.449 

.43406 

90,1 

.90088 

43,4 

.63755 

90,i 

.95467 

20,9 

25  43  32.90 

0.450 

0.43497 

90,0 

0.90045 

43,5' 

9.63845 

89,9 

9.95446 

21,0 

25  46  59.16 

u 

isinhiu 

«F0' 

cosh  iu 

«FO' 

ion$lnh  lu 
100  , 

«F0' 

oo  cosh  iu 

«FO' 

u 

SMITHSONIAN  TABLES 


2OO 


Circular  Functions. 


u 

sin  u 

»F0' 

cos  u 

«  Fo' 

log  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

0.450 

0.43497 

00,0 

0.90045 

43,5 

9.63845 

89,9 

9.95446 

21,0 

25°46/59/.'i6 

.451 

.43587 

00,0 

.90001 

43,6 

.63935 

89,7 

.95425 

21,0 

25  50  25.43 

.452 

.43677 

90,0 

.89958 

43,7 

.64025 

89,4 

.95404 

21,1 

25  53  51.69 

•453 

.43766 

89,9 

43,8 

.64114 

89,2 

.95383 

21,1 

25  57  17.96 

•454 

.43856 

89,9 

.89870 

43,9 

.64203 

89,0 

.95361 

21,2 

26  oo  44.22 

0.455 

0.43946 

89,8 

0.89826 

43,9 

9.64292 

88,8 

9-95340 

21,2 

26  04  10.49 

.456 

.44036 

89,8 

.89782 

44,0 

.64381 

88,5 

.95319 

21,3 

26  07  36.75 

•457 

.44126 

89,7 

.89738 

44,1 

.64469 

88,3 

.95298 

21,4 

26  ii  03.02 

.458 

.44216 

89,7 

.89694 

44,2 

.64557 

88,1 

.95276 

21,4 

26  14  29.28 

•  459 

.44305 

89,6 

.89650 

44,3 

.64645 

87,9 

.95255 

21,5 

26  17  55-55 

0.460 

0.44395 

89,6 

0.89605 

44,4 

9.64733 

87,7 

9.95233 

21,5 

26  21  21.  8l 

.461 

.44484 

89,6 

.89561 

44,5 

.64821 

87,4 

.95212 

21,6 

26  24  48.08 

.462 

•44574 

89,5 

.89516 

44,6 

.64908 

87,2 

.95100 

21,6 

26  28  14.34 

.463 

.44663 

89,5 

.89472 

44,7 

.64995 

87,0 

.95169 

21,7 

26  31  40.6l 

.464 

•44753 

89,4 

.89427 

44,8 

.65082 

86,8 

.95147 

21,7 

26  35  06.87 

0.465 

0.44842 

89,4 

0.89382 

44,8 

9.65169 

86,6 

9.95125 

21,8 

26  38  33-13 

.466 

.44932 

89,3 

.89337 

44,9 

.65255 

86,4 

.95103 

21,8 

26  41  59.40 

.467 

.45021 

89,3 

.89292 

45,0 

.65341 

86,1 

.95081 

21,9 

26  45  25.66 

.468 

.4$no 

89,2 

.89247 

45,i 

.65428 

85,9 

.95059 

22,0 

26  48  51.93 

.469 

•45199 

89,2 

.89202 

45,2 

.65513 

85,7 

.95037 

22,0 

26  52  18.19 

0.470 

0.45289 

89,2 

0.89157 

45,3 

9.65599 

85,5 

9.95015 

22,1 

26  55  44.46 

.471 

•45378 

89,1 

.89111 

45,4 

.65684 

85,3 

•94993 

22,1 

26  59  10.72 

.472 

.45467 

89,1 

.89066 

45,5 

.65769 

85,1 

.94971 

22,2 

27  02  36.99 

•473 

.45556 

89,0 

.80021 

45,6 

•65854 

84,9 

.94949 

22,2 

27  06  03.25 

•  474 

.45645 

89,0 

.88975 

45,6 

.65939 

84,7 

.94927 

22,3 

27  09  29.52 

0.475 

0.4573'4 

88,9 

0.88929 

45,7 

9.66024 

84,4 

9.94904 

22,3 

27  12  55.78 

.476 

.45823 

88,9 

.88883 

45,8 

.66108 

84,2 

.94882 

22,4 

27  16  22.05 

•477 

.45912 

88,8 

.88838 

45,9 

.66192 

84,0 

.94860 

22,4 

27  19  48.31 

.478 

.46000 

88,8 

.88792 

46,0 

.66276 

83,8 

.94837 

22,5 

27  23  14.58 

.479 

.46089 

88,7 

.88746 

46,1 

.66360 

83,6 

.94815 

22,6 

27  26  40.84 

0.480 

0.46178 

88,7 

0.88699 

46,2 

9-66443 

83,4 

9.94792 

22,6 

27  30  07.11 

.481 

.46267 

88,7 

.88653 

46,3 

.66527 

83,2 

.94769 

22,7 

27  33  33-37 

.482 

.46355 

88,6 

.88607 

46,4 

.66610 

83,0 

.94747 

22,7 

27  36  59.64 

.483 

.46444 

88,6 

.88561 

46,4 

.66693 

82,8 

.94724 

22,8 

27  40  25.90 

.484 

.46532 

88,5 

.88514 

46,5 

.66775 

82,6 

•94701 

22,8 

27  43  52.17 

0.485 

0.46621 

88,5 

0.88467 

46,6 

9.66858 

82,4 

9.94678 

22,9 

27  47  18.43 

.486 

.46709 

88,4 

.88421 

46,7 

.66940 

82,2 

.94655 

22,9 

27  50  44-70 

.487 

.46798 

88,4 

.88374 

46,8 

.67022 

82,0 

.94633 

23,0 

27  54  10.96 

.488 

.46886 

88,3 

.88327 

46,9 

.67104 

81,8 

.94609 

23,1 

27  57  37.23 

.489 

.46974 

88,3 

.88280 

47,o 

.67186 

81,6 

.94586 

23,1 

28  01  03.49 

0.400 

0.47063 

88,2 

0.88233 

47,1 

9.67268 

81,4 

9.94563 

23,2 

28  04  29.76 

.491 

.47151 

88,2 

.88186 

47,2 

.67349 

81,2 

•94540 

23,2 

28  07  56.02 

•  492 

.47239 

88,1 

.88139 

47,2 

.67430 

81,0 

.94517 

23,3 

28  ii  22.28 

•  493 

•47327 

88,1 

.88092 

47,3 

.67511 

80,8 

•94493 

23,3 

28  14  48.55 

•  494 

.47415 

88,0 

.88044 

47,4 

.67592 

80,6 

•94470 

23,4 

28  18  14.81 

0-495 

0.47503 

88,0 

0.87997 

47,5 

9.67672 

80,5 

9.94447 

23,4 

28  21  41.08 

.496 

.47591 

87,9 

.87949 

47,6 

.67753 

80,3 

.94423 

23,5 

28  25  07.34 

•  497 

.47679 

87,9 

.87902 

47,7 

.67833 

80,  i 

.94400 

23,6 

28  28  33.61 

.498 

.47767 

87,9 

.87854 

47,8 

.67913 

79,9 

.94376 

23,6 

28  31  59.87 

.499 

.47855 

87,8 

.87806 

47,9 

.67993 

79,7 

.94352 

23,7 

28  35  26.14 

0.500 

0.47943 

87,8 

0.87758 

47,9 

9.68072 

79,5 

9.94329 

23,7 

28  38  52.40 

u 

-isinhiu 

«F0' 

cosh  iu 

«F0' 

,0  *«nh  »" 

wF0' 

log  cosh  iu 

«F0' 

u 

loo  . 

SMITHSONIAN  TABLES 


201 


Circular  Functions. 


u 

sin  u 

«F.' 

cos  u 

<«>  Fo' 

log  sin  u 

«  Fo' 

log  cos  u 

«Ff' 

n 

u 

O     /     94 

0.500 

0.47943 

87,8 

0.87758 

47,9 

9.68072 

79,5 

9.94329 

23,7 

28  38  52.40 

.501 

.48030 

87,7 

.87710 

48,0 

.68152 

79,3 

•94305 

23,8 

28  42  18.67 

.502 

.48118 

87,7 

.87662 

48,1 

.68231 

79,1 

.94281 

23,8 

28  45  44-93 

.503 

.48206 

87,6 

.87614 

48,2 

.68310 

78,9 

.94257 

23,9 

28  49  i  i  .  20 

.504 

.48293 

87,6 

.87566 

48,3 

.68389 

78,7 

.94233 

24,0 

28  52  37.46 

0.505 

0.48381 

87,5 

0.87517 

48,4 

9.68467 

78,6 

9.94209 

24,0 

28  56  03-73 

.506 

.48468 

87,5 

.87469 

48,5 

.68546 

78,4 

.94185 

24,1 

28  59  29.99 

.507 

.48556 

87,4 

.87421 

48,6 

.68624 

78,2 

.94161 

24,1 

29  02  56.26 

.508 

.48643 

87,4 

.87372 

48,6 

.68702 

78,0 

.94137 

24,2 

29  06  22.52 

.509 

.48730 

87,3 

.87323 

48,7 

.68780 

77,8 

.94H3 

24,2 

29  09  48.79 

0.510 

0.48818 

87,3 

0.87274 

48,8 

9.68858 

77,6 

9.94089 

24,3 

29  13  15.05 

.511 

.48905 

87,2 

.87226 

48,9 

.68935 

77,5 

.94064 

24,3 

29  16  41.32 

.512 

.48992 

87,2 

.87177 

49,0 

.69013 

77,3 

.94040 

24,4 

29  20  07.58 

.513 

.49079 

87,1 

.87128 

49J 

.69090 

77,i 

.94016 

24,5 

29  23  33.85 

.514 

.49166 

87,1 

.87078 

49,2 

.69167 

76,9 

.93991 

24,5 

29  27  oo.ii 

0.515 

0.49253 

87,0 

0.87029 

49,3 

9.69244 

76,7 

9.93967 

24,6 

29  30  26.38 

.516 

.49340 

87,0 

.86980 

49,3 

.69320 

76,6 

•93942 

24,6 

29  33  52.64 

.517 

.49427 

86,9 

.86931 

49,4 

.69397 

76,4 

.93917 

24,7 

29  37  18.90 

.518 

.495H 

86,9 

.86881 

49,5 

.69473 

76,2 

.93893 

24,8 

29  40  45-17 

.519 

.49601 

86,8 

.86832 

49,6 

.69549 

76,0 

.93868 

24,8 

29  44  U.43 

0.520 

0.49688 

86,8 

0.86782 

49,7 

9.69625 

75,9 

9.93&43 

24,9 

29  47  37-70 

.521 

•49775 

86,7 

.86732 

49,8 

.69701 

75,7 

.938l8 

24,9 

29  51  03.96 

.522 

.49861 

86,7 

.86682 

49,9 

.69777 

75,5 

•93793 

25,0 

29  54  30.23 

.523 

.49948 

86,6 

.86632 

49,9 

.69852 

75,3 

.93768 

25,0 

29  57  56.49 

.524 

.50035 

86,6 

.86582 

50,0 

.69927 

75,2 

•93743 

25,1 

30  01  22.76 

0.525 

0.50121 

86,5 

0.86532 

50,1 

9.70002 

75,o 

9.93718 

25,2 

30  04  49-02 

.526 

.50208 

86,5 

.86482 

50,2 

.70077 

74,8 

.93603 

25,2 

30  08  15.29 

.527 

.50294 

86,4 

.86432 

50,3 

.70152 

74,6 

.93667 

25,3 

30  n  41-55 

.528 

•50381 

86,4 

.86382 

50,4 

.70226 

74,5 

.93642 

25,3 

30  15  07.82 

.529 

.50467 

86,3 

.86331 

50,5 

.70301 

74,3 

.93617 

25,4 

30  18  34.08 

0.530 

0.50553 

86,3 

0.86281 

50,6 

9.70375 

74,1 

9.93591 

25,4 

3O  22  OO.35 

.531 

.50640 

86,2 

.86230 

50,6 

.70449 

74,0 

.93566 

25,5 

30  25  26.61 

.532 

.50726 

86,2 

.86179 

50,7 

.70523 

73,8 

•93540 

25,6 

30  28  52.88 

•  533 

.50812 

86,1 

.86129 

50,8 

.70597 

73,6 

.93515 

25,6 

30  32  19.14 

.534 

.50898 

86,1 

.86078 

50,9 

.70670 

73,4 

.93489 

25,7 

30  35  45-41 

0.535 

0.50984 

86,0 

0.86027 

5i,o 

9.70743 

73,3 

9.93463 

25,7 

30  39  11.67 

-536 

.51070 

86,0 

.85976 

51,1 

.70817 

73,1 

.93438 

25,8 

30  42  37-94 

•  537 

.51156 

85,9 

.85925 

51,2 

.70890 

72,9 

.93412 

25,9 

30  46  04.20 

.538 

.51242 

85,9 

.85874 

51,2 

.70063 

72,8 

.93386 

25,9 

30  49  30-47 

.539 

.5U28 

85,8 

.85822 

51,3 

.71035 

72,6 

.93360 

26,0 

30  52  56.73 

0.540 

O.SMH 

85,8 

0.85771 

51,4 

9.71108 

72,5 

9-93334 

26,0 

30  56  23.00 

•  541 

.51499 

85,7 

.85719 

51,5 

.71180 

72,3 

.93308 

26,1 

30  59  49.26 

.542 

.51585 

85,7 

.85668 

5i,6 

.71252 

72,1 

.93282 

26,2 

31  03  15.52 

•  543 
•  544 

.51671 
.51756 

85,6 
85,6 

.85616 
.85565 

51,7 
51,8 

.71324 
.71396 

72,0 
7i,8 

.93256 
.93229 

26,2 
26,3 

31  06  41.79 
31  10  08.05 

0.545 

0.51842 

85,5 

0.85513 

51,8 

9.7H68 

7i,6 

9.93203 

26,3 

31  13  34.32 

.546 

.51927 

85,5 

.85461 

5i,9 

.71540 

7i,5 

.93177 

26,4 

31  17  00.58 

.547 

.52013 

85,4 

.85409 

52,0 

.71611 

7i,3 

.93150 

-><>,4 

31  20  26.85 

.548 

.52008 

85,4 

.85357 

52,1 

.71682 

71,2 

.93124 

26,5 

31  23  53.  n 

•  549 

.52183 

85,3 

.85305 

52,2 

.71753 

7i,o 

.93097 

26,6 

31  27  19-38 

0.550 

0.52269 

85,3 

0.85252 

52,3 

9.71824 

70,8 

9.93071 

26^ 

31  30  45.64 

u 

isinhiu 

«F,/ 

cosh  iu 

-FO' 

._  ««nh  iu 

•  IV 

log  cosh  iu 

-F,,' 

u 

log   . 

SMITHSONIAN  TABLES 


202 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  oos  u 

«Fo' 

u 

0.550 

0.52269 

85,3 

0.85252 

52,3 

9.71824 

70,8 

9.93071 

20\6 

3i°3o'4s'.'64 

.551 

.52354 

85,2 

.85200 

52,4 

.71895 

70,7 

.93044 

26,7 

31  34  11.91 

.552 

.52439 

85,1 

.85148 

52,4 

.71966 

70,5 

.93017 

26,7 

3i  37  38.17 

•  553 

.52524 

85,1 

.85095 

52,5 

.72036 

70,4 

.92991 

26,8 

31  41  04.44 

•  554 

.52609 

85,0 

.85043 

52,6 

.72106 

70,2 

.92964 

26,9 

31  44  30.70 

0.555 

0.52604 

85,0 

0.84090 

52,7 

9.72176 

70,o 

9.92937 

26,9 

31  47  56.97 

.556 

.52779 

84,9 

.84937 

52,8 

.72246 

69,9 

.92910 

27,0 

31  51  23.23 

•  557 

.52864 

84,9 

.84884 

52,9 

.72316 

69,7 

.92883 

27,0 

3-1  54  49.50 

.558 

.52949 

84,8 

.84832 

52,9 

.72386 

69,6 

.92856 

27,1 

31  58  15.76 

•  559 

.53034 

84,8 

.84779 

53,o 

.72455 

69,4 

.92829 

27,2 

32  01  42.03 

0.560 

0.53H9 

84,7 

0.84726 

53,1 

9.72525 

69,3 

9.92801 

27,2 

32  05  08.29 

.561 

.53203 

84,7 

.84672 

53,2 

.72594 

69,1 

.92774 

27,3 

32  08  34.56 

.562 

.53288 

84,6 

.84619 

53,3 

.72663 

69,0 

.92747 

27,3 

32  12  00.82 

.563 

.53373 

84,6 

.84566 

53,4 

.72732 

68,8 

.92719 

27,4 

32  15  27.09 

.564 

•53457 

84,5 

.84512 

53,5 

.72801 

68,7 

.92692 

27,5 

32  18  53-35 

0.565 

0.53542 

84,5 

0.84459 

53,5 

9.72869 

68,5 

9.92665 

27,5 

32  22  19.62 

.566 

.53626 

84,4 

.84405 

53,6 

.72938 

68,4 

.92637 

27,0 

32  25  45-88 

067 

•53710 

84,4 

.84352 

53,7 

.73006 

68,2 

.92609 

27,7 

32  29  12.15 

.568 

.53795 

84,3 

.84298 

53,8 

•73074 

68,1 

.92582 

27,7 

32  32  38.41 

.569 

.53879 

84,2 

.84244 

53,9 

.73142 

67,9 

.92554 

27,8 

32  36  04.67 

0.570 

0.53963 

84,2 

0.84190 

54,0 

9-73210 

67,8 

9.92526 

27,8 

32  39  30.94 

•  571 

.54047 

84,1 

.84136 

54,0 

.73277 

67,6 

.92498 

27,9 

32  42  57.20 

.572 

.54131 

84,1 

.84082 

54,1 

.73345 

67,5 

.92470 

28,0 

32  46  23.47 

•  573 

.54216 

84,0 

.84028 

54,2 

.73412 

67,3 

.92442 

28,0 

32  49  49.73 

•  574 

•54300 

84,0 

.83974 

54,3 

.73480 

67,2 

.92414 

28,1 

32  53  16.00 

0.575 

0.54383 

83,9 

0.83919 

54,4 

9.73547 

67,0 

9.92386 

28,1 

32  56  42.26 

.576 

.54467 

83,9 

.83865 

54,5 

.73614 

66,9 

.92358 

28,2 

33  oo  08.53 

•  577 

.54551 

83,8 

.83810 

54,6 

.73680 

66,7 

.92330 

28,3 

33  03  34-79 

.578 

.54635 

83,8 

.83756 

54,6 

.73747 

66,6 

.92301 

28,3 

33  07  01.  06 

•  579 

.54719 

83,7 

.83701 

54,7 

.73814 

66,4 

.92273 

28,4 

33  10  27.32 

0.580 

0.54802 

83,6 

0.83646 

54,8 

9.73880 

66,3 

9.92245 

28,5 

33  13  53-59 

.581 

.54886 

83,6 

.83591 

54,9 

.73946 

66,2 

.92216 

28,5 

33  17  19-85 

.582 

.54970 

83,5 

.83536 

55,o 

.74012 

66,0 

.92188 

28,6 

33  20  46.12 

.583 

.55053 

83,5 

.83481 

55,i 

.74078 

65,9 

.92159 

28,6 

33  24  12.38 

.584 

.55137 

83,4 

.83426 

55,i 

.74144 

65,7 

.92130 

28,7 

33  27  38.65 

0.585 

0.55220 

83,4 

0.83371 

55,2 

9.74210 

65,6 

9.92102 

28,8 

33  31  04.91 

.586 

.55303 

83,3 

.83316 

55,3 

.74275 

65,4 

.92073 

28,8 

33  34  3Li8 

.587 

.55387 

83,3 

.83261 

55,4 

•74340 

65,3 

.92044 

28,9 

33  37  57-44 

.588 

•55470 

83,2 

.83205 

55,5 

.74406 

65,1 

.92015 

29,0 

33  41  23.71 

.589 

•55553 

83,I 

.83150 

55,6 

•74471 

65,0 

.91986 

29,0 

33  44  49-97 

0.590 

0.55636 

83,I 

0.83094 

55,6 

9.74536 

64,9 

9.91957 

29,1 

33  48  16.24 

-iS9i 

•552.13 

83,0 

.§3038 

55,7 

.74600 

64,7 

.91928 

29,1 

33  51  42.50 

•  592 

.55802 

83,0 

.82983 

55,8 

.74665 

64,6 

.91809 

29,2 

33  55  08.77 

•  593 

.55885 

82,9 

.82927 

55,9 

•74730 

64,4 

.91869 

29,3 

33  58  35.03 

•  594 

.55968 

82,9 

.82871 

56,0 

•74794 

64,3 

.91840 

29,3 

34  02  01.29 

0.595 

0.56051 

82,8 

0.82815 

56,1 

9.74858 

64,2 

9.91811 

29,4 

34  05  27.56 

.596 

.56134 

82,8 

.82759 

56,i 

.74922 

64,0 

.91781 

29,5 

34  08  53-82 

•  597 

.56216 

82,7 

.82703 

56,2 

.74986 

63,9 

.91752 

29,5 

34  12  20.09 

.598 

.56299 

82,6 

.82646 

56,3 

.75050 

63,8 

.91722 

29,6 

34  15  46.35 

•  599 

.56382 

82,6 

.82590 

56,4 

.75H4 

63,6 

.91693 

29,6 

34  19  12.62 

0.600 

0.56464 

82,5 

0.82534 

56,5 

9.75177 

63,5 

9.91663 

29,7 

34  22  38.88 

u 

-i  sinh  iu 

«F0' 

cosh  iu 

«•>  Fo' 

sinh  iu 

-Fo' 

log  cosh  iu 

•  IV 

u 

loo  . 

SMITHSONIAN  TABLES 


203 


Circular  Functions. 


u 

sin  u 

U.FO' 

cos  u 

<•>  Fo'   log  sin  u 

<-  Fo' 

log  cos  u 

-Fa' 

u 

0.600 

0.56464 

82,5 

0.82534 

56,5 

9.75177 

63,5 

9.91663 

29,7 

34°  22'  38.  '88 

.001 

.56547 

82,5 

.82477 

56,5 

.75241 

63,3 

.91633 

29,8 

34  26  05.15 

.602 

.56629 

82,4 

.82420 

56,6 

.75304 

63,2 

.91604 

29,8 

34  29  31.41 

.603 

.56712 

82,4 

.82364 

56,7 

•75367 

63,1 

.91574 

29,9 

34  32  57-68 

.604 

.56794 

82,3 

.82307 

56,8 

•75430 

62,9 

.91544 

30,0 

34  36  23.94 

0.605 

0.56876 

82,3 

0.82250 

56,9 

9-75493 

62,8 

9.91514 

30,0 

34  39  50.21 

.606 

.56958 

82,2 

.82193 

57,0 

.75556 

62,7 

.91484 

30,1 

34  43  16.47 

.607 

.57041 

82,1 

.82136 

57,0 

.75618 

62,5 

.91454 

30,2 

34  46  42.74 

.608 

.57123 

82,1 

.82079 

57,1 

.75681 

62,4 

.9H23 

30,2 

34  50  09.00 

.609 

.57205 

82,0 

.82022 

57,2 

•75743 

62,3 

.91393 

30,3. 

34  53  35.27 

0.610 

0.57287 

82,0 

0.81965 

57,3 

9.75805 

62,1 

9.91363 

30,4 

34  57  01.53 

.611 

•57369 

81,9 

.81907 

57,4 

.75867 

62,O 

.91332 

30,4 

35  oo  27.80 

.612 

.57451 

81,9 

.81850 

57,5 

.75929 

61,9 

.91302 

30,5 

35  03  54-06 

.613 

•57532 

81,8 

.81793 

57,5 

.75991 

6i,7 

.91271 

30,5 

35  07  20.33 

.614 

.57614 

8i,7 

.81735 

57,6 

.76053 

61,6 

.91241 

30,6 

35  10  46.59 

0.615 

0.57696 

8i,7 

0.81677 

57,7 

9.76114 

6i,5 

9.91210 

30,7 

35  14  12.86 

.616 

.57778 

81,6 

.81620 

57,8 

.76176 

61,4 

.91179 

30,7 

35  17  39.12 

.617 

.57859 

81,6 

.81562 

57,9 

.76237 

61,2 

.91149 

30,8 

35  21  05.39 

.618 

•  57941 

8i,5 

.81504 

57,9 

.76298 

61,1 

.91118 

30,9 

35  24  31.65 

.619 

.58022 

81,4 

.81446 

58,0 

.76359 

61,0 

.91087 

30,9 

35  27  57.92 

0.620 

0.58104 

81,4 

0.81388 

58,1 

9.76420 

60,8 

9.91056 

31,0 

35  31  24.18 

.621 

.58185 

81,3 

.81330 

58,2 

.76481 

60,7 

.91025 

3i,i 

35  34  50.44 

.622 

.58266 

81,3 

.81271 

58,3 

.76542 

60,6 

.90994 

3i,i 

35  38  16.71 

.623 

.58347 

81,2 

.81213 

58,3 

.76602 

60,4 

.90963 

31,2 

35  41  42.97 

.624 

•58429 

81,2 

.81155 

58,4 

.76663 

60,3 

.90931 

31,3 

35  45  09.24 

0.625 

0.58510 

81,1 

0.81096 

58,5 

9.76723 

60,2 

O.OOOOO 

31,3 

35  48  35.50 

.626 

.58591 

81,0 

.81038 

58,6 

.76783 

60,1 

.90869 

3i,4 

35  52  01.77 

.627 

.58672 

81,0 

.80979 

58,7 

.76843 

59,9 

.90837 

31,5 

35  55  28.03 

.628 

.58753 

80,9 

.80920 

58,8 

.76903 

59,8 

.90806 

31,5 

35  58  54.30 

.629 

.58834 

80,9 

.80862 

58,8 

.76963 

59,7 

.90774 

31,6 

36  02  20.56 

0.630 

0.58914 

80,8 

0.80803 

58,9 

9.77022 

59,6 

9.90743 

3i,7 

36  05  46.83 

.631 

.58995 

80,7 

.80744 

59,o 

.77082 

59,4 

.90711 

3i,7 

36  09  13.09 

.632 

.59076 

80,7 

.80685 

59,1 

.77141 

59,3 

.90679 

31,8 

36  12  39.36 

.633 

.59157 

80,6 

.80626 

59,2 

.77200 

59,2 

.90647 

3i,9 

36  16  05.62 

.634 

.59237 

80,6 

.80566 

59,2 

.77259 

59,1 

.90615 

3i,9 

36  19  31-89 

0.635 

0.59318 

80,5 

0.80507 

59,3 

9.77318 

58,9 

9.90583 

32,0 

36  22  58.15 

.636 

.59398 

80,4 

.80448 

59,4 

•77377 

58,8 

.90551 

32,1 

36  26  24.42 

.637 

•59479 

80,4 

.80388 

59,5 

.77436 

58,7 

.90519 

32,1 

36  29  50.68 

.638 

.  59559 

80,3 

.80329 

59,6 

•77495 

58,6 

.90487 

32,2 

36  33  16.95 

.639 

.59639 

80,3 

.80269 

59,6 

.77553 

58,5 

.90455 

32,3 

36  36  43.21 

0.640 

0.59720 

80,2 

0.80210 

59,7 

9.77612 

58,3 

9.90423 

32,3 

36  40  09.48 

.641 

.50800 

80,  i 

.80150 

59,8 

.77670 

58,2 

.90390 

32,4 

36  43  35-74 

.642 

.50880 

80,  i 

.80090 

59,9 

.77728 

58,i 

.90358 

32,5 

36  47  02.  01 

•643 

.59960 

80,0 

.80030 

60,0 

.77786 

58,o 

.90325 

32,5 

36  50  28.27 

.644 

.60040 

80,0 

.79970 

60,0 

.77844 

57,8 

.90293 

32,6 

36  53  54-54 

0.645 

0.60120 

79,9 

0.79910 

60,  i 

9.77902 

57,7 

9.90260 

32,7 

36  57  20.80 

.646 

.60200 

79,8 

.79850 

60,2 

•77959 

•57,6 

.90227 

32,7 

37  oo  47-06 

.647 

.60280 

79,8 

.79790 

60,3 

.78017 

57,5 

.90195 

32,8 

37  04  13-33 

.648 

.60359 

79J 

.79729 

60,4 

.78074 

57,4 

.90162 

32,9 

37  07  39-59 

.649 

.60439 

79,7 

.79669 

60,4 

.78132 

57.-' 

.90129 

32,9 

37  u  05.86 

0.650 

0.60519 

79,6 

0.79608 

60,5 

9.78189 

57,1 

9.00096 

33,0 

37  M  32.12 

u 

-isinhiu 

-Fo' 

cosh  iu 

-Fo' 

lofl«»nh  iu 

-Fo' 

log  cosh  iu 

-FO' 

u 

log  , 

SMITHSONIAN  TABLCS 


204 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«Fo' 

loo  sin  u 

«  Fo' 

log  cos  u 

o>Fo' 

u 

0.650 

0.60519 

79,6 

0.79608 

60,5 

9.78189 

57,i 

9.00096 

33,0 

Q    4     it 

37  14  32.12 

.651 

.60598 

79,5 

.79548 

60,6 

.78246 

57,o 

.90063 

33,1 

37  17  58.39 

.652 

.60678 

79,5 

.79487 

60,7 

.78303 

56,9 

.90030 

33,2 

37  21  24.65 

.653 

.60757 

79,4 

.79426 

60,8 

.78360 

56,8 

.89997 

33,2 

37  24  50.92 

.654 

.60837 

79,4 

.79366 

60,8 

.78416 

56,7 

.89963 

33,3 

37  28  17.18 

0.655 

0.60916 

79,3 

0.79305 

60,9 

9.78473 

56,5 

9.89930 

33,4 

37  31  43-45 

.656 

.60995 

79,2 

.79244 

61,0 

.78530 

56,4 

.80897 

33,4 

37  35  09.71 

.657 

.61074 

79,2 

.79183 

61,1 

.78586 

56,3 

.89863 

33,5 

37  38  35.98 

.658 

.61154 

79,1 

.79122 

61,2 

.7864^ 

56,2 

.89830 

33,6 

37  42  02.24 

.659 

.61233 

79,1 

.79060 

61,2 

.78698 

56,1 

.89796 

33,6 

37  45  28,51 

0.660 

0.61312 

79,0 

0.78099 

61,3 

9.78754 

56,o 

9.89762 

33,7 

37  48  54-77 

.661 

.61391 

78,9 

'78938 

61,4 

.78810 

55,8 

.89729 

33,8 

37  52  21.04 

.662 

.61470 

78,9 

.78876 

6i,5 

.78866 

55,7 

.89695 

33,8 

37  55  47.30 

.663 

.61548 

78,8 

.78815 

6i,5 

.78922 

55,6 

.89661 

33,9 

37  59  13.57 

.664 

.61627 

78,8 

.78753 

61,6 

.78977 

55,5 

.89627 

34,0 

38  02  39.83 

0.665 

0.61706 

78,7 

0.78692 

6i,7 

9.79033 

55,4 

9.89593 

34,1 

38  06  06.  10 

.666 

.61785 

78,6 

.78630 

61,8 

.79088 

55,3 

.89559 

34,1 

38  09  32.36 

.667 

.61863 

78,6 

.78568 

61,9 

.79143 

55,2 

.89525 

34,2 

38  12  58.63 

.668 

.61942 

78,5 

.78506 

61,9 

.79198 

55,o 

.89490 

34,3 

38  16  24.89 

.669 

.62O2O 

78,4 

.78444 

62,0 

.79253 

54,9 

.89456 

34,3 

38  19  51.16 

0.670 

0.62099 

78,4 

0.78382 

62,1 

9.79308 

54,8 

9.89422 

34,4 

38  23  17.42 

.671 

.62177 

78,3 

.78320 

62,2 

.79363 

54,7 

.89387 

34,5 

38  26  43.68 

.672 

.62255 

78,3 

.78258 

62,3 

.79418 

54,6 

.89353 

34,5 

38  30  09.95 

.673 

.62333 

78,2 

.78196 

62,3 

.79472 

54,5 

.89318 

34,6 

38  33  36.21 

.674 

.62412 

78,1 

.78133 

62,4 

.79527 

54,4 

.89284 

34,7 

38  37  02.48 

0.675 

0.62400 

78,1 

0.78071 

62,5 

9.79581 

54,3 

9.89249 

34,8 

38  40  28.74 

.676 

.62568 

78,0 

.78008 

62,6 

.79635 

54,1 

.89214 

34,8 

38  43  55.01 

.677 

.62646 

77,9 

.77946 

62,6 

.79689 

54,0 

.89179 

34,9 

38  47  21.27 

.678 

.62724 

77,9 

.77883 

62,7 

.79743 

53,9 

•89144 

35,0 

38  50  47-54 

.679 

.62802 

77,8 

.77820 

62,8 

•79797 

53,8 

.89109 

35,0 

38  54  I3.8o 

0.680 

0.62879 

77,8 

0.77757 

62,9 

9.79851 

53,7 

9.89074 

35,1 

38  57  40.07 

.681 

.62957 

77,7 

.77694 

63,0 

.79904 

53,6 

.89039 

35,2 

39  01  06.33 

.682 

.63035 

77,6 

.77631 

63,0 

.79958 

53,5 

35,3 

39  04  32.60 

.683 

.63112 

77,6 

.77568 

63,1 

.80011 

53,4 

.88968 

35,3 

39  07  58.86 

.684 

.63190 

77,5 

.77505 

63,2 

.80065 

53,3 

.88933 

35,4 

39  u  25.13 

0.685 

0.63267 

77,4 

0.77442 

63,3 

9.80118 

53,2 

9.88898 

35,5 

39  14  51.39 

.686 

.63345 

77,4 

.77379 

63,3 

.80171 

53,1 

.88862 

35,6 

39  18  17.66 

.687 

.63422 

77,3 

.77315 

63,4 

.80224 

52,9 

.88826 

35,6 

39  21  43>92 

.688 

.63499 

77,3 

.77252 

63,5 

.80277 

52,8 

.88791 

35,7 

39  25  10.19 

.689 

.63577 

77,2 

.77188 

63,6 

.80330 

52,7 

.88755 

35,8 

39  28  36.45 

0.600 

0.63654 

77J 

0.77125 

63,7 

9.80382 

'  52,6 

9.88719 

35,8 

39  32  02.72 

.691 

.63731 

77,1 

.77061 

63,7 

.80435 

52,5 

.88683 

35,9 

39  35  28.98 

.692 

.63808 

77,o 

.76997 

63,8 

.80487 

52,4 

.88647 

36,0 

39  38  55.25 

.693 

.63885 

76,9 

.76933 

63,9 

.80540 

52,3 

.885ii 

36,1 

39  42  21.51 

.694 

.63962 

76,9 

.76869 

64,0 

.80592 

52,2 

.88575 

36,1 

39  45  47.78 

0.695 

0.64039 

76,8 

0.76805 

64,0 

9.80644 

5'2,i 

9.88539 

36,2 

39  49  14.04 

.696 

.64115 

76,7 

.76741 

64,1 

.80696 

52,0 

.88503 

36,3 

39  52  40.31 

.697 

.64192 

76,7 

.76677 

64,2 

.80748 

51,9 

.88467 

36,4 

39  56  06.57 

.698 

.64269 

76,6 

.76613 

64,3 

.80800 

5i,8 

.88430 

36,4 

39  59  32.83 

.699 

.64345 

76,5 

.76549 

64,3 

.80852 

5i,7 

.88394 

36,5 

40  02  59.10 

0.700 

0.64422 

76,5 

0.76484 

64,4 

9-80903 

5i,6 

9.88357 

36,6 

40  06  25.36 

u 

-isinhiu 

•  IV 

cosh  iu 

«F0' 

sinh  iu 

wF0' 

log  cosh  iu 

«FO' 

u 

log  . 

SMITHSONIAN  TABLES 


205 


Circular  Functions. 


1 

sin  u 

-FO' 

COS  U 

«Fo* 

log  sin  u 

w  Fo' 

log  cos  u 

-FO' 

u 

0.700 

0.64422 

76,5 

0.76484 

64,4 

9.80903 

5i,6 

9.88357 

36,6 

40°o6'  25".'  36 

.701 

.64498 

76,4 

.76420 

64,5 

.80955 

5i,5 

.88321 

36,7 

40  09  51.63 

.702 

.64575 

76,4 

.76355 

64,6 

.81006 

5'i,4 

.88284 

36,7 

40  13  17.89 

.703 

.64651 

76,3 

.76291 

64,7 

.81057 

51,2 

.88247 

36,8 

40  16  44.16 

.704 

.64727 

76,2 

.76226 

64,7 

.81109 

5i,i 

.88210 

36,9 

40  20  10.42 

0.705 

0.64803 

76,2 

0.76161 

64,8 

9.8ll6o 

5i,o 

9.88173 

37,0 

40  23  36.69 

.706 

.64880 

76,1 

.76096 

64,9 

.81211 

50,9 

.88136 

37,o 

40  27  02.95 

.707 

.64956 

76,0 

.76031 

65,0 

.81262 

50,8 

.88099 

37,i 

40  30  29.22 

.708 

.65032 

76,0 

.75966 

65,0 

.81312 

50,7 

.88^62 

37,2 

40  33  55.48 

..709 

.65108 

75,9 

.75901 

65,1 

.81363 

50,6 

.88025 

37,3 

40  37  2I«75 

0.710 

0.65183 

75,8 

0.75836 

65,2 

9.81414 

50,5 

9.87588 

37,3 

40  40  48.01 

.711 

.65259 

75,8 

.75771 

65,3 

.81464 

50,4 

.87950 

37,4 

40  44  14-28 

.712 

.65335 

75,7 

.75706 

65,3 

.81515 

50,3 

.87913 

37,5 

40  47  40.54 

.713 

.65411 

75,6 

.75640 

65,4 

.81565 

50,2 

.87875 

37,6 

40  51  06.  81 

.714 

.65486 

75,6 

•75575 

65,5 

.81615 

50,1 

.87838 

37,6 

40  54  33.07 

0.715 

0.65562 

75,5 

0.75509 

65,6 

9.8l665 

50,0 

9.87800 

37,7 

40  57  59-34 

.716 

•65637 

75,4 

•75444 

65,6 

.81715 

49,9 

.87762 

37,8 

41  01  25.60 

.717 

.65713 

75,4 

•75378 

65,7 

.81765 

49,8 

.87724 

37,9 

41  04  51-87 

.718 

.65788 

75,3 

.75312 

65,8 

.81815 

49,7 

.87687 

37,9 

41  08  18.13 

.719 

.65863 

75,2 

.75246 

65,9 

.81864 

49,6 

.87649 

38,0 

41  ii  44.40 

0.720 

0.65938 

75,2 

0.75181 

65,9 

9.81914 

49,5 

9.87611 

38,1 

41  15  10.66 

.721 

.66014 

75,1 

•75II5 

66,0 

.81963 

49,4 

.87572 

38,2 

41  18  36.93 

.722 

.66089 

75,0 

.75049 

66,1 

.82013 

49,3 

.87534 

38,2 

41  22  03.19 

.723 

.66164 

75,o 

.74982 

66,2 

.82062 

49,2 

.87496 

38,3 

41  25  29.45 

.724 

.66239 

74,9 

.74916 

66,2 

.82111 

49,1 

.87458 

38,4 

41  28  55-72 

0.725 

0.66314 

74,8 

0.74850 

66,3 

9.82160 

49,0 

9-87419 

38,5 

41  32  21.98 

.726 

.66388 

74,8 

.74784 

66,4 

.82209 

48,9 

.87381 

38,6 

41  35  48.25 

.727 

.66463 

74,7 

.74717 

66,5 

.82258 

48,8 

.87342 

38,6 

41  39  U.5I 

.728 

.66538 

74,7 

.74651 

66,5 

.82307 

48,7 

.87303 

38,7 

41  42  40.78 

.729 

.66612 

74,6 

.74584 

66,6 

.82356 

48,6 

.87265 

38,8 

41  46  07.04 

0.730 

0.66687 

74,5 

0.74517 

66,7 

9.82404 

48,5 

9.87226 

38,9 

41  49  33.31 

.731 

.66761 

74,5 

•74451 

66,8 

.82453 

48,4 

.87187 

38,9 

41  52  59.57 

.732 

.66836 

74,4 

.74384 

66,8 

.82501 

48,3 

.87148 

39,o 

41  56  25.84 

•733 

.66910 

74,3 

.74317 

66,9 

.82549 

4«,2 

.87109 

39J 

41  59  52.10 

.734 

.66984 

74,3 

.74250 

67,0 

.82597 

48,1 

.87070 

39,2 

42  03  18.37 

0.735* 

0.67059 

74,2 

0.74183 

67,1 

9.82646 

48,0 

9-87030 

39,3 

42  06  44.63 

.736 

.67133 

74,1 

.74n6 

67,1 

.82694 

47,9 

.86091 

39,3 

42  10  10.90 

.737 

.67207 

74,0 

.74049 

67,2 

.82741 

47,9 

.86952 

39,4 

42  13  37.16 

.738 

.67281 

74,0 

.73982 

67,3 

.82789 

47,8 

.86912 

39,5 

42  17  03.43 

•  739 

.67355 

73,9 

.73914 

67,4 

.82837 

47,7 

.86873 

39,6 

4!2  2O  29.69 

0.740 

0.67429 

73,8 

0.73847 

67,4 

9.82885 

47,6 

9.86833 

39,7 

42  23  55.96 

•  741 

.67503 

73,8 

•73779 

67,5 

.82932 

47,5 

.86794 

39,7 

42  27  22.22 

.742 

.67576 

73,7 

•73712 

67,6 

.82979 

47,4 

.86754 

39,8 

42  30  48.49 

•  743 

.67650 

73,6 

.73644 

67,7 

.83027 

47,3 

.86714 

39,9 

42  34  14.75 

•  744 

.67724 

73,6 

•73577 

67,7 

.83074 

47,2 

.86674 

40,0 

42  37  41-02 

0.745 

0.67797 

73,5 

0.73509 

67,8 

9.83I2I 

47,1 

9.86634 

40,0 

42  41  07.28 

.746 

.67871 

73,4 

.73441 

67,9 

.83168 

47,0 

.86594 

40,1 

42  44  33-55 

•  747 

.67944 

73,4 

•73373 

67,9 

.83215 

46,9 

.86554 

40,2 

42  47  59-8i 

.748 

.68017 

73,3 

.73305 

68,0 

.83262 

46,8 

.86513 

40,3 

42  51  26.08 

•  749 

.68091 

73,2 

.73237 

68,1 

.83309 

46,7 

.86473 

40,4 

42  54  52.34 

0.750 

0.68164 

73,2 

0.73169 

68,2 

9.83355 

46,6 

9.86433 

40,5 

42  58  18.60 

I 

-itinhiu 

-F" 

cosh  iu 

-F0' 

lm,slnh  iu 

»FV 

log  cosh  iu 

«Fo' 

u 

log  , 

SMITHSONIAN  TABLES 


2O6 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«FO' 

log  sin  u 

«FO' 

log  cos  u 

«FV 

u 

0.750 

0.68164 

73,2 

0.73169 

68,2 

9-83355 

46,6 

9.86433 

40,5 

42°  58'  i8'.'6o 

.751 

.68237 

73,i 

.73101 

68,2 

.83402 

46,5 

.86392 

40,5 

43  01  44-87 

.752 

.68310 

73,o 

.73032 

68,3 

.83448 

46,4 

.86352 

40,6 

43  05  11.13 

•  753 

.68383 

73,o 

.72964 

68,4 

.83495 

46,3 

.86311 

40,7 

43  08  37.40 

•  754 

.68456 

72,9 

.72896 

68,5 

.83541 

46,2 

.86270 

40,8 

43  12  03.66 

0.755 

0.68529 

72,8 

0.72827 

68,5 

9.83587 

46,2 

9.86229 

40,9 

43  IS  29.93 

.756 

.68602 

72,8 

.72759 

68,6 

•83633 

46,1 

.86188 

40,9 

43  18  56.19 

•  757 

.68674 

72,7 

.72690 

68,7 

.83679 

46,0 

.86147 

41,0 

43  22  22.46 

•  758 

•68747 

72,6 

.72621 

68,7 

.83725 

45,9 

.86106 

41,1 

43  25  48.72 

•  759 

.68820 

72,6 

.73552 

68,8 

.83771 

45,8 

.86065 

41,2 

43  29  14.99 

0.760 

0.68892 

72,5 

0.72484 

68,9 

9.83817 

45,7 

9.86024 

41,3 

43  32  41.25 

.761 

.68965 

72,4 

.72415 

69,0 

.83863 

45,6 

.85983 

4i,4 

43  36  07.52 

.762 

.69037 

72,3 

.72346 

69,0 

.83908 

45,5 

.85941 

4i,4 

43  39  33.78 

.763 

.69109 

72,3 

.72277 

69,1 

.83954 

45,4 

.85900 

4i,5 

43  43  00.05 

.764 

.69182 

72,2 

.72207 

69,2 

.83999 

45,3 

.85858 

41,6 

43  46  26.31 

0.765 

0.69254 

72,i 

0.72138 

69,3 

9.84044 

45,2 

9.85817 

41,7 

43  49  52.58 

.766 

.69326 

72,1 

.72069 

69,3 

.84089 

45,1 

.85775 

41,8 

43  53  18.84 

.767 

.69398 

72,0 

.72000 

69,4 

.84135 

45,1 

.85733 

4i,9 

43  56  45.ii 

.768 

.69470 

71,9 

.71930 

69,5 

.84180 

45,0 

.85691 

4i,9 

44  oo  11.37 

.769 

.69542 

71,9 

.71861 

69,5 

.84225 

44,9 

.85649 

42,0 

44  03  37.64 

0.770 

0.69614 

7i,8 

0.71791 

69,6 

9.84269 

44,8 

9-85607 

42,1 

44  07  03.90 

.771 

.69685 

7i,7 

.71721 

69,7 

.84314 

44,7 

.85565 

42,2 

44  10  30.17 

.772 

.09757 

7i,7 

.71652 

69,8 

.84359 

44,6 

.85523 

42,3 

44  13  56.43 

•  773 

.69829 

7i,6 

.71582 

69,8 

.84403 

44,5 

.85480 

42,4 

44  17  22.70 

•  774 

.69900 

7i,5 

.71512 

69,9 

.84448 

44,4 

.85438 

42,5 

44  20  48.96 

0.775 

0.69972 

7i,4 

0.71442 

70,o 

9.84492 

44,3 

9.85395 

42,5 

44  24  15.22 

.776 

.70043 

7i,4 

.71372 

70,0 

.84536 

44,3 

.85353 

42,6 

44  27  4L49 

•  777 

.70114 

7i,3 

.71302 

7o,i 

.84581 

44,2 

.85310 

42,7 

44  31  07.75 

•  778 

.70186 

71,2 

.71232 

70,2 

.84625 

44,1 

.85267 

42,8 

44  34  34.02 

•  779 

•702S7 

71,2 

.71162 

70,3 

.84669 

44,0 

.85225 

42,9 

44  38  00.28 

0.780 

0.70328 

7i,i 

0.71091 

70,3 

9.84713 

•  43,9 

9.85182 

43,0 

44  41  26.55 

.781 

.70309 

71,0 

.71021 

70,4 

.84757 

43,8 

.85139 

43,o 

44  44  52.81 

.782 

.70470 

71,0 

.70951 

70,5 

.84800 

43,7 

.85096 

43,1 

44  48  19.08 

.783 

.70541 

70,9 

.70880 

70,5 

.84844 

43,6 

.85052 

43,2 

44  51  45-34 

.784 

.70612 

70,8 

.70809 

70,6 

.84888 

43,6 

.85009 

43,3 

44  55  II.  6l 

0.785 

0.70683 

70,7 

0.70739 

70,7 

9.84931 

43,5 

9.84966 

43,4 

44  58  37.87 

.786 

.70753 

70,7 

.70668 

70,8 

.84975 

43,4 

.84922 

43,5 

45  02  04.14 

.787 

.70824 

70,6 

.70597 

70,8 

.85018 

43,3 

.84879 

43,6 

45  05  30.40 

.788 

.70894 

70,5 

.70526 

70,9 

.85061 

43,2 

.84835 

43,7 

45  08  56.67 

.789 

.70965 

70,5 

.70456 

71,0 

.85104 

43,1 

.84792 

43,7 

45  12  22.93 

0.790 

0.71035 

70,4 

0.70385 

71,0 

9.85147 

43,0 

9.84748 

43,8 

45  15  49-20 

.791 

.71106 

70,3 

.70313 

7i,i 

.85190 

42,9 

.84704 

43,9 

45  19  15.46 

.792 

.7H76 

70,2 

.70242 

71,2 

.85233 

42,9 

.84660 

44,0 

45  22  41.73 

•  793 

.71246 

70,2 

.70171 

71,2 

.85276 

42,8 

.84616 

44,1 

45  26  07.99 

.794 

.71316 

7o,i 

.70100 

7i,3 

•85319 

42,7 

.84572 

44,2 

45  29  34.26 

0.795 

0.71386 

70,0 

0.70028 

7i,4 

9.85362 

42,6 

9.84527 

44,3 

45  33  00.52 

.796 

.71456 

70,0 

.69957 

7i,5 

.85404 

42,5 

.84483 

44,4 

45  36  26.79 

•  797 

.71526 

69,9 

.69886 

7i,5 

.85447 

42,4 

.84439 

44,4 

45  39  53-05 

.798 

.71596 

69,8 

.69814 

7i,6 

.85489 

42,3 

.84394 

44,5 

45  43  19.32 

•  799 

.71666 

69,7 

.69742 

7i,7 

.85531 

42,3 

.84350 

44,6 

45  46  45.58 

0.800 

0.71736 

69,7 

0.69671 

7i,7 

9-85573 

42,2 

9.84305 

44,7 

45  50  11.84 

u 

-isinhiu 

<-F0' 

cosh  iu 

«FO' 

sinh  iu 

«F0' 

log  cosh  iu 

«F0' 

u 

tog   . 

SMITHSONIAN  TABLES 


207 


Circular  Functions. 


u 

sin  u 

«FO' 

cos  u 

«F0' 

log  sin  u 

-  Fo' 

log  cos  u 

«FO' 

u 

0.800 

0.71736 

69,7 

0.69671 

71,7 

9-85573 

42,2 

9.84305 

44,7 

45°5o'n/./84 

.801 

.71805 

69,6 

.69599 

7i,8 

.85616 

42,1 

.84260 

44,8 

45  53  38.11 

.802 

.71875 

69,5 

.69527 

7i,9 

.85658 

42,0 

.84215 

44,9 

45  57  04-37 

.803 

.71944 

69,5 

.69455 

7i,9 

.85700 

41,9 

.84170 

45,o 

46  oo  30.64 

.804 

.72014 

69,4 

.69383 

72,0 

.85742 

41,8 

.84125 

45,i 

46  03  56.90 

0.805 

0.72083 

69,3 

0.69311 

72,1 

9.85783 

41,8 

9.84080 

45,2 

46  07  23.17 

.806 

.72152 

69,2 

.69239 

72,2 

.85825 

4i,7 

.84035 

45,3 

46  10  49-43 

.807 

.72222 

69,2 

.69167 

72,2 

.85867 

41,6 

.83990 

45,3 

46  14  15.70 

.808 

.72291 

69,1 

.69095 

72,3 

.85908 

4i,5 

.83944 

45,4 

46  17  41.96 

.809 

.72360 

69,0 

.69022 

72,4 

.85950 

4'i,4 

.83899 

45,5 

46  21  08.23 

0.810 

0.72429 

68,9 

0.68950 

72,4 

9.85991 

41,3 

9.83853 

45,6 

46  24  34.49 

.811 

.72498 

68,9 

.68877 

72,5 

.86032 

4i,3 

.83808 

45,7 

46  28  00.76 

.812 

.72566 

68,8 

.68805 

72,6 

.86074 

41,2 

.83762 

45,8 

46  31  27.02 

.813 

.72635 

68,7 

.68732 

72,6 

.86115 

41,1 

.83716 

45,9 

46  34  53.29 

.814 

.72704 

68,7 

.68660 

72,7 

.86156 

41,0 

.83670 

46,0 

46  38  19.55 

0.815 

0.72773 

68,6 

0.68587 

72,8 

9.86197 

40,9 

9-83624 

46,1 

46  41  45.82 

.816 

.72841 

68,5 

.68514 

72,8 

.86238 

40,8 

.83578 

46,2 

46  45  12.08 

.817 

.72910 

68,4 

.68441 

72,9 

.86278 

40,8 

.83532 

46,3 

46  48  38.35 

.818 

.72978 

68,4 

.68368 

73,0 

.86319 

40,7 

.83485 

46,4 

46  52  04.61 

.819 

.73046 

68,3 

.68295 

73,0 

.86360 

40,6 

.83439 

46,5 

46  55  30.88 

0.820 

0.73i'i5< 

68,2 

0.68222 

73,1 

9.86400 

40,5 

9.83393 

46,5 

46  58  57-14 

.821 

.73183 

68,1 

.68149 

73,2 

.86441 

40,4 

.83346 

46,6 

47  02  23.41 

.822 

.73251 

68,1 

.68076 

73,3 

.86481 

40,4 

.83299 

46,7 

47  05  49.67 

.823 

.73319 

68,0 

.68002 

73,3 

.86522 

40,3 

.83252 

46,8 

47  09  15-94 

.824 

.73387 

67,9 

.67929 

73,4 

.86562 

40,2 

.83206 

46,9 

47  12  42.20 

0.825 

0.73455 

67,9 

0.67856 

73,5 

9.86602 

40,1 

9.83159 

47,o 

47  16  08.47 

.826 

.73523 

67,8 

.67782 

73,5 

.86642 

40,0 

.83112 

47,1 

47  19  34.73 

.827 

.73590 

67,7 

.67709 

73,6 

.86682 

40,0 

.83064 

47,2 

47  23  00.99 

.828 

.73658 

67,6 

.67635 

73,7 

.86722 

39,9 

.83017 

47,3 

47  26  27.26 

.829 

.73726 

67,6 

.67561 

73,7 

.86762 

.82970 

47,4 

47  29  53.52 

0.830 

0.73793 

67,5 

0.67488 

7,3,8 

9.86802 

39,7 

9.82922 

47,5 

47  33  19.79 

.831 

.73861 

67,4 

.67414 

73,9 

.86841 

39,6 

.82875 

47,6 

47  36  46.05 

.832 

.73928 

67,3 

.67340 

73,9 

.86881 

39,6 

.82827 

47,7 

47  40  12.32 

.833 

.73995 

67,3 

.67266 

74,0 

.86920 

39,5 

.82779 

47,8 

47  43  38.58 

.834 

.74062 

67,2 

.67192 

74,1 

.86960 

39,4 

.82732 

47,9 

47  47  04.85 

0.835 

0.74130 

67,1 

0.67118 

74,1 

9.86999 

39,3 

9.82684 

48,0 

47  50  31.  II 

.836 

.74197 

67,0 

.67044 

74,2 

.87038 

39,2 

.82636 

48,1 

47  53  57.38 

.837 

.74264 

67,0 

.66969 

74,3 

.87078 

39,2 

.82588 

48,2 

47  57  23.64 

.838 

.74331 

66,9 

.66895 

74,3 

.87H7 

39,1 

•82539 

48,3 

48  oo  49.91 

.839 

.74398 

66,8 

.66821 

74,4 

.87156 

39,0 

.82491 

48,4 

48  04  16.17 

0.840 

0.74464 

66,7 

0.66746 

74,5 

9.87195 

38,9 

9.82443 

48,5 

48  07  42.44 

.841 

•74531 

66,7 

.66672 

74,5 

.87234 

38,8 

.82394 

48,5 

48  n  08.70 

.842 

.74598 

66,6 

.66597 

74,6 

.87273 

38,8 

.82346 

48,6 

48  14  34-97 

.843 

.74664 

66,5 

.66523 

74,7 

.873" 

38,7 

.82297 

48,7 

48  18  01.23 

.844 

•74731 

66,4 

.66448 

74,7 

.87350 

38,6 

.82248 

48,8 

48  21  27.50 

0.845 
.846 

0.74797 
.74863 

66,4 
66,3 

0.66373 
.66298 

74,8 
74,9 

9.87388 
.87427 

38,5 
38,5 

9.82199 
.82150 

48,9 
49,0 

48  24  53.76 
48  28  20.03 

.847 

.74930 

r/,,2 

.66223 

74,9 

.87465 

38,4 

.82IOI 

49,1 

48  31  46.29 

.848 

.  74906 

66,1 

.66148 

75,0 

.87504 

38,4 

.82052 

49,2 

48  35  12.56 

.849 

.75062 

66,1 

.66073 

75,i 

.87542 

38,2 

.82003 

49,3 

48  38  38.82 

0.850 

0.75128 

66,0 

0.65998 

75,1 

9.87580 

38,2 

9.81953 

49»4 

48  42  05.09 

u 

-itinhiu 

«F0' 

cosh  iu 

-Fo' 

,oo'^u 

-Fo' 

log  cosh  iu 

«F0' 

u 

SMITHSONIAN  TABLKS 


208 


Circular  Functions. 


u 

sin  u 

-FO' 

cos  u 

-Fo' 

log  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

0.850 

0.75128 

66,0 

0.65998 

75,1 

9.87580 

38,2 

9.81953 

49,4 

48  42  05.09 

.851 

•75194 

65,9 

.65923 

75,2 

.87618 

38,1 

.81904 

49,5 

48  45  31.35 

.852 

.75200 

65,8 

.65848 

75,3 

.87656 

38,0 

.81854 

49,6 

48  48  57.61 

.853 

.75326 

65,8 

.65773 

75,3 

.87694 

37,9 

.81805 

49,7 

48  52  23.88 

.854 

•75391 

65,7 

.65697 

75.4 

.87732 

37,8 

.81755 

49,8 

48  55  50.14 

0.855 

0.75457 

65,6 

0.65622 

75,5 

9.87770 

37,8 

9.81705 

49,9 

48  59  16.41 

.856 

.75523 

65,5 

.65546 

75,5 

.87808 

37,7 

.81655 

5o,o 

49  02  42.67 

.857 

•75588 

65,5 

.65471 

75,6 

.87845 

37,6 

.81605 

5o,i 

49  06  08.94 

.858 

.75654 

65,4 

.65395 

75,7 

.87883 

37,5 

.81555 

50,2 

49  09  35.20 

.859 

.75719 

65,3 

.65320 

75,7 

.87920 

37,5 

.81504 

50,3 

49  13  01.47 

0.860 

0.75784 

65,2 

0.65244 

75,8 

9.87958 

37,4 

9.81454 

50,4 

49  16  27.73 

.861 

.75849 

65,2 

.65168 

75,8 

.87995 

37,3 

.81403 

50,5 

49  19  54-00 

.862 

.75915 

65,1 

.65092 

75,9 

.88033 

37,2 

.81353 

50,7 

49  23  20.26 

.863 

.75980 

65,0 

.65016 

76,0 

.88070 

37,2 

.81302 

50,8 

49  26  46.53 

.864 

.76045 

64,9 

.64940 

76,0 

.88107 

37,1 

.81251 

50,9 

49  30  12.79 

0.865 

0.76110 

64,9 

0.64864 

76,1 

9.88144 

37,0 

9.81200 

5i,o 

49  33  39.06 

.866 

.76174 

64,8 

.64788 

76,2 

.88181 

36,9 

.81149 

5i,i 

49  37  05.32 

.867 

.76239 

64,7 

.64712 

76,2 

.88218 

36,9 

.81098 

51,2 

49  40  31.59 

.868 

64,6 

.64635 

76,3 

.88255 

36,8 

.81047 

5i,3 

49  43  57.85 

.869 

.76368 

64,6 

.64559 

76,4 

.88291 

36,7 

.80996 

5i,4 

49  47  24.12 

0.870 

0.76433 

64,5 

0.64483 

76,4 

9.88328 

36,6 

9.80944 

5i,5 

49  50  50.38 

.871 

.76497 

64,4 

.64406 

76,5 

.88365 

36,6 

.80893 

51,6 

49  54  16.65 

.872 

.76562 

64,3 

.64330 

76,6 

.88401 

36,5 

.80841 

5i,7 

49  57  42.91 

.873 

.76626 

64,3 

.64253 

76,6 

.88438 

36,4 

.80789 

5i,8 

50  01  09.18 

.874 

.76690 

64,2 

.64176 

76,7 

.88474 

36,3 

.80738 

5i,9 

50  04  35-44 

0.875 

0.76754 

•64,1 

0.64100 

76,8 

9.88510 

36,3 

9.80686 

52,0- 

50  08  01.71 

.876 

.76818 

64,0 

.64023' 

76,8 

.88547 

36,2 

.80634 

52,1 

50  II  27.97 

.877 

.76882 

63,9 

.63946 

76,9 

.88583 

36,1 

.'80581 

52,2 

50  14  54.24 

.878 

.76946 

63,9 

.63869 

76,9 

.88619 

36,0 

.80529 

52,3 

50  18  20.50 

.879 

.77010 

63,8 

.63792 

77,o 

.88655 

36,0 

.80477 

52,4 

50  21  46.76 

0.880 

0.77074 

63,7 

0.63715 

77,i 

9.88691 

35,9 

9.80424 

52,5 

50  25  13.03 

.881 

.77138 

63,6 

.63638 

77,i 

.88727 

35,8 

.80372 

52,6 

50  28  39-29 

.882 

.77201 

63,6 

.63561 

77,2 

.88762 

35,8 

.80319 

52,7 

50  32  05  .56 

.883 

.77265 

63,5 

.63484 

77,3 

.88798 

3'5,7 

.80266 

52,9 

50  35  31-82 

.884 

.77328 

63,4 

.63406 

77,3 

.88834 

35,6 

.80213 

53,0 

50  38  58.09 

0.885 

0.77391 

63,3 

0.63329 

77,4 

9.88869 

35,5 

9.80160 

53,i 

50  42  24.35 

.886 

.77455 

63,3 

.63252 

77,5 

.88905 

35,5 

.80107 

53,2 

50  45  50.62 

.887 

.77518 

63,2 

.63174 

77,5 

.88940 

35,4 

.80054 

53,3 

50  49  16.88 

.888 

.77581 

63,1 

.63096 

77,6 

.88976 

35,3 

.80001 

53,4 

50  52  43.15 

.889 

.77644 

63,0 

.63019 

77,6 

.89011 

35,2 

.79947 

53,5 

50  56  09.41 

0.800 

0.77707 

62,9 

0.62941 

77,7 

9.89046 

35,2 

9.79894 

53,6 

50-59  35-68 

.891 

•77770 

62,9 

.62863 

77,8 

.89081 

35,i 

•79840 

53,7 

51  03  01.94 

.892 

.77833 

62,8 

.62786 

77,8 

.89116 

35,o 

.79786 

53,8 

51  06  28.21 

.893 

.77896 

62,7 

.62708 

77,9 

.89151 

35,o 

.79732 

53,9 

51  09  54-47 

.894 

.77958 

62,6 

.62630 

78,0 

.89186 

34,9 

.79678 

54,1 

51  13  20.74 

0.895 

0.78021 

62,6 

0.62552 

78,o 

9.89221 

34,8 

9.79624 

54,2 

51  16  47.00 

.896 

.78083 

62,5 

.62474 

78,i 

.89256 

34,7 

.79570 

54,3 

51  20  13.27 

•  897 

.78146 

62,4 

.62396 

78,i 

.89291 

34,7 

.79515 

54,4 

5i  23  39-53 

.898 

.78208 

62,3 

.62318 

78,2 

.89325 

34,6 

.79461 

54,5 

51  27  05.80 

.899 

.78270 

62,2 

.62239 

78,3 

.89360 

34,5 

.79406 

54,6 

51  30  32.06 

0.900 

0.78333' 

62,2 

0.62161 

78,3 

9.89394 

34,5 

9.79352 

54,7 

51  33  58.33 

u 

-isinhiu 

-Fo' 

cosh  iu 

-FO' 

sinh  iu 

<«>  Fo' 

log  cosh  iu 

«FO' 

u 

log   . 

SMITHSONIAN  TABLES 


20Q 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«Fo' 

log  sin  u 

«F0' 

log  cos  u 

•  Fo' 

u 

0.900 

0.78333 

62,2 

0.62161 

78,3 

9.89394 

34,5 

9.79352 

54,7 

5i°33'58'.'33 

.901 

.78395 

62,1 

.62083 

78,4 

.89429 

34,4 

.79297 

54,8 

51  37  24.59 

.902 

.78457 

62,0 

.62004 

78,5 

.89463 

34,3 

•79242 

55,o 

51  40  50.86 

.903 

.78519 

6i,9 

.61926 

78,5 

.89497 

34,3 

.79187 

55,i 

51  44  17.12 

.904 

.78581 

61,8 

.61847 

78,6 

.89532 

34,2 

.79132 

55,2 

51  47  43.38 

0.905 

0.78643 

61,8 

0.61769 

78,6 

9.89566 

34,1 

9-79077 

55,3 

51  51  09.65 

.006 

.78704 

6i,7 

.61690 

7&7 

.89600 

34,0 

.79021 

55,4 

51  54  35-91 

.007 

.78766 

61,6 

.61611 

78,8 

.89634 

34,0 

.78966 

.55,5 

51  58  02.18 

.908 

.78827 

61,5 

.61532 

78,8 

.89668 

33,9 

.78910 

55,6 

52  01  28.44 

.909 

.78889 

61,5 

.61453 

78,9' 

.89702 

33,8 

.78855 

55,8 

52  04  54-71 

0.910 

0.78950 

61,4 

0.61375 

79,0 

9.89735 

33,8 

9.78799 

55,9 

52  08  20.97 

.911 

.70012 

6i,3 

.61296 

79,0 

.89769 

33,7 

.78743 

56,0 

52  II  47.24 

.912 

.79073 

61,2 

.61217 

79J 

.89803 

33,6 

.78687 

56,i 

52  15  13-50 

.913 

.79134 

61,1 

.61137 

79,1 

.89836 

33,6 

.78631 

56,2 

52  18  39-77 

.914 

.79195 

61,1 

.61058 

79,2 

.89870 

33,5 

.78574 

56,3 

52  22  06.03 

0.915 

0.79256 

61,0 

0.60979 

79,3 

9.89903 

33,4 

9.78518 

56,4 

52  25  32.30 

.916 

.79317 

60,9 

.60900 

79,3 

•89937 

33,3 

.78462 

56,6  52  28  58.56 

.917 

.79378 

60,8 

.60820 

79,4 

.89970 

33,3 

.78405 

56,7 

52  32  24.83 

.918 

.79439 

60,7 

.60741 

79,4 

.00003 

33,2 

.78348 

56,8 

52  35  51-09 

.919 

.79500 

60,7 

.60662 

79,5 

.90036 

33>i 

.78291 

56,9 

52  39  17.36 

0.920 

0.79500 

60,6 

0.60582 

79,6 

9.90070 

33,1 

9.78234 

57,0 

52  42  43.62 

.921 

.79621 

60,5 

.60502 

79,6 

.90103 

33,0 

.78177 

57,2 

52  46  09.89 

.922 

.79681 

60,4 

.60423 

79,7 

.90136 

32,9 

.78120 

57,3 

52  49  36.15 

•  923 

.79742 

60,3 

.60343 

79,7 

.90168 

32,9 

.78063 

57,4 

52  53  02.42 

.924 

.79802 

60,3 

.60263 

79,8 

.90201 

32,8 

.78005 

57,5 

52  56  28.68 

0.925 

0.79862 

60,2 

0.60183 

79,9 

9.90234 

32,7 

9.77948 

57,6 

52  59  54-95 

.926 

.79922 

60,1 

.60104 

79,9 

.90267 

32,7 

•77800 

57,7 

53  03  21.21 

.927 

•79982 

60,0 

.60024 

80,0 

.00299 

32,6 

.77832 

57,9 

53  06  47.48 

.928 

.80042 

59,9 

•59944 

80,0 

.90332 

32,5 

•77774 

58,0 

53  10  13.74 

.929 

.80102 

59,9 

.59864 

80,1 

.90364 

32,5 

.77716 

58,1 

53  13  40.01 

0.930 

0.80162 

59,8 

0.59783 

80,2 

9.90397 

32,4 

9.77658 

58,2 

53  17  06.27 

•  931 

.80222 

59,7 

.59703 

80,2 

.90429 

32,3 

.77600 

58,4 

53  20  32.53 

•  932 

.80281 

59,6 

.59623 

80,3 

.90461 

32,3 

•77541 

58,5 

53  23  58-80 

•933 

.80341 

59,5 

•59543 

80,3 

.90494 

32,2 

.77483 

58,6 

53  27  25.06 

•934 

.80400 

59,5 

.59462 

80,4 

.90526 

32,1 

.77424 

58,7 

53  30  51-33 

0.935 

0.80460 

59,4 

0.59382 

80,5 

9.90558 

32,1 

9.77365 

58,8 

53  34  17-59 

.936 

.80519 

59,3 

•59301 

80,5 

.90590 

32,0 

.77306 

59,o 

53  37  43-86 

•  937 

.80579 

59,2 

.59221 

80,6 

.90622 

3L9 

•77247 

59,1 

53  41  10.12 

.938 

.80638 

59,1 

.59140 

80,6 

.90654 

31,9 

.77188 

59,2 

53  44  36.39 

•939 

.80697 

59,1 

.59060 

80,7 

.90686 

31,8 

.77129 

59,3 

53  48  02.65 

0.940 

0.80756 

59,0 

0.58979 

80,8 

9.90717 

31,7 

9.77070 

59,5 

53  51  28.92 

.941 

.80815 

58*9 

58898 

80,8 

.90749 

31,7 

.77010 

59,6 

53  54  55.i8 

.942 

.80874 

58£ 

.58817 

80,9 

.90781 

31,6 

.76950 

59,7 

53  58  21.45 

•  943 

.80932 

58,7 

.58736 

80,9 

.00812 

31,5 

.76891 

59,8 

54  01  47-71 

•944 

.80991 

58,7 

.58655 

81,0 

.90844 

31,5 

.76831 

60,0 

54  05  13.98 

0.945 

0.81050 

58,6 

0.58574 

81,0 

9.90875 

31,4 

9.76771 

60,1 

54  08  40.24 

.946 

.81108 

58,5 

.58493 

81,1 

.90906 

31,3 

.76711 

60,2 

54  12  06.51 

•947 

.81167 

58,4 

.58412 

81,2 

.90938 

31,3 

.76650 

60,3 

54  15  32.77 

.948 

.81225 

58,3 

.58331 

81,2 

.90969 

31,2 

.76590 

60,5 

54  18  59.04 

•949 

.81283 

58,2 

.58250 

81,3 

.91000 

3i,i 

.76529 

60,6 

54  22  25.30 

0.950 

0.81342 

58,2 

0.58168 

81,3 

9.9I03I 

3U 

9.76469 

60,7 

54  25  51-57 

u 

-i  sinh  iu 

-Fo' 

cosh  iu 

-Fo' 

l««ilnh  lu 

«FU' 

log  cosh  iu 

-Fo' 

u 

100  , 

SMITHSONIAN  TABLES 


2IO 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«Fo' 

log  sin  u 

«  Fo' 

log  cos  u 

«F0' 

u 

O    /     44 

0.950 

0.81342 

58,2 

0.58168 

8l,3 

9.9I03I 

31,1 

9.76469 

60,7 

54  25  5L57 

.951 

.81400 

58,1 

.58087 

81,4 

.91062 

31,0 

.76408 

60,9 

54  29  17.83 

.952 

.81458 

58,0 

.58006 

8i,5 

.91093 

30,9 

.76347 

61,0 

54  32  44-10 

.953 

.81516 

57,9 

.  57924 

8i,5 

.91124 

30,9 

.76286 

61,1 

54  36  10.36 

.954 

.81574 

57,8 

.57842 

81,6 

•91155 

30,8 

.76225 

61,2 

54  39  36.63 

0.955 

0.81631 

57,8 

0.57761 

81,6 

9.91186 

30,7 

9.76163 

61,4 

54  43  02.89 

.956 

.81689 

57,7 

.57679 

8i,7 

.91216 

30,7 

.76102 

6i,5 

54  46  29.15 

•957 

.81747 

57,6 

.57597 

8i,7 

.91247 

30,6 

.76040 

61,6 

54  49  55-42 

.958 

.81804 

57,5 

.57516 

81,8 

.91278 

30,5 

•75979 

61,8 

54  53  21.68 

•  959 

.81862 

57,4 

•57434 

81,9 

.91308 

30,5 

.75917 

61,9 

54  56  47-95 

0.960 

0.81919 

57,4 

0.57352 

81,9 

9.91339 

30,4 

9.75855 

62,0 

55  oo  -14.21 

.961 

0.81976 

57,3 

.57270 

82,0 

.91369 

30,3 

•75793 

62,2 

55  03  40.48 

.962 

.82034 

57,2 

.57188 

82,0 

.91399 

30,3 

.75731 

62,3 

55  07  06.74 

.963 

.82091 

57,1 

.57106 

82,1 

.91429 

30,2 

.75668 

62,4 

55  10  33-01 

.964 

.82148 

57,0 

.57024 

82,1 

.91460 

30,1 

.75606 

62,6 

55  13  59.27 

0.965 

0.82205 

56,9 

0.56942 

82,2 

9.91490 

30,i 

9-75543 

62,7 

55  17  25.54 

.966 

.82262 

56,9 

.56859 

82,3 

.91520 

30,0 

.75480 

62,8 

55  20  51.80 

.967 

.82319 

56,8 

.56777 

82,3 

.91550 

29,9 

.75417 

63,0 

55  24  18.07 

.968 

.82375 

56,7 

.56695 

82,4 

.91580 

29,9 

.75354 

63,1 

55  27  44-33 

.969 

.82432 

56,6 

.56612 

82,4 

.91610 

29,8 

.75291 

63,2 

55  31  10.  60 

0.970 

0.82489 

56,5 

0.56530 

82,5 

9.91639 

29,8 

9.75228 

63,4 

55  34  36.86 

.971 

•82545 

56,4 

.56447 

82,5 

.91669 

29,7 

.75164 

63,5 

55  38  03.13 

.972 

.82601 

56,4 

.56365 

82,6 

.91699 

29,6 

.75101 

63,6 

55  41  29-39 

•  973 

.82658 

56,3 

.56282 

82,7 

.91728 

29,6 

.75037 

63,8 

55  44  55-66 

•974 

.82714 

56,2 

.56200 

82,7 

.91758 

29,5 

•74973 

63,9 

55  48  21.92 

0.975 

0.82770 

56,i 

0.56117 

82,8 

9.91787 

29,4 

9.74009 

64,1 

55  51  48.19 

.976 

.82826 

56,0 

.56034 

82,8 

.91817 

29,4 

.74845 

64,2 

55  55  14.45 

•  977 

.82882 

56,0 

•55951 

82,9 

.91846 

29,3 

.74781 

64,3 

55  58  40.72 

.978 

.82938 

55,9 

.55868 

82,9 

•91875 

29,2 

.74717 

64,5 

56  02  06.98 

•  979 

.82994 

55,8 

.55785 

83,0 

.91905 

29,2 

.74652 

64,6 

56  05  33.25 

0.980 

0.83050 

55,7 

0.55702 

83,0 

9.91934 

29,1 

9.74587 

64,8 

56  08  59.51 

.981 

.83105 

55,6 

.55619 

83,1 

.91963 

29,1 

•74522 

64,9 

56  12  25-77 

.982 

.83161 

55,5 

.55536 

83,2 

.91992 

29,0 

•74457 

65,0 

56  15  52.04 

.983 

.83216 

55,5 

•55453 

83,2 

.92021 

28,9 

.74392 

65,2 

56  19  I8.3O 

•  984 

.83272 

55,4 

•55370 

83,3 

.92050 

28,9 

.74327 

65,3 

56  22  44-57 

0.985 

0.83327 

55,3 

0.55286 

83,3 

9.92079 

28,8 

9.74262 

65,5 

56  26  10.83 

.986 

.83382 

55,2 

.55203 

83,4 

.92107 

28,8 

.74196 

65,6 

56  29  37.10 

.987 

.83438 

55,i 

.55120 

83,4 

.92136 

28,7 

.74131 

65,7 

56  33  03.36 

.988 

.83493 

55,o 

•55036 

83,5 

.92165 

28,6 

.74065 

65,9 

56  36  29.63 

.989 

.83548 

55,0 

•54953 

83,5 

.92193 

28,6 

.73999 

66,0 

56  39  55.89 

0.090 

0.83603 

54,9 

0.54869 

83,6 

9.92222 

28,5 

9.73933 

66,2 

56  43  22.16 

.991 

.83657 

54,8 

.54785 

83,7 

.92250 

28,4 

66,3 

56  46  48.42 

.992 

.83712 

54,7 

.54702 

83,7 

.92279 

28,4 

1  738oo 

66,5 

56  50  14-69 

•993 

.83767 

54,6 

.54618 

83-8 

.92307 

28,3 

.73734 

66,6 

56  53  40.95 

.994 

.83821 

54,5 

•54534 

83,8 

.92335 

28,3 

.73667 

66,8 

56  57  07.22 

0.995 

0.83876 

54,5 

0.54450 

83,9 

9.92364 

28,2 

9.73600 

66,9 

57  oo  33-48 

.996 

.83930 

54,4 

.54366 

83,9 

.92392 

28,1 

•73533 

67,0 

57  03  59.75 

•  997 

.83985 

54,3 

.54282 

84,0 

.92420 

28,1 

.73466 

67,2 

57  07  26.01 

.998 

.84039 

54,2 

.54198 

84,0 

.92448 

28,0 

•73399 

67,3 

57  10  52.28 

.999 

.84093 

54,1 

•54II4 

84,1 

.92476 

27,9 

•73331 

67,5 

57  14  i8.54 

I.OOO 

0.84147 

54,0 

0.54030 

84,1 

9.92504 

27,9 

9.73264 

67,6 

57  17  44.8i 

u 

-isinhiu 

»F0' 

cosh  iu 

«FO' 

sinh  iu 

coFo' 

log  cosh  iu 

»FO' 

u 

tog   . 

SMITHSONIAN  TABLES 


211 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

•  Fo' 

u 

I.OOO 

0.84147 

54,0 

0.54030 

84,1 

9.92504 

27,9 

9.73204 

67,6 

57  I7'44"8i 

.001 

.84201 

53,9 

.53946 

84,2 

.92532 

27,8 

.73196 

67,8 

57  21  11.07 

.002 

.84255 

53,9 

.53862 

84,3 

.92560 

27,8 

.73128 

67,9 

57  24  37.34 

.003 

.84309 

53,8 

.53778 

84,3 

.92587 

27,7 

•73060 

68,1 

57  28  03.60 

.004 

•84363 

53,7 

.53693 

84,4 

.92615 

27,6 

.72992 

68,2 

57  31  29.87 

1.  005 

0.84416 

53,6 

0.53609 

84,4 

9.92643 

27,6 

9.72924 

68,4 

57  34  56.13 

.006 

.84470 

53,5 

.53524 

84,5 

.92670 

27,5 

.72855 

68,5 

57  38  22.40 

.007 

.84523 

53,4 

.53440 

84,5 

.92698 

27,5 

.72787 

68,7 

57  4i  48.66 

.008 

.84577 

53,4 

.53355 

84,6 

.92725 

27,4 

.72718 

68,8 

57  45  14.92 

.009 

.84630 

53,3 

.53271 

84,6 

.92752 

27,3 

.72049 

69,0 

57  48  41.19 

1.  010 

0.84683 

53,2 

0.53186 

84,7 

9.92780 

27,3 

9.72580 

69,1 

57  52  07.45 

.on 

.84736 

53>i 

•53IOI 

84,7 

.92807 

27,2 

.72511 

69,3 

57  55  33-72 

.012 

.84789 

53,0 

.53017 

84,8 

.92834 

27,2 

.72441 

69,5 

57  58  59.98 

.013 

.84842 

52,9 

.52932 

84,8 

.9285: 

27,1 

.72372 

69,6 

58  02  26.25 

.014 

.84895 

52,8 

.52847 

84,9 

.92888 

27,0 

.72302 

69,8 

58  05  52.51 

1.  015 

0.84948 

52,8 

0.52762 

85,0 

9.92915 

27,0 

9.72232 

69,9 

58  09  18.78 

.Ol6 

.85001 

52,7 

.52677 

85,0 

.92942 

26,9 

.72162 

70,1 

58  12  45.04 

.017 

.85053 

52,6 

.52592 

85,1 

.92969 

26,9 

.72092 

70,2 

58  16  11.31 

.018 

.85106 

52,5 

.52507 

85,1 

.92996 

26,8 

.72022 

70,4 

58  19  37.57 

.OI9 

.85158 

52,4 

.52422 

85,2 

.93023 

26,7 

.71951 

70,6 

58  23  03.84 

I.O2O 

0.85211 

52,3 

0.52337 

85,2 

9.93049 

26,7 

9.71881 

70,7 

58  26  30.10 

.O2I 

.85263 

52,3 

.52251 

85,3 

.93076 

26,6 

.71810 

70,9 

58  29  56.37 

.022 

.85315 

52,2 

.52166 

85,3 

.93103 

26,6 

.71739 

7i,o 

58  33  22.63 

.023 

.85367 

52,1 

.52081 

85,4 

.93129 

26,5 

.71668 

71,2 

58  36  48.90 

.024 

.85419 

52,0 

•51995 

85,4 

.93156 

26,4 

•71596 

71,3 

58  40  15.16 

1.025 

0.85471 

51,9 

0.51910 

85,5 

9.93182 

26,4 

9.71525 

7i,5 

58  43  41.43 

.026 

.85523 

51,8 

.51824 

85,5 

.93208 

26,3 

.71453 

7i,7 

58  47  07.69 

.027 

.85575 

5i,7 

.51739 

85,6 

.93235 

26,3 

.71382 

7i,8 

58  50  35-96 

.028 

.85627 

51,7 

.51653 

85,6 

.93261 

26,2 

.71310 

72,0 

58  54  00.22 

.029 

.85678 

5i,6 

•51568 

85,7 

.93287 

26,1 

.71238 

72,2 

58  57  26.49 

1.030 

0.85730 

5i,5 

0.51482 

85,7 

9.93313 

26,1 

9.71165 

72,3 

59  oo  52-75 

.O3I 

.85781 

5i,4 

.51396 

85,8 

•93339 

26,0 

.71093 

72,5 

59  04-  19-02 

.032 

•85833 

5i,3 

.51310 

85,8 

.93365 

26,0 

.71020 

72,6 

59  07  45.28 

.033 

.85884 

5i,2 

.51224 

85,9 

.93391 

25,9 

.70948 

72,8 

59  ii  11-54 

.034 

.85935 

5i,i 

.5H39 

85,9 

.93417 

25,8 

.70875 

73,o 

59  14  37-8i 

1  .035 

0.85086 

5i,i 

0.51053 

86,0 

9.93443 

25.8 

9.70802 

73,1 

59  18  04.07 

.036 

.86037 

5i,o 

.50967 

86,0 

.93469 

25,7 

.70729 

73,3 

59  21  30.34 

.037 

.86088 

5O,9 

.50881 

86,1 

•93494 

25,7 

.70655 

73,5 

59  24  56.60 

.038 

.86139 

50,8 

.50794 

86,1 

•93520 

25,6 

.70582 

73,6 

59  28  22.87 

•  039 

.86190 

50,7 

.50708 

86,2 

.93546 

25,6 

.70508 

73,8 

59  31  49.13 

1.040 

0.86240 

50,6 

0.50622 

86,2 

9.93571 

25,5 

9.70434 

74,0 

59  35  15.40 

.041 

.86291 

50,5 

.50536 

85,3 

•93597 

25,4 

.70360 

74v2 

59  38  41-66 

.042 

.86341 

50,4 

.50449 

85,3 

.93622 

25,4 

.70286 

74,3 

59  41  07.93 

.043 

.86392 

50,4 

.50363 

86,4 

.93647 

25,3 

.  7O2I  I 

74,5 

59  45  34-19 

.044 

.86442 

50,3 

.50277 

86,4 

.93673 

25,3 

.70137 

74,7 

59  49  00.46 

1.045 

0.86492 

50,2 

0.50190 

86,5 

9.93698 

25,2 

9.70062 

74,8 

59  52  26.72 

.046 

.85543 

50,1 

.50104 

85,5 

.93723 

25,1 

.69987 

75,0 

59  55  52.99 

.047 

.86593 

50,o 

.50017 

86,6 

.93748 

25J 

.69912 

75,2 

59  59  i<).-'5 

.048 

.86643 

49,9 

•49930 

86,6 

•93773 

25,0 

.<*Av 

75,4 

60  02  45.52 

.049 

.86693 

49,8 

.49844 

86,7 

.93798 

25,0 

.69761 

75,5 

6b  06  1  1  .  78 

1.050 

0.86742 

49,8 

0.49757 

86,7 

9.93823 

24,9 

<;.<*X>Hf> 

75,7 

60  09  38.05 

u 

-isinhiu 

-F,/ 

cosh  iu 

*F0' 

,  .sinh  iu 

-Fo* 

log  cosh  iu 

-F0' 

u 

loo   . 

SMITHSONIAN  TABLCS 


213 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«Fo' 

u 

1.050 

0.86742 

49,8 

0.49757 

86,7 

9.93823 

24,9 

9.69686 

75,7 

6o°09/  38"o5 

.051 

.86792 

49,7 

.49670 

86,8 

.93848 

24,9 

.69610 

75,9 

60  13  04.31 

.052 

.86842 

49,6 

.49584 

86,8 

.93873 

24,8 

.69534 

AI 

60  16  30.58 

•  053 

.86891 

49,5 

.49497 

86,9 

.93898 

24,7 

.69458 

76,2 

60  19  56.84 

.054 

.86941 

49,4 

.49410 

86,9 

•93922 

24,7 

.69381 

76,4 

60  23  23.11 

1.055 

0.86090 

49,3 

0.49323 

87,0 

9.93947 

24,6 

9.69305 

76,6 

60  26  49.37 

.056 

.87039 

49,2 

.49236 

87,0 

.93972 

24,6 

.69228 

76,8 

60  30  15.64 

.057 

.87088 

49,1 

.49149 

87,1 

.93996 

24,5 

.69151 

77,o 

60  33  4L90 

.058 

.87138 

49,1 

.49062 

87,1 

.94021 

24,5 

.69074 

77,1 

60  37  08.17 

.059 

.87187 

49,0 

.48974 

87,2 

•94045 

24,4 

.68997 

77,3 

60  40  34-43 

i.  060 

0.87236 

48,9 

0.48887 

87,2 

9.94069 

24,3 

9.68920 

77,5 

60  44  00.69 

.061 

.87284 

48,8 

.48800 

87,3 

.94094 

24,3 

.68842 

77,7 

60  47  26.96 

.062 

.87333 

48,7 

.48713 

87,3 

.94118 

24,2 

.68764 

77,9 

60  50  53.22 

.063 

.87382 

48,6 

.48625 

87,4 

.94142 

24,2 

.68686 

78,o 

60  54  19.49 

.064 

.87430 

48,5 

.48538 

87,4 

.94166 

24,1 

.68608 

78,2 

60  57  45-75 

1.065 

0.87479 

48,5 

0.48450 

87,5 

9.94190 

24,1 

9.68530 

78,4 

61  01  12.  02 

.066 

.87527 

48,4 

.48363 

87,5 

.94214 

24,0 

.68451 

78,6 

61  04  38.28 

.067 

.87576 

48,3 

.48275 

87,6 

.94238 

23,9 

.68373 

78,8 

61  08  04.55 

.068 

.87624 

48,2 

.48188 

87,6 

.94262 

23,9 

.68294 

79,0 

61  ii  30.81 

.069 

.87672 

48,1 

.48100 

87,7 

.94286 

23,8 

.68215 

79,2 

61  14  57.08 

. 
1.070 

0.87720 

48,0 

0.48012 

87,7 

9.94310 

23,8 

9.68135 

79,3 

61  18  23.34 

.071 

.87768 

47,9 

.47925 

87,8 

.94334 

23,7 

.68056 

79,5 

61  21  49.61 

.072 

.87816 

47,8 

.47837 

87,8 

•94357 

23,7 

.67976 

79,7 

61  25  15.87 

.073 

.87864 

47,7 

•47749 

87,9 

.94381 

23,6 

.67896 

79,9 

61  28  42.14 

.074 

.879H 

47,7 

.47661 

87,9 

.94405 

23,6 

.67816 

80,1 

61  32  08.40 

1.075 

0.87959 

47,6 

0.47573 

88,0 

9.04428 

23,5 

9-67736 

80,3 

61  35  34.67 

.076 

.88007 

47,5 

.47485 

88,0 

.94451 

23,4 

.67656 

80,5 

61  39  00.93 

.077 

.88054 

47,4 

•47397 

88,1 

.94475 

23,4 

.67575 

80,7 

61  42  27.20 

.078 

.88101 

47,3 

.47309 

88,1 

.94498 

23,3 

.67494 

80,9 

61  45  53.46 

•079 

.88149 

47,2 

.47221 

88,1 

.94522 

23,3 

.67414 

81,1 

61  49  19.73 

1.080 

0.88196 

47,1 

0.47133 

88,2 

9-94545 

23,2 

9.67332 

81,3 

61  52  45.99 

.081 

.88243 

47,0 

.47045 

88,2 

.94568 

23,2 

.67251 

8i,5 

61  56  12.26 

.082 

.88290 

47,0 

.46956 

88,3 

.94591 

23,1 

.67169 

81,7 

61  59  38.52 

.083 

.88337 

46,9 

.46868 

88,3 

.94614 

23,0 

.67088 

81,9 

62  03  04-79 

.084 

.88384 

46,8 

.46780 

88,4 

.94637 

23,0 

.67006 

82,1 

62  06  31.05 

1.085 

0.88430 

46,7 

0.46691 

88,4 

9.94660 

22,9 

9.66924 

82,3 

62  09  57.31 

.086 

.88477 

46,6 

.46603 

88,5 

.94683 

22,9 

.66841 

82,5 

62  13  23.58 

.087 

.88524 

46,5 

.46514 

88,5 

.94706 

22,8 

.66759 

82,7 

62  16  49.84 

.088 

.88570 

46,4 

.46426 

88,6 

.94729 

22,8 

.66676 

82,9 

62  20  16.11 

.089 

.88616 

46,3 

.46337 

88,6 

•94751 

22,7 

.66593 

83,1 

62  23  42.37 

1.090 

0.88663 

46,2 

0.46249 

88,7 

9-94774 

22,7 

9.66516 

83,3 

62  27  08.64 

.091 

.88709 

46,2 

.46160 

88,7 

.94797 

22,6 

.66426 

83,5 

62  30  34.90 

.092 

.88755 

46,1 

.46071 

88,8 

.94819 

22,5 

.66343 

83,7 

62  34  01.17 

.093 

.88801 

46,0 

88,8 

.94842 

22,5 

.66259 

83,9 

62  37  27.43 

.094 

.88847 

45,9 

.45894 

88,8 

.94864 

22,4 

.66175 

84,1 

62  40  53.70 

1.095 

0.88893 

45,8 

0.45805 

88,9 

9.94887 

22,4 

9.66091 

84,3 

62  44  19.96 

.096 

.88939 

45,7 

.45716 

88,9 

•94909 

22,3 

.66007 

84,5 

62  47  46.23 

.097 

.88984 

45,6 

.45627 

89,0 

•94931 

22,3- 

.65922 

84,7 

62  51  12.49 

.098 

.89030 

45,5 

.45538 

89,0 

•94954 

22,2 

.65837 

84,9 

62  54  38.76 

.099 

.89075 

45,4 

.45449 

89,1 

.94976 

22,2 

.65752 

85,1 

62  58  05.02 

I.IOO 

0.89121 

45,4 

0.45360 

89,1 

9.94998 

22,1 

9.65667 

85,3 

63  01  31-29 

u 

-isinhiu 

«F0' 

cosh  iu 

«FO' 

sinh  iu 

«F0' 

log  cosh  iu 

«FO' 

u 

loo  . 

SMITHSONIAN  TABLES 


213 


Circular  Functions. 


u 

sin  u 

•  IV 

cos  u 

*>Fo' 

log  sin  u 

-  Fo' 

log  cos  u 

<•>  FO' 

u 

I.IOO 

O.89I2I 

45,4 

0.45360 

89,1 

9.94998 

22,1 

9.65667 

85,3 

63°oi'3i"29 

.101 

.89166 

45,3 

.45270 

89,2 

.95020 

22,0 

.65581 

85,5 

63  04  57.55 

.102 

.89211 

45,2 

.45181 

89,2 

.95042 

22,0 

.65496 

85,8 

63  08  23.82 

.103 

.89256 

45,1 

.45092 

89,3 

.95064 

21,9 

.65410 

86,0 

63  n  50.08 

.104 

.89301 

45,0 

.45003 

89,3 

.95086 

2-1,9 

•65324 

86,2 

63  15  16.35 

1.105 

0.89346 

44,9 

0.44913 

89,3 

9.95108 

21,8 

9.65238 

86,4 

63  18  42.61 

.106 

.89391 

44,8 

.44824 

89,4 

.95130 

21,8 

.65151 

86,6 

63  22  08.88 

.107 

.89436 

44,7 

.44735 

89,4 

.95151 

21,7 

.65064 

86,8 

63  25  35.14 

.108 

.89481 

44,6 

.44645 

89,5 

.95173 

21,7 

.64977 

87,0 

63  29  OI.4I 

.109 

•89525 

44,6 

.44556 

89,5 

•95195 

21,6 

.64890 

87,3 

63  32  27.67 

I.  IIO 

0.89570 

44,5 

0.44466 

89,6 

9.95216 

21,6 

9.64803* 

87,5 

63  35  53-93 

.III 

.89614 

44,4 

•44377 

89,6 

.95238 

21,5 

.64715 

87,7 

63  39  20.20 

.112 

.89659 

44,3 

.44287 

89,7 

-95259 

21,5 

.64628 

87,9 

63  42  46.46 

.113 

.89703 

44,2 

.44197 

89,7 

.95281 

21,4 

.64540 

88,1 

63  46  1,2.73 

.114 

.89747 

44,1 

.44108 

89,7 

•95302 

21,3 

.64451 

88,4 

63  49  38.99 

1.  115 

0.89791 

44,0 

0.44018 

89,8 

9.95323 

21,3 

9-64363 

88,6 

63  53  05.26 

.116 

.89835 

43,9 

.43928 

89,8 

•95345 

21,2 

.64274 

88,8 

63  56  31.52 

.117 

.89879 

43,8 

.43838 

89,9 

.95366 

21,2 

.64185 

89,0 

63  59  5-7-79 

.118 

.89923 

43,7 

.43748 

89,9 

.95387 

21,1 

.64096 

89,3 

64  03  24.05 

.119 

.89966 

43,7 

.43658 

90,0 

.95408 

21,1 

.64007 

89,5 

64  06  50.32 

I.I2O 

0.90010 

43,6 

0.43568 

90,0 

9.95429 

2I,O 

9.63917 

89,7 

64  10  16.58 

.121 

.90054 

43,5 

.43478 

90,i 

•95450 

21,0 

.63827 

90,0 

64  13  42.85 

.122 

.00097 

43,4 

.43388 

90,1 

.95471 

20,9 

.63737 

90,2 

64  17  09.11 

.123 

.90140 

43,3 

.43208 

90,1 

.95492 

20,9 

.63647 

90,4 

64  20  35.38 

.124 

.90184 

43,2 

.43208 

90,2 

.95513 

20,8 

.63556 

90,6 

64  24  01.64 

1.  125 

0.90227 

43,1 

0.43118 

90,2 

9-95534 

20,8 

9-63466 

90,9 

64  27  27.91 

.126 

.90270 

43,0 

.43027 

90,3 

.95554 

20,7 

.63375 

91,1 

64  30  54.17 

.127 

•90313 

42,9 

.42937 

90,3 

•95575 

:20,6 

.63283 

9i,3 

64  34  20.44 

.128 

.903-56 

42,8 

.42847 

90,4 

.95596 

20,6 

.63192 

91,6 

64  37  46.70 

.129 

•90398 

42,8 

.42756 

90,4 

.95616 

20,5 

.63100 

91,8 

64  41  12-97 

I.I30 

0.90441 

42,7 

0.42666 

90,4 

9.95637 

20,5 

9.63008 

92,i 

64  44  39-23 

.131 

.00484 

42,6 

.42576 

90,5 

.95657 

20,4 

.62916 

92,3 

64  48  05.50 

.132 

.90526 

42,5 

.42485 

90,5 

.95678 

20,4 

.62824 

92,5 

64  51  31.76 

•133 

.90569 

42,4 

.42394 

90,6 

.95698 

20,3 

.62731 

92,8 

64  54  58.03 

•134 

.90611 

42,3 

.42304 

90,6 

.95718 

20,3 

.62638 

93,0 

64  58  24.29 

I-I35 

0.00653 

42,2 

0.42213 

90,7 

9.95738 

2O,2 

9-62545 

93,3 

65  oi  50.56 

.136 

.90696 

42,1 

.42123 

90,7 

•95759 

20,2 

.62451 

93,5 

65  05  16.82 

•137 

.90738 

42,0 

.42032 

90,7 

.95779 

2O,  I 

.62358 

93,8 

65  08  43-08 

.138 

.90780 

41,9 

.41941 

90,8 

.95799 

20,1 

.62264 

94,o 

65  12  09-35 

•139 

.90822 

41,9 

.41850 

90,8 

.95819 

2O,O 

.62170 

94,2 

65  15  35.6l 

I.I40 

0.90863 

41,8 

0.41759 

90,9 

9.95839 

20,O 

9.62075 

94,5 

65  19  01.88 

.141 

.90905 

41,7 

.41669 

90,9 

.95859 

19,9 

.61981 

94,7 

65  22  28.14 

.142 

•90947 

41,6 

.41578 

90,9 

•  95879 

19,9 

.61886 

95,0 

65  25  54-41 

.143 

.90988 

41,5 

.41487 

91,0 

.95859 

19,8 

.61791 

95,2 

65  29  20.67 

.144 

.91030 

41,4 

.41396 

91,0 

.95918 

19,7 

.61095 

95,5 

65  32  46.94 

1.  145 

0.91071 

41,3 

0.41305 

91,1 

9.95938 

19,7 

9.61600 

95,8 

65  36  13.20 

.146 

.91112 

41,2 

.41214 

91,1 

.95958 

19,6 

.61504 

96,0 

65  39  39-47 

.147 

.91153 

41,1 

.41122 

91,2 

•95977 

19,6 

.61408 

96,3 

65  43  05.73 

.148 

.9H95 

41,0 

.41031 

91,2 

•95997 

19,5 

.61311 

</>0 

65  46  32.00 

.149 

.91235 

40,9 

.40940 

9L2 

.96016 

19,5 

.61215 

96,8 

65  49  58.26 

i.i'SO 

0.91276 

40,8 

0.40849 

91,3 

9-96036 

19,4 

9.6lll8 

97fl 

65  53  24-53 

u 

-isinhiu 

«Fo' 

cosh  iu 

-FO' 

Ion8inh  JU 

-Fo' 

log  cosh  iu 

u 

log  , 

SMITHSONIAN  TABLES 


214 


Circular  Functions. 


11 

sin  u 

«Fo' 

cos  u 

«F0' 

log  sin  u 

«   Fo' 

log  cos  u 

-PC' 

u 

1.150 

0.91276 

40,8 

0.40849 

91,3 

9.96036 

19,4 

9.6lll8 

97,o 

65°53/24/./53 

.151 

.91317 

40,8 

.40757 

91,3 

•96055 

19,4 

.6lO2I 

97,3 

65  56  50.79 

.152 

.91358 

40,7 

.40666 

9i,4 

.96075 

19,3 

.60923 

97,6 

66  oo  17.06 

.153 

.91399 

40,6 

.40575 

91,4 

.96094 

19,3 

.60826 

97,8 

66  03  43.32 

.154 

.91439 

40,5 

.40483 

91,4 

.96II31 

19,2 

.60728 

98,i 

66  07  09-59 

1.  155 

0.91479 

40,4 

0.40392 

91,5 

9.96132 

19,2 

9.60629 

98,4 

66  10  35.85 

.156 

.91520 

40,3 

.40300 

91,5 

.96152 

19,1 

.60531 

98,6 

66  14  02.  12 

.157 

.91560 

40,2 

.40209 

91,6 

.96171 

19,1 

.60432 

98,9 

66  17  28.38 

.158 

.91600 

40,1 

.40117 

91,6 

.96190 

19,0 

.60333 

99,2 

66  20  54.65 

.159 

.91640 

40,0 

.40026 

91,6 

.96209 

19,0 

.60234 

99,4 

66  24  20.91 

1.160 

0.91680 

39,9 

0.39934 

9i»7 

9.96228 

18,9 

9.60134 

99,7 

66  27  47.18 

.161 

.91720 

39,8 

.39842 

91,7 

.96246 

18,9 

.60034 

100,0 

66  31  13.44 

.162 

.91760 

39,8 

.39751 

91,8 

.96265 

18,8 

•59934 

100,3 

66  34  39.70 

.163 

.91800 

39,7 

.39659 

91,8 

.96284 

18,8 

.59834 

100,5 

66  38  05.97 

.164 

.91839 

39,6 

.39567 

91,8 

.96303 

18,7 

•59733 

100,8 

66  41  32.23 

1.165 

0.91879 

39,5 

0.39475 

91,9 

9-96322 

18,7 

9.59632 

IOI,I 

66  44  58.50 

.166 

.91918 

39,4 

.39383 

91,9 

.96340 

18,6 

.59531 

101,4 

66  48  24.76 

.167 

.91958 

39,3 

.39291 

92,0 

•96359 

18,6 

.59430 

101,6 

66  51  51.03 

.168 

.91997 

39,2 

.39199 

92,0 

•96377 

18,5 

.59328 

101,9 

66  55  17.29 

.169 

.92036 

39,1 

.39107 

92,0 

.96396 

18,5 

.59226 

102,2 

66  58  43.56 

1.170 

0.92075 

39,0 

0.39015 

92,1 

9.96414 

18,4 

9.59123 

102,5 

67  02  09.82 

.171 

.92114 

38,9 

.38923 

92,1 

•96433 

18,4 

.59021 

102,8 

67  05  36.09 

.172 

.92153 

38,8 

.38831 

92,2 

.96451 

18,3 

103,1 

67  09  02.35 

.173 

.92192 

38,7 

.38739 

92,2 

.96469 

18,2 

.58815 

103,4 

67  12  28.62 

.174 

.92230 

38,6 

.38647 

92,2 

.96487 

18,2 

.58711 

103,6 

67  15  54-88 

I.I75 

0.92269 

38,6 

0.38554 

92,3 

9.96506 

18,1 

9.58607 

103,9 

67  19  21.15 

.176 

.92307 

38,5 

.38462 

92,3 

.96524 

18,1 

.58503 

104,2 

67  22  47.41 

.177 

.92346 

38,4 

.38370 

92,3 

.96542 

18,0 

.58399 

104,5 

67  26   13.68 

.178 

.92384 

38,3 

.38277 

92,4 

.96560 

18,0 

.58204 

104,8 

67  29  39-94 

.179 

.92422 

38,2 

.38185 

92,4 

.96578 

17,9 

.58189 

105,1 

67  33  06.21 

1.180 

0.92461 

38,1 

0.38092 

92,5 

9.96596 

17,9 

9-58084 

105,4 

67  36  32.47 

.181 

.92499 

38,0 

.38000 

92,5 

.96614 

17,8 

.57978 

105,7 

67  39  58.74 

.182 

.92537 

37,9 

.37907 

92,5 

.96631 

17,8 

.57872 

106,0 

67  43  25.00 

.183 

•92574 

37,8 

.37815 

92,6 

.96649 

17,7 

.57766 

106,3 

67  46  51.27 

.184 

.92612 

37,7 

•37722 

92,6 

.96667 

17,7 

.-57660 

106,6 

67  50  17.53 

1.185 

0.92650 

37,6 

0.37630 

92,6 

9.96684 

17,6 

9-57553 

106,9 

67  53  43.8o 

.186 

.92687 

37,5 

•37537 

92,7 

.96702 

17,6 

•57446 

107,2 

*>7  57  10.  06 

.187 

.92725 

37,4 

.37444 

92,7 

.96720 

17,5 

•57339 

107,5 

68  oo  36.33 

.188 

.92762 

37,4 

•37352 

92,8 

.96737 

17,5 

.57231 

107,9 

68  04  02.59 

.189 

.92800 

37,3 

.37259 

92,8 

.96755 

17,4 

.57123 

108,2 

68  07  28.85 

1.190 

0.92837 

37,2 

0.37166 

92,8 

9.96772 

17,4 

9.570I5 

108,5 

68  10  55.12 

.191 

.92874 

37,1 

.37073 

92,9 

.96789 

17,3 

.56906 

108,8 

68  14  21.38 

.192 

.9291-1 

37,o 

.36980 

92,9 

.96807 

17,3 

•56797 

109,1 

68  17  47.65 

.193 

.92948 

36,9 

.36887 

92,9 

.96824 

17,2 

.56688 

109,4 

68  21  13.91 

.194 

.92985 

36,8 

.36794 

93,o 

.96841 

17,2 

.56578 

109,8 

68  24  40.18 

1.  195 

0.93022 

36,7 

0.36701 

93,0 

9-96858 

I7,i 

9.56468 

IIO,  I 

68  28  06.44 

.196 

.93058 

36,6 

.36608 

93,i 

.96875 

17,1 

.56358 

110,4 

68  31  32.71 

.93095 

36,5 

•36515 

93,1 

.96893 

17,0 

.56247 

110,7 

68  34  58.97 

.198 

.93131 

36,4 

.36422 

93,1 

.06910 

i7,o 

.56137 

III,O 

68  38  25.24 

.199 

.93168 

36,3 

•36329 

93,2 

.96927 

16,9 

.56025 

111,4 

68  41  51.50 

i.  200 

0.93204 

36,2 

0.36236 

93,2 

9.96943 

16,9 

9.55914 

m,7 

68  45  17.77 

u 

—  i  sinh  iu 

»F0' 

cosh  iu 

wF0' 

sinh  iu 

«FO' 

log  cosh  iu 

«FO' 

u 

loo      . 

SMITHSONIAN  TABLES 


215 


Circular  Functions. 


u 

sin  u 

<-F0' 

cos  u 

«F0* 

log  sin  u 

-    Fo' 

log  cos  u 

"Fo' 

u 

I.2OO 

0.93204 

36,2 

0.36236 

93,2 

9.96943 

16,9 

9.55914 

111,7 

68°4s'  i  7^77 

.201 

.93240 

36,1 

.36143 

93,2 

.96960 

16,8 

.55802 

112,0 

68  48  44.03 

.202 

.932/6 

36,0 

.36049 

93,3 

.96977 

16,8 

.55650 

1  12,4 

68  52  10.30 

.203 

•93312 

36,0 

.35956 

93,3 

.96994 

16,7 

•55577 

112,7 

68  55  36.56 

.204 

.93348 

35,9 

.35863 

93,3 

.97011 

16,7 

•  55464 

113,0 

68  59  02.83 

1.205 

0.93384 

35,8 

0.35769 

93,4 

9.97027 

16,6 

9-55351 

113,4 

69  02  29.09 

.206 

•93420 

35,7 

.35676 

93,4 

•97044 

16,6 

.55237 

H3,7 

69  05  55.36 

.207 

•93455 

35,6 

.35582 

93,5 

.97060 

16,5 

.55124 

114,1 

69  09  21.62 

.208 

•93491 

35,5 

.35489 

93,5 

.97077 

16,5 

.55009 

114,4 

69    12   47.89 

.209 

.93526 

35,4 

•35395 

93,5 

.97093 

16,4 

.54895 

114,8 

69  16  14.15 

I.2IO 

0.93562 

35,3 

0.35302 

93,6 

9.97IIO 

16,4 

9.54780 

i  i'5,i 

69  19  40.42 

.211 

.93597 

35,2 

.35208 

93,6 

.97126 

16,3 

.54665 

H5,5 

69  23  06.68 

.212 

.93632 

35,i 

.35H5 

93,6 

.97142 

16,3 

•54549 

H5,8 

69  26  32.95 

.213 

.93667 

35,o 

•35021 

93,7 

.97159 

16,2 

•54433 

116,2 

69  29  59.21 

.214 

•93702 

34,9 

•34927 

93,7 

•97175 

16,2 

•54317 

"6,5 

69  33  25-47 

1.  215 

0-93737 

34,8 

0.34834 

93,7 

9.97I9I 

16,1 

9-54200 

116,9 

69  36  51-74 

.216 

.93772 

34,7 

.34740 

93,8 

•97207 

16,1 

.54083 

117,2 

69  40  18.00 

.217 
.218 

.93806 
.93841 

34,6 
34,6 

.34646 
.34552 

93,8 
93,8 

.97223 
.97239 

16,0 
16,0 

.'53848 

117,6 
118,0 

69  43  44.27 
69  47  10.  S31 

.219 

.93876 

34,5 

•34458 

93,9 

.97255 

15,9 

.53730 

"8,3 

69  50  36.80 

I.22O 

0.93910 

34,4 

0.34365 

93,9 

9.97271 

15,9 

9.536n 

"8,7 

69  54  03.06 

.221 

•93944 

34,3 

.34271 

93,9 

.97287 

15,8 

•53492 

119,1 

69  57  29.33 

.222 

.93978 

34,2 

.34177 

94,0 

.97303 

15,8 

.53373 

"9,4 

70  oo  55-59 

•  223 

.94013 

34,1 

•34083 

94,0 

.97319 

15,7 

.53253 

"9,8 

70  04  21.86 

.224 

.94047 

34,0 

.33989 

94,0 

•97334 

15,7 

.53133 

120,2 

70  07  48.12 

1.  225 

0.94081 

33,9 

0.33895 

94,1 

9-  97350 

15,6 

9.53013 

120,5 

70  ii  14.39 

.226 

.94114 

33,8 

.33800 

94,1 

.97366 

15,6 

.52892 

120,9 

70  14  40.65 

.227 

.94148 

33,7 

.33706 

94,1 

.97381 

15,5 

.52771 

121,3 

70  18  06.92 

.228 

.94182 

33,6 

.33612 

94,2 

•97397 

15,5 

.52650 

121,7 

70  21  33.18 

.229 

.94215 

33,5 

.33518 

94,2 

.97412 

15,5 

•52528 

122,1 

70  24  59-44 

I.23O 

0.94249 

33,4 

0.33424 

94,2 

9.97428 

15,4 

9-52406 

122,5 

70  28  25.71 

.231 

.94282 

33,3 

•33330 

94,3 

•97443 

15,4 

.52283 

122,9 

70  31  51.98 

.232 

.94316 

33,2 

.33235 

94,3 

.97458 

15,3 

.52160 

123,2 

70  35  18.24 

•233 

.94349 

33,1 

.33141 

94,3 

•97474 

15,3 

.52036 

123,6 

70  38  44.51 

•234 

.94382 

33,0 

.33047 

944 

.97489 

15,2 

.51913 

124,0 

70  42  10.77 

1.235 

0.04415 

33,0 

0.32952 

94,4 

9.97504 

15,2 

9.51788 

124,4 

70  45  37.04 

.236 

.94448 

32,9 

.32858 

94,4 

•97519 

I5,i 

•51664 

124,8 

70  49  03.30 

.237 

•9448i 

32,8 

.32763 

94,5 

.97534 

I5,i 

•51539 

125,2 

70  52  29-57 

.238 

.94513 

32,7 

.32669 

94,5 

•97549 

I5,o 

.51413 

125,6 

70  55  55.83 

•239 

.94546 

32,6 

.32574 

94,5 

.97564 

I5,o 

.51287 

126,1 

70  59  22.09 

1.240 

0.94578 

32,5 

0.32480 

94,6 

9-97579 

14,9 

9.5n6i 

126,5 

71  02  48.36 

.241 

.9461/1 

3^,4 

.32385 

94,6 

•97594 

14,9 

.51034 

126,9 

71  06  14.  <>j 

.242 

.94643 

32,3 

.32290 

94,6 

.97609 

14,8 

.50007 

127,3 

71  09  40.89 

•243 

.94675 

32,2 

.32196 

94,7 

.97624 

14,8 

.50780 

127,7 

71  13  07.15 

•  244 

.94708 

32,1 

.32101 

94,7 

.97638 

14,7 

.50652 

128,1 

71  16  33.42 

1.245 

0.94740 

32,0 

0.32006 

94,7 

9.97653' 

14,7 

9.50524 

128,6 

71  19  59.68 

.246 
.247 

.94772 
•94003 

31,9 
3i,8 

.31912 
.31817 

94,8 
94,8 

.97668 
.97682 

14,6 
14,6 

•50395 
.50266 

129,0 
129,4 

71  23  25.95 
71  26  52.21 

.248 

3i,7 

.31722 

94,8 

.97607 

14,5 

.50136 

129,8 

71  30  18.48 

•  249 

.94867 

31,6 

.31627 

94,9 

•977II 

14,5 

.50006 

130,3 

71  3'3  44-74 

1.250 

0.94898 

3i,5 

0.31532 

94,9 

9.97726 

14,4 

9.49875 

130,7 

71  37  ".oi 

u 

isinhiu 

•  F«/ 

cosh  iu 

-Fo' 

i««tlnh  lu 

»FV 

loo  cosh  iu 

-FO' 

u 

log     , 

SMITHSONIAN  TABLES 


JI'i 


Circular  Functions. 


u 

sin  u 

«FO' 

cos  u 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

*>Fo' 

u 

O           /            H 

1.250 

0.94898 

3i,5 

0.31532 

94,9 

9.97726 

14,4 

9.49875 

130,7 

71  37  11.  01 

.251 

.94930 

31,4 

.31437 

94,9 

.97740 

14,4 

.49745 

131,1 

71  40  37-27 

.252 

.94961 

31,3 

.31342 

95,0 

•97755 

14,3 

.49613 

131,6 

71  44  03.54 

.253 

.94993 

31,2 

.31247 

95,0 

.97769 

14,3 

.49481 

132,0 

71  47  29.80 

.254 

.95024 

31,2 

.31152 

95,0 

.97783 

14,2 

•49349 

132,5 

71  50  56.07 

1.255 

0.95055 

31,1 

0.31057 

95,1 

9-97797 

14,2 

9.40216 

132,9 

71  54  22.33 

.256 

.95086 

31,0 

.30962 

95,i 

.97812 

14,1 

.49083 

133,4 

71  57  48.60 

•  257 

.95H7 

30,9 

.30867 

95,i 

.97826 

14,1 

.48950 

133,8 

72  01  14.86 

.258 

.95148 

30,8 

.30772 

95,i 

.97840 

14,0 

.48816 

134,3 

72  04  41.13 

.259 

.95178 

30,7 

.30677 

95,2 

.97854 

14,0 

.48681 

134,7 

72  08  07.39 

1.260 

0.95209 

30,6 

0.30582 

95,2 

9.97868 

13,9 

9.48546 

135,2 

72  II  33.66 

.261 

.95240 

30,5 

.30486 

95,2 

.97882 

13,9 

.48411 

135,7 

72  14  59.92 

.262 

.95270 

30,4 

.30391 

95,3 

.9780 

13,9 

.48275 

136,1 

72  18  26.19 

.263 

•95300 

30,3 

.30296 

95,3 

.97909 

13,8 

.48138 

136,6 

72  21  52.45 

.264 

•95331 

30,2 

.30201 

95,3 

.97923 

13,7 

.48002 

i'37,i 

72  25  18.72 

1.265 

0.95361 

30,1 

0.30105 

95,4 

9.97937 

13,7 

9.47864 

137,6 

72  28  44-98 

.266 

•  95391 

30,0 

.30010 

95,4 

.97951 

13,7 

.47726 

138,0 

72  32  11.24 

.267 

•95421 

29,9 

.29914 

95,4 

.97064 

13,6 

.47588 

138,5 

72  35  37-51 

.268 

•95451 

29,8 

.29819 

95,5 

.97978 

13,6 

•47449 

I39,o 

72  39  03-77 

.269 

.95480 

29,7 

.29724 

95,5 

.97991 

13,5 

•47310 

139,5 

72  42  30.04 

1.270 

0.95510 

29,6 

0.29628 

95,5 

9.98005 

13,5 

9.47170 

140,0 

72  45  56.30 

.271 

.95540 

29,5 

.29533 

95,5 

.98018 

13,4 

.47030 

140,5 

72  49  22.57 

.272 

.95569 

29,4 

.29437 

95,6 

.98032 

13,4 

.46889 

141,0 

72  52  48.83 

.273 

•95599 

29,3 

.29341 

95,6 

.98045 

13,3 

.46748 

Hi,5 

72  56  15.10 

.274 

.95628 

29,2 

.29246 

95,6 

.98058 

13,3 

.46606 

142,0 

72  59  41.36 

1.275 

0.95657 

29,2 

0.29150 

95,7 

9.98072 

13,2 

9.46464 

142,5 

73  03  07.63 

.276 

.95686 

29,1 

.29054 

95,7 

.98085 

13,2 

.46321 

I43,o 

73  06  33.89 

.277 

.95715 

29,0 

.28959 

95,7 

.98098 

I3,i 

.46178 

143,5 

73  10  oo.  16 

.278 

•95744 

28,9 

.28863 

95,7 

.98111 

I3,i 

.46034 

144,1 

73  13  26.42 

.279 

.95773 

28,8 

.28767 

95,8 

.98124 

13,0 

.45890 

144,6 

73  16  52.69 

1.280 

0.95802 

28,7 

0.28672 

95,8 

9.98137 

13,0 

9-45745 

I45,i 

73  20  18.95 

.281 

.95830 

28,6 

.28576 

95,8 

.98150 

I3,o 

.45600 

145,6 

73  23  45.22 

.282 

.95859 

28,5 

.28480 

95,9 

.98163 

12,9 

•45454 

146,2 

73  27  11.48 

.283 

.95887 

28,4 

.28384 

95,9 

.98176 

12,9 

•  45307 

146,7 

73  30  37.75 

.284 

.95916 

28,3 

.28288 

95,9 

.98189 

12,8 

•45160 

147,3 

73  34  04.01 

1.285 

0.95944 

28,2 

0.28192 

95,9 

9.98202 

12,8 

9.45013 

147,8 

73  37  30.28 

.286 

•95972 

28,1 

.28096 

96,0 

.98214 

12,7 

.44865 

148,3 

73  40  56.54 

.287 

.96000 

28,0 

.28000 

06,0 

.98227 

12,7 

.44716 

148,9 

73  44  22.81 

.288. 

.96028 

27,9 

.27004 

96,0 

.98240 

12,6 

.44567 

149,5 

73  47  49-07 

.289 

.96056 

27,8 

.27808 

96,1 

.98252 

12,6 

.44417 

150,0 

73  51  15.34 

1.290 

0.96084 

27,7 

0.27712 

06,1 

9.98265 

12,5 

9.44267 

150,6 

73  54  41.60 

.291 

.96111 

27,6 

.27616 

96,i 

.98277 

12,5 

.44116 

151,1 

73  58  07.86 

.292 

.96139 

'27,5 

.27520 

96,1 

.98290 

12,4 

.43965 

I5i,7 

74  01  34.13 

.293 

.96166 

27,4 

.27424 

96,2 

.08302 

12,4 

•43813 

152,3 

74  05  00.39 

.294 

.96194 

27,3 

.27328 

96,2 

.98315 

12,3 

.43660 

152,9 

74  08  26.66 

1.295 

0.96221 

27,2 

0.27231 

96,2 

9.98327 

12,3 

9.43507 

153,5 

74  II  52.92 

.296 

.96248 

27,1 

.27135 

96,2 

.98339 

12,2 

•43353 

I54,o 

74  15  19.19 

•  297 

.96275 

27,0 

.27039 

96,3 

.98351 

12,2 

.43199 

154,6 

74  18  45-45 

.298 

.06302 

26,9 

.26943 

96,3 

.98364 

12,2 

.43044 

155,2 

74  22  11.72 

.299 

.96329 

26,8 

.26846 

96,3 

.98376 

12,1 

.42888 

155,8 

74  25  37.98 

1.300 

0.96356 

26,7 

0.26750 

96,4 

9.98388 

12,1 

9.42732 

156,4 

74  29  04.25 

u 

-i  sinhiu 

•  Fo" 

cosh  iu 

wFo' 

sinh  iu 

«F0' 

log  cosh  iu 

«FO' 

u 

loo      . 

SMITHSONIAN  TABLES 


217 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

1.300 

0.96356 

26,7 

0.26750 

96,4 

9.98388 

12,1 

9.42/32 

156,4 

74  29  04.25 

.301 

•96383 

26,7 

.26654 

96,4 

.98400 

12,0 

.42575 

i'57,o 

74  32  30.51 

.302 

.96409 

26,6 

.26557 

96,4 

.98412 

12,0 

.42418 

157,7 

74  35  56.78 

.303 

.96436 

26,5 

.26461 

96,4 

.98424 

11,9 

.42260 

158,3 

74  39  23.04 

.304 

.96462 

26,4 

.26364 

96,5 

.98436 

11,9 

.42102 

158,9 

74  42  49.31 

1.305 

0.96488 

26,3 

0.26268 

96,5 

9.98447 

11,8 

9.41942 

159,5 

74  46  15.57 

.306 

.96515 

26,2 

.26171 

96,5 

.98459 

11,8 

.41782 

160,2 

74  49  41.84 

.307 

.96541 

26,1 

.26075 

96,5 

.9&47I 

n,7 

.41622 

160,8 

74  53  08.10 

.308 

.96567 

26,0 

.25978 

96,6 

.98483 

n,7 

.41461 

161,4 

74  56  34-37 

.309 

•96593 

25,9 

.25882 

96,6 

.98494 

11,6 

.41299 

162,1 

75  oo  00.63 

1.310 

0.96618 

25,8 

0.25785 

96,6 

9.98506 

11,6 

9.4H37 

162,7 

75  03  26.90 

.311 

.96644 

25,7 

.25688 

96,6 

.98518 

n,5 

.40974 

163,4 

75  06  53.16 

.312 

.96670 

25,6 

.25592 

96,7 

.98529 

n,5 

.40810 

164,0 

75  10  19-43 

.313 

.96695 

25,5 

.25495 

96,7 

•98541 

ii,5 

.40646 

164,7 

75  13  45.69 

.314 

.96721 

25,4 

.25398 

96,7 

.98552 

11,4 

.40481 

165,4 

75  17  11-0 

1.315 

0.06746 

25,3 

0.25302 

96,7 

9.98563 

11,4 

9.40315 

166,1 

75  20  38.22 

.316 

.96771 

25,2 

.25205 

96,8 

.98575 

n,3 

.40148 

166,7 

75  24  04.49 

.317 

.96797 

25,1 

.25108 

96,8 

.98586 

n,3 

•39981 

167,4 

75  27  30.75 

.318 

.96822 

25,0 

.25011 

96,8 

.98597 

11,2 

.39814 

168,1 

75  30  57-01 

.319 

.96847 

24,9 

.24914 

96,8 

.98608 

11,2 

.39645 

168,8 

75  34  23.28 

1.3-20 

0.96872 

24,8 

0.24818 

96,9 

9.98620 

II,  I 

9.39476 

169,5 

75  37  49.54 

.321 

.96896 

24,7 

.24721 

96,9 

.98631 

II,  I 

.39306 

170,2 

75  41  I5.8i 

.322 

.96921 

24,6 

.  24624 

96,9 

.98642 

11,0 

.39135 

170,9 

75  44  42.07 

.323 

.96046 

24,5 

.24527 

96,9 

.98653 

11,0 

.38964 

i7i,7 

75  48  08.34 

.524 

.96970 

24,4 

.24430 

97,0 

.98664 

10,9 

.38792 

172,4 

75  5i  34-6o 

1.325 

0.06994 

24,3 

0.24333 

97,o 

9.98675 

10,9 

9.38619 

i73,i 

75  55  00.87 

.326 

.97019 

24,2 

.24236 

97,o 

.98686 

10,8 

.38446 

173,9 

75  58  27.13 

.327 

.97043 

24,1 

.24139 

97,o 

.98696 

10,8 

.38272 

174,6 

76  01  53-40 

.328 

.97067 

24,0 

.24042 

97,1 

.98707 

10,8 

•38097 

175,3 

76  05  19.66 

.329 

.97091 

23,9 

.23945 

97,1 

.98718 

10,7 

•37921 

176,1 

76  08  45-93 

1.330 

0.97H5 

23,8 

0.23848 

97,1 

9.98729 

10,7 

9-37744 

176,9 

76   12    12.19 

.331 

.97139 

23,8 

.23750 

97,1 

•98739 

10,6 

.37567 

177,6 

76  15  38.46 

.332 

.97162 

23,7 

.23653 

97,2 

.98750 

1  0,6 

.37389 

178,4 

76  19  04.72 

.333 

.97186 

23,6 

.23556 

97,2 

.98760 

10,5 

•37210 

179,2 

76  22  30.99 

•  334 

.97209 

'23,5 

.23459 

97,2 

.98771 

10,5 

.37031 

180,0 

76  25   57-25 

1-335 

0.97233 

23,4 

0.23362 

97,2 

9.98781 

10,4 

9.36851 

180,8 

76  29  23.52 

.336 

.97256 

23,3 

.23264 

97,3 

.98792 

10,4 

.36669 

181,6 

76  32  49.78 

.337 

.97279 

23,2 

.23167 

97,3 

.98802 

10,3 

.36487 

182,4 

76  36    l6.O5 

.338 

.97303 

23,1 

.23070 

97,3 

.98812 

10,3 

•36305 

183,2 

76  39  42.31 

•339 

.97326 

23,0 

.22973 

97,3 

.98823 

10,3 

.36121 

184,0 

76  43  08.58 

1.340 

0.97348 

22,9 

0.22875 

97,3 

9.98833 

10,2 

9-35937 

184,8 

76  46  34-84 

•  341 

.97371 

22,8 

.22778 

97,4 

.98843 

10,2 

.35751 

185,7 

76  50  oi.n 

•  342 

•97394 

22,7 

.22681 

97,4 

.98853 

10,1 

.35565 

186,5 

76  53  27.37 

•  343 

.97417 

22,6 

.22583 

97,4 

.98863 

10,1 

.35378 

187,3 

76  56  53.63 

•  344 

•97439 

22,5 

.22486 

97,4 

.98873 

10,0 

.35191 

188,2 

77  oo  19.90 

1-345 

0.97462 

22,4 

0.22388 

97,5 

9.98883 

IO,O 

9.35002 

189,1 

77  03  46.16 

.346 

.97484 

22,3 

.22291 

97,5 

•98893 

9,9 

.34813 

189,9 

77  07  12.43 

•  347 

.97506 

22,2 

.22193 

97,5 

.98903 

9,9 

.34622 

100,8 

77  10  38.69 

•  348 

•97528 

22,1 

.22006 

97,5 

.08913 

9,8 

.34431 

i9i,7 

77  14  04.96 

.349 

.97550 

'22,0 

.21998 

97,6 

.98023 

9,8 

.34239 

192,6 

77  17  31.22 

1.350 

0.97572 

21,9 

0.21901 

97,6 

9.98933 

9,7 

9.34046 

193,5 

77  20  57-49 

u 

-isinhiu 

«Fo' 

cosh  iu 

«F0' 

,00^ 

«F0' 

ogcosh  iu 

«F0' 

u 

SMITHSONIAN  TABLES 


218 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«F0' 

log  sin  u 

«   Fo' 

log  cos  u 

«F0' 

u 

1.350 

0.97572 

21,9 

O.2I9OI 

97,6 

9.98933 

9,7 

9.34046 

i93,5 

77°2o'  57"49 

.351 

•97594 

21,8 

.21803 

97,6 

.98942 

9,7 

.33852 

194,4 

77  24  23.75 

.352 

.97616 

21,7 

.21705 

97,6 

.98952 

9,7 

.33657 

i95,3 

77  27  50.02 

•  353 

.97638 

21,6 

.2l6o8 

97,6 

,98962 

9,6 

.33461 

196,2 

77  31  16.28 

•  354 

.97659 

21,5 

.21510 

97,7 

.98971 

9,6 

.33264 

197,2 

77  34  42.55 

1.355 

0.97681 

21,4 

O.2I4I3 

97,7 

9.98981 

9,5 

9.33067 

198,1 

77  38  08.  81 

.356 

.97702 

21,3 

•21315 

97,7 

.98990 

9,5 

.32868 

199,1 

77  4i  35.o8 

.357 

.97723 

2  1,  '2 

.21217 

97,7 

.09000 

9,4 

.32669 

200,0 

77  45  01.34 

.358 

•97744 

21,1 

.21119 

97,7 

.09009 

9,4 

.32468 

201,0 

77  48  27.61 

.359 

.97765 

2I,O 

.2IO22 

97,8 

.90019 

9,3 

.32267 

202,0 

77  51  53.87 

.  1.360 

0.97786 

20,9 

0.20924 

97,8 

9.00028 

9,3 

9.32064 

203,0 

77  55  20.14 

.361 

.97807 

20,8 

.20826 

97,8 

.99037 

9,2 

.31861 

204,0 

77  58  46.40 

.362 

.97828 

20,7 

.20728 

97,8 

.99046 

9,2 

.31656 

205,0 

78  02  12.67 

.363 

.97849 

20,6 

.20630 

97,8 

.99056 

9,2 

.31451 

2O6,0 

78  05  38.93 

.364 

.97869 

20,5 

.20533 

97,9 

.99065 

9,1 

.31244 

207,0 

78  09  05.20 

1.365 

0.97890 

20,4 

0.20435 

97,9 

9.99074 

9,i 

9.31037 

2O8,O 

78    12  3L46 

.366 

.97910 

20,3 

.20337 

97,9 

.99083 

9,0 

.30828 

209,1 

78  15  57.73 

.367 

.97931 

20,2 

.20239 

97,9 

.00092 

9,0 

.30619 

210,1 

78  19  23.99 

.368 

•97951 

20,1 

.20141 

98,0 

.99101 

8,9 

.30408 

211,2 

78  22  50.25 

.369 

.97971 

2O,O 

.20043 

98,0 

.99110 

8,9 

.30106 

212,3 

78  26   16.52 

1.370 

0.97991 

19,9 

0.19945 

98,0 

9.99II9 

8,8 

9.29983 

213,4 

78  29  42.78 

.371 

.98011 

19,8 

.19847 

98,0 

.99127 

8,8 

.29769 

214,5 

78  33  09.05 

•  372 

.98031 

19,7 

•  19749 

08.0 

.99136 

8,7 

.29554 

215,6 

78  36  35-31 

•  373 

.98050 

19,7 

.19651 

98,1 

.99145 

8,7 

•29338 

216,7 

78  40  01.58 

•  374 

.98070 

19,6 

.  19553 

98,1 

.09154 

8,7 

.29121 

217,8 

78  43  27.84 

1.375 

0.98080 

19,5 

0.19455 

98,1 

9.99162 

8,6 

9.28903 

219,0 

78  46  54.ii 

.376 

.98109 

19,4 

.  19357 

08,  i 

.99171 

8,6 

.28683 

220,1 

78  50  20.37 

•  377 

.98128 

19,3 

.  19259 

98,1 

.99179 

8,5 

.28462 

221,3 

78  53  46.64 

.378 

.98147 

19,2 

.19160 

08,  t 

.99188 

8,5 

.  28240 

222,5 

78  57  12.90 

•  379 

.98166 

19,1 

.19062 

98,2 

.99196 

8,4 

.28017 

223,7 

79  00  39.17 

1.380 

0.98185 

19,0 

0.18964 

98,2 

9.99205 

8,4 

9.27793 

224,9 

79  04  05-43 

.381 

.98204 

18,9 

.18866 

98,2 

.99213' 

8,3 

.27568 

226,1 

79  07  31.70 

.382 

.08223 

18,8 

.18768 

98,2 

.99221 

8,3 

.27341 

227,3 

79  10  57.96 

.383 

.98242 

18,7 

.18669 

98,2 

.99230 

8,3 

.27113 

228,5 

79  14  24.23 

.384 

.98260 

18,6 

.18571 

98,3 

.99238 

8,2 

.26884 

229,8 

79  17  50.49 

1.385 

0.98279 

18,5 

0.18473 

98,3 

9.99246 

8,2 

9.26654 

231,1 

79  21  16.76 

.386 

.98297 

18,4 

.18375 

98,3 

.99254 

8,1 

.  26422 

232,3 

79  24  43-02 

.387 

.98316 

18,3 

.  18276 

98,3 

.99262 

8,1 

.26189 

233,6 

79  28  09.29 

.388 

•98334 

18,2 

.18178 

98,3 

.99270 

8,0 

•25955 

234,9 

79  31  35-55 

.389 

.98352 

18,1 

.18080 

98,4 

.99278 

8,0 

.25719 

236,3 

79  35  01.82 

1.390 

0.08370 

18,0 

o.  17981 

98,4 

9.99286 

7,9 

9.25482 

237,6 

79  38  28.08 

.391 

.98388 

17,9 

.17883 

98,4 

.99294 

7,9 

.25244 

238,9 

79  41  54-35 

•  392 

.98406 

17,8 

.17785 

98,4 

.99302 

7,8 

.25004 

240,3 

79  45  20.61 

•  393 

.98424 

17,7 

.17686 

98,4 

.99310 

7,8 

.24763 

241,7 

79  48  46.88 

.394 

.98441 

17,6 

.17588 

98,4 

.99318 

7,8 

.24521 

243,1 

79  52  13.14 

1.395 

0.98459 

17,5 

0.17489 

98,5 

9.99325 

7,7 

9.24277 

244,5 

79  55  39.40 

.396 

.98476 

17,4 

.  17391 

98,5 

•99333 

7,7 

.24032 

245,9 

79  59  05.67 

•  397 

.98494 

17,3 

.17292 

98,5 

.99341 

7,6 

.23785 

247,4 

80  02  31.93 

.398 

.08511 

17,2 

.17194 

98,5 

.99348 

7,6 

•23537 

248,8 

80  05  58.20 

•  399 

.98528 

I7,i 

.17095 

98,5 

•99356 

7,5 

.23288 

250,3 

80  09  24.46 

1.400 

0.98545 

I7,o 

0.16997 

98,5 

9.99363 

7,5 

9.23036 

251,8 

80  12  50.73 

u 

-isinhiu 

<«>  FO' 

cosh  iu 

«FO' 

.     sinh  iu 

c-Fo' 

log  cosh  iu 

-FO' 

u 

loo      j 

SMITHSONIAN  TABLES 


2IQ 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

-F«* 

log  sin  u 

«    Fo' 

log  cos  u 

«F0'               u 

1.400 

0.98545 

17,0 

0.16997 

98,5 

9.99363 

7,5 

9-23036 

251,8    80°  12  50"  73 

.401 

.98562 

16,9 

.  16898 

98,6 

.99371 

7,4 

.22784 

253,3     80  16  16.99 

.402 

.98579 

16,8 

.16800 

98,6 

.99378 

7,4 

.22530 

254,8    80  19  43.26 

.403 

.98596 

16,7 

.  16701 

98,6 

.99386 

7,4 

.22274 

256,4    80  23  09.52 

.404 

.98612 

16,6 

.16602 

98,6 

•99393 

7,3 

.22OI7 

258,0 

80  26  35-79 

1.405 

0.98629 

16,5 

0.16504 

98,6 

9.99400 

7,3 

9.21758 

259,5 

80  30  02.05 

.406 

.98645 

16,4 

.16405 

98,6 

.99408 

7,2 

.21498 

261,1 

80  33  28.32 

.407 

.98662 

16,3 

.16306 

98,7 

.99415 

7,2 

.21236 

262,8 

80  36  54.58 

.408 

.98678 

16,2 

.16208 

98,7 

.99422 

7,1 

.20972 

264,4 

80  40  20.85 

.  409 

.98694 

16,1 

.16109 

98,7 

.99429 

7,i 

.20707 

266,1 

80  43  47.ii 

1.410 

0.98710 

16,0. 

0.16010 

98,7 

9.99436 

7,o 

9.20440 

267,8 

80  47  13.38 

.411 

.98726 

15,9 

.15912 

98,7 

•99443 

7,o 

.20172 

269,5 

80  50  39.64 

.412 

.98742 

15,8 

.15813 

98,7 

.99450 

7,0 

.19901 

271,2 

80  54  05.91 

.413 

.98758 

15,7 

.15714 

98,8 

•99457 

6,9 

.19629 

272,9 

80  57  32.17 

.414 

.98773 

15,6 

.15615 

98,8 

.99464 

6,9 

•  19355 

274,7 

81  oo  58.44 

1.415 

0.98789 

15,5 

0.15517 

98,8 

9.99471 

6,8 

9.19080 

276,5 

81  04  24.70 

.416 

.98804 

15,4 

.15418 

98,8 

.99478 

6,8 

.18802 

278,3 

81  07  50.97 

.417 

.98820 

15,3 

.15319 

98,8 

.99484 

6,7 

.18523 

280,2 

81  ii  17.23 

.418 

.98835 

15,2 

.  15220 

58,8 

.99491 

6,7 

.  18242 

282,0 

81  14  43-50 

.419 

.98850 

i'5,i 

.15121 

58,9 

.99498 

6,6 

.17959 

283,9 

81  18  09.76 

1.4120 

0.98865 

i5,o 

0.15023 

98,9 

9-99504 

6,6 

9.17674 

285,8 

81  21  36.02 

.421 

.98880 

14,9 

.  14924 

98,9 

•995II 

6,6 

.17388 

287,8 

81  25  02.29 

.422 

.98895 

14,8 

.14825 

98,9 

.99517 

6,5 

.17009 

289,7 

81  28  28.55 

.423 

.98910 

14,7 

.  14726 

58,9 

.99524 

6,5 

.16808 

291,7 

81  31  54.82 

.424 

.98924 

14,6 

.  14627 

98,9 

•99530 

6,4 

.16515 

293,7 

81  35  21.08 

1.425 

0.98939 

14,5 

0.14528 

98,9 

9-99537 

6,4 

9.16221 

295,8 

81  38  47-35 

.426 

.98954 

14,4 

.14429 

99,0 

•99543 

6,3 

.15924 

297,8 

81  42  13.61 

.427 

.98968 

14,3 

.  14330 

99,0 

•99549 

6,3 

.  15625 

209,9 

81  45  39-88 

.428 

.98982 

14,2 

.  14231 

99,0 

.99556 

6,2 

.  15324 

302,1 

81  49  06.14 

.4129 

.98906 

14,1 

.  14132 

99,0 

.99562 

6,2 

.I5O2I 

304,2 

81  52  32.41 

1.430 

O.99OIO 

14,0 

o.  14033 

99,0 

9.99568 

6,2 

9.14716 

306,4 

81  55  58.67 

.431 

.99024 

13,9 

.13934 

99,0 

•99574 

6,1 

.14408 

308,6 

81  59  24.94 

.432 

.99038 

13,8 

.13835 

99,0 

.09580 

6,1 

.14098 

3io,9 

82  02  51.20 

•  433 

.00052 

13,7 

.  13736 

99,i 

.99586 

6,0 

.13786 

313,2 

82  06  17.47 

•434 

.99066 

13,6 

.  13637 

99J 

.99592 

6,0 

.13472 

315,5 

82  09  43-73 

1-435 

.99079 

13,5 

0.13538 

99,1 

9.99598 

5,9 

9.I3I55 

317,8 

82  13  10.00 

.436 

.99093 

13,4 

.  13439 

99,1 

.99604 

5,9 

.12836 

320,2 

82  16  36.26 

•  437 

.99106 

13,3 

.13340 

99,1 

.99610 

5,8 

.12515 

322,7 

82  20  02.53 

.438 

.99120 

13,2 

.  13241 

99,1 

.06616 

5,8 

.12191 

325J 

82  23  28.79 

•  439 

.99133 

I3,i 

.13142 

99,1 

.99622 

5,8 

.11865 

327,6 

82  26  55.06 

1.440 

0.99146 

I3,o 

0.13042 

99,1 

9.99627 

5,7 

9.II536 

330,1 

82  30  21.32 

.441 

.99159 

12,9 

.12943 

99,2 

.09633 

5,7 

.II2O4 

332,7 

82  33  47-59 

.442 

.99172 

12,8 

.12844 

99,2 

.9039 

5,6 

.10870 

335,3 

82  37  13.85 

•  443 

.09185 

12,7 

•  12745 

99,2 

.99644 

5,6 

.10534 

338,0 

82  40  40.12 

•  444 

.99197 

12,6 

.12646 

99,2 

.99650 

5,5 

.10194 

340,7 

82  44  06.38 

1.445 

0.99210 

12,5 

o.  12546 

99,2 

9.99655 

5,5 

9-09852 

343,4 

82  47  32.65 

.446 

.99222 

12,4 

.12447 

99,2 

.99661 

5,4 

.09507 

346,2 

82  50  58.91 

•447 

.99235 

12,3 

.12348 

99,2 

.9</>66 

5,4 

.0)160 

349,0 

82  54  25.17 

.448 

.99247 

12,2 

.12249 

99,2 

.99672 

5,4 

.oSSog 

351,9 

82  57  51-44 

.449 

.99259 

12,1 

.12150 

99,3 

.99677 

5,3 

.08456 

354,8 

83  01  17.70 

1-450 

0.99271 

12,1 

0.12050 

99,3 

9.09682 

5,3 

9.08100 

357,8 

83  04  43-97 

u 

-isinhiu 

«F,,' 

cosh  iu 

*»Fo' 

.0.'^ 

-Fo' 

log  cosh  iu 

»tt 

u 

SMITHSONIAN  TABLCS 


220 


Circular  Functions. 


I 

u 

sin  u 

-Fo' 

cos  u 

«Fo* 

loo  sin  u 

«  Fo' 

log  cos  u 

«FO' 

u 

1.450 

0.09271 

12,1 

o.  12050 

99,3 

9.99682 

5,3 

9.08100 

357,8 

83°04'43"97 

.451 

.99283 

12,0 

.11951 

99,3 

.99688 

5,2 

.0/740 

300,8 

83  08  10.23 

.452 

.99295 

11,9 

.11852 

99,3 

.99693 

5,2 

.07378 

363,9 

83  ii  36.50 

•  453 

.99307 

11,8 

.11752 

99,3 

.99608 

5,1 

.07013 

367,0 

83  15  02.76 

•454 

.99319 

n,7 

.11653 

99,3 

.99703 

5,1 

.06644 

370,i 

83  18  29.03 

1-455 

0.99330 

11,6 

O.I  1554 

99,3 

9.99708 

5,i 

9.06272 

373,4 

83    21    55.29 

.456 

•99342 

n,5 

.11454 

99,3 

•99713 

5,o 

.05897 

376,7 

83   25   21.56 

•  457 

.99353 

11,4 

.11355 

99,4 

.99718 

5,o 

.05519 

380,0 

83    28  47.82 

.458 

.99365 

n,3 

.11256 

99,4 

.99723 

4,9 

.05137 

383,4 

83   32    14.09 

•  459 

.99376 

11,2 

.11156 

99,4 

.99728 

4,9 

.04752 

386,8 

83  35  40.35 

1.460 

0.99387 

11,1 

o.i  1057 

99,4 

9-99733 

4,8 

9.04364 

390,4 

83  39  06.62 

.461 

.99398 

II,O 

.10958 

99,4 

•99738 

4,8 

.03971 

394,o 

83  42  32.88 

.462 

•99409 

10,9 

.10858 

99,4 

.99742 

4,7 

.03576 

397,6 

83  45  59.15 

.463 

.90420 

10,8 

.  10759 

99,4 

•99747 

4,7 

.03176 

401,3 

83  49  25.41 

.464 

.99430 

10,7 

.10659 

99,4 

.99752 

4,7 

.02773 

405,1 

83  52  51-68 

1.465 

0.99441 

10,6 

0.10560 

99,4 

9.99756 

4,6 

9.02366 

409,0 

83  56  17.94 

.466 

•99451 

10,5 

.10460 

99,5 

.99761 

4,6 

.01955 

412,9 

83  59  44-21 

.467 

.99462 

10,4 

.  10361 

99,5 

.99766 

4,5 

.01540 

416,9 

84  03  10.47 

.468 

•99472 

10,3 

.  10262 

99,5 

•99770 

4,5 

.OII2I 

421,0 

84  06  36.74 

.469 

.99482 

10,2 

.  10162 

99,5 

•99775 

4,4 

.00698 

4^5,2 

84  10  03.00 

1.470 

0.09492 

IO,I 

0.10063 

99,5 

9-99779 

4,4 

9.O027I 

429,4 

84  13  29.27 

.471 

.99502 

IO,O 

.09963 

99,5 

.99783 

4,3 

8.99839 

433,7 

84  16  55-53 

.472 

.99512 

9,9 

.09864 

99,5 

.99788 

4,3 

.99403 

438,2 

84  20  21.79 

•473 

.99522 

9,8 

.09764 

99,5 

.99792 

4,3 

.98963 

442,7 

84  23  48.06 

•474 

•99532 

9,7 

.09665 

99,5 

.99796 

4,2 

.98518 

447,3 

84  27  14.32 

1-475 

0.99542 

9,6 

0.09565 

99,5 

9.99800 

4,2 

8.98068 

452,0 

84  30  40-59 

.476 

•99551 

9,5 

.09465 

99,6 

.99805 

4,1 

.97614 

456,8 

84  34  06.85 

•477 

.99560 

9,4 

.09366 

99,6 

.90809 

4,1 

•97155 

461,7 

84  37  33-12 

•  478 

•99570 

9,3 

.09266 

99,6 

.99813 

4,0 

.96691 

466,7 

84  40  59.38 

•479 

•99579 

9,2 

.09167 

99,6 

•99817 

4,0 

.96222 

471,8 

84  44  25.65 

1.480 

0.99588 

9,1 

0.09067 

99,6 

9.99821 

4,0 

8.95747 

477,0 

84  47  5I.9I 

.481 

•99597 

9,0 

.08968 

99,6 

.99825 

3,9 

.95267 

482,3 

84  51  18.18 

.482 

.99606 

8,9 

.08868 

99,6 

.99829 

3,9 

.94782 

487,8 

84  54  44-44 

.483 

.99615 

8,8 

.08768 

99,6 

.99832 

3,8 

.94292 

493,4 

84  58  10.71 

.484 

.99624 

8,7 

.08669 

99,6 

.99836 

3,8 

.93796 

499,1 

85  oi  36.97 

1.485 

0.99632 

8,6 

0.08569 

99,6 

9.99840 

3,7 

8.93294 

504,9 

85  05  03.24 

.486 

.99641 

8,5 

.08469 

99,6 

.99844 

3,7 

.92786 

5io,9 

85  08  29.50 

.487 

.99649 

8,4 

.08370 

99,6 

.90847 

3,6 

.92272 

5i7,i 

85  ii  55-77 

.488 

.99657 

8,3 

.08270 

99,7 

.99851 

3,6 

.91751 

523,3 

85  15  22.03 

.489 

.99666 

8,2 

.08171 

99,7 

.99855 

3,6 

.91225 

529,8 

85  18  48.30 

1.490 

0.09674 

8,1 

0.08071 

99,7 

9.99858 

3,5 

8.90692 

536,3 

85  22    14.56 

.491 

.99682 

8,0 

.07971 

99,7 

.99862 

3,5 

.90152 

543,1 

85   25  40.83! 

.492 

.99690 

7,9 

.07871 

99,7 

.99865 

3,4 

.89606 

550,0 

85   29  07.09 

•  493 

.99698 

7,8 

.07772 

99,7 

.09868 

3,4 

.89052 

557,i 

85  32  33.36 

•  494 

.99705 

7,7 

.07672 

99,7 

.99872 

3,3 

.88491 

564,4 

85  35  59.62 

1.495 

0.99713 

7,6 

0.07572 

99,7 

9.99875 

3,3 

8.87923 

57i,9 

85  39  25.89 

.496 

.99720 

7,5 

•07473 

99,7 

.99878 

3,3 

.87348 

579,6 

85  42  52.15 

•  497 

.99728 

7,4 

.07373 

99,7 

.09882 

3,2 

.86764 

587,4 

85  46  18.41 

.498 

•99735 

7,3 

.07273 

99,7 

.99885 

3,2 

.86I73 

595,5 

85  49  44-68 

.499 

.99742 

7,2 

.07173 

99,7 

.99888 

3,i 

.85573 

603,9 

85  53  10.94 

I.5OO 

0-99749 

7,i 

0.07074 

99,7 

9.99891 

3,i 

8.84065 

612,4 

85  56  37.21 

u 

-isinhiu 

«F0' 

cosh  iu 

«F0' 

sinh  iu 

wF0' 

og  cosh  iii 

•  Fo' 

u 

tog 

SMITHSONIAN  TABLES 


221 


Circular  Functions. 


u 

sin  u 

«F0' 

cos  u 

w  Fo'  !  log  sin  u 

»  Fo' 

log  cos  u 

«FO' 

u 

1.500 

0.99749 

7,1 

0.07074 

99,7 

9.99891 

3,1 

8.84965 

612,4 

^5°  56  37-21 

.501 

•99757 

7,0 

.06974 

99,8 

.99894 

3,1 

.84348 

621,2 

86  oo  03.47 

.502 

.99763 

6,9 

.06874 

99,8 

.90897 

3,0 

.83722 

630,3 

86  03  29.74 

.503 

•99770 

6,8 

.06774 

99,8 

.99900 

2,9 

.83087 

639,6 

86  06  56.00 

.504 

•99777 

6,7 

.06675 

99,8 

.99903 

2,9 

.82443 

649,2 

86  10  22.27 

1.505 

0.99784 

6,6 

0.06575 

99,8 

9.99906 

2,9 

8.81789 

659,1 

86  13  48.53 

.506 

.99790 

6,5 

.06475 

99,8 

.99909 

•  2,8 

.81125 

669,3 

86  17  14.80 

.507 

•99797 

6,4 

.06375 

99,8 

.99912 

2,8 

.80450 

679,8 

86  20  41.06 

.508 

.99803 

6,3 

.06276 

99,8 

.99914 

2,7 

.79765 

690,7 

86  24  07.33 

.509 

.99809 

6,2 

.06176 

99,8 

.99917 

2,7 

.79069 

701,9 

86  27  33-59 

1.510 

0.99815 

6,1 

0.06076 

99,8 

9.99920 

2,6 

8.78361 

7i3,5 

86  30  59-86 

.511 

.99821 

6,0 

.05976 

99,8 

.99922 

2,6 

.77642 

725,4 

86  34  26.12 

.512 

.99827 

5,9 

.05876 

99,8 

.99925 

2,6 

.76910 

737,8 

86  37  52.39 

.513 

.99833 

5,8 

.05776 

99,8 

.99927 

2,5 

.76166 

750,6 

86  41  18.65 

.514 

.99839 

5,7 

"  .05677 

99,8 

.99930 

2,5 

.75409 

763,8 

86  44  44-92 

1.515 

0.09844 

5,6 

0.05577 

99,8 

9.99932 

2,4 

8.74638 

777,5 

86  48  11.  18 

.516 

.99850 

5,5 

.05477 

99,8 

•99935 

2,4 

.73853 

791,8 

86  51  37-45 

.517 

.99855 

5,4 

.05377 

99,9 

•99937 

2,3 

•73054 

806,5 

86  55  03.71 

.518 

.99861 

5,3 

•05277 

99,9 

•99939 

2,3 

.72240 

821,8 

86  58  29.98 

.519 

.99866 

5,2 

.05177 

99,9 

.99942 

2,3 

.71410 

837,7 

87  01  56.24 

1.520 

0.99871 

5,1 

0.05077 

99,9 

9-99944 

2,2 

8.70565 

854,2 

87  05  22.51 

.521 

.99876 

5,o 

.04978 

99,9 

.99946 

2,2 

.69702 

871,4 

87  08  48.77 

.522 

.99881 

4,9 

.04878 

99,9 

.90948 

2,1 

.68821 

889,3 

87  12  15.04 

.523 

.99886 

4,8 

.04778 

99,9 

.99950 

2,1 

.67923 

907,9 

87  15  41-30 

.524 

.99891 

4,7 

.04678 

99,9 

•99952 

2,0 

.67005 

927,4 

87  19  07.56 

1.525 

0.99895 

4,6 

0.04578 

99,9 

9-99954 

2,0 

8.66068 

947,7 

87  22  33.83 

.526 

.09900 

4,5 

.04478 

99,9 

.99956 

1,9 

.65110 

968,8 

87  26  00.09 

.527 

•99904 

4,4 

.04378 

99,9 

.95958 

i,9 

.64130 

99i,o 

87  29  26.36 

.528 

.99908 

4,3 

.04278 

99,9 

.90960 

i,9 

.63127 

1014,2 

87  32  52.62 

.529 

•99913 

4,2 

.04178 

99,9 

.99962 

1,8 

.62IOI 

1038,5 

87  36  18.89 

1.530 

0.99917 

4,1 

0.04079 

99,9 

9.99964 

1,8 

8.61050 

1064,0 

87  39  45-15 

.531 

.99921 

4,0 

.03979 

99,9 

.99966 

i,7 

•59973 

1090,7 

87  43  11-42 

.532 

•99925 

3,9 

.03879 

99,9 

.99967 

i,7 

.58868 

1  1  18,9 

87  46  37-68 

•533 

.99929 

3,8 

.03779 

99,9 

•99969 

1,6 

•57735 

1148,5 

87  50  03.95 

•  534 

.99932 

3,7 

.03679 

99,9 

•99971 

1,6 

•56571 

1179,7 

87  53  30.21 

1-535 

0.99936 

3,6 

0.03579 

99,9 

9.99972 

1,6 

8-55375 

1212,7 

87  56  56.48 

.536 

•99939 

3,5 

.03479 

99,9 

•99974 

i,5 

.54145 

1247,6 

88  oo  22.74 

•  537 

•99943 

3,4 

.03379 

99,9 

.99975- 

i,5 

.52879 

1284,5 

88  03  49.01 

.538 

.99946 

3,3 

.03279 

99,9 

•99977 

i,4 

.51575 

1323,7 

88  07  15.27 

•  539 

•99949 

3,2 

.03179 

99,9 

.99978 

1,4 

.50230 

1365,4 

88  10  41.54 

1.540 

0.99953 

3,1 

0.03079 

IOO,O 

9.99979 

i,3 

8.48843 

1409,8 

88  14  07.80 

•  541 

.99956 

3,0 

.02979 

1  00,0 

.99981 

i,3 

.47410 

1457,1 

88  17  34-07 

.542 

.99959 

2,9 

.02879 

100,0 

.99982 

i,3 

.45928 

1507,7 

88  21  00.33 

•  543 

.99961 

2,8 

.02779 

100,0 

•99983 

1,2 

.44393 

1562,0 

88  24  26.60 

•  544 

.99964 

2,7 

.02679 

100,0 

•99984 

1,2 

.42802 

1620,3 

88  27  52.86! 

1.545 

0.09967 

2,6 

0.02579 

100,0 

9.09986 

i,i 

8.41151 

1683,2 

88  31  I9.I3 

.546 

.99969 

2,5 

.02479 

100,0 

.99987 

1,1 

•39434 

I75i,i 

88  34  45-39 

•  547 

.99972 

2,4 

.02379 

100,0 

.<//>S8 

1,0 

.37647 

1824,7 

88  38  11.66 

.548 

•99974 

2,3 

.02279 

100,0 

.99089 

1,0 

.35783 

1904,8 

88  41  37-92 

..549 

.99976 

2,2 

.02179 

100,0 

.99990 

0,9 

.33835 

1992,2 

88  45  04.18 

1-550 

0.99978 

2,1 

0.02079 

100,0 

9.99991 

o,9 

8.31796 

2088,0 

88  48  30.45 

u 

-isinhiu 

«Fo' 

cosh  iu 

-FO' 

|0  «inh  iu 

«F0' 

ogcoshiu 

•  Fo' 

u 

100  , 

SMITHSONIAN  TABLES 


222 


Circular  Functions. 


u 

sin  u 

«F0' 

COS  U 

«FO' 

log  sin  u 

wF0' 

log  cos  u 

wF0' 

U 

o       /        // 

1.550 

0.99978 

2,1 

+0.02079 

100,0 

9.99991 

0,9 

8.31796 

2088,0 

88  48  30.45 

.551 

.99980 

2,O 

.01980 

.99991 

0,9 

.29656 

2193,5 

88  51  56.71 

.552 

.99982 

1,9 

.01880 

.99992 

0,8 

.27405 

2310,3 

88  55  22.98 

•  553 

.99984 

1,8 

.01780 

•99993 

0,8 

•25031 

2440,1 

88  58  49-24 

•  554 

.99986 

i,7 

.01680 

.99994 

o,7 

.22519 

2585,4 

89  02   15.51 

1-555 

0.99988 

1,6 

+0.01580 

100,0 

9.99995 

o,7 

8.19854 

2749,1 

89  05  4L77 

•  556 

.99989 

i,5 

.01480 

•  99995 

0,6 

.17014 

2934,9 

89  09  08.04 

•  557 

.99990 

1,4 

.01380 

.99996 

0,6 

.  13975 

3H7,7 

89    12   34.30 

.558 

.99992 

1,3 

.01280 

.99996 

0,6 

.  10707 

3393,7 

89  16  00.57 

.559 

•99993 

1,2 

.01180 

.99997 

o,5 

.07174 

368i,4 

89  19  26.83 

1.560 

0.99994 

1,1 

+0.01080 

100,0 

9-99997 

o,5 

8.03327 

4022,5 

89  22   53.10 

.561 

.99995 

1,0 

.00080 

.99998 

0,4 

7.99106 

4433,1 

89  26    19.36 

.562 

.90996 

0,9 

.00880 

.99098 

0,4 

•94430 

4937,1 

89  29  45.63 

.563 

.99997 

0,8 

.00780 

•99999 

o,3 

.89189 

5570,4 

89  33  11-89 

.564 

.99998 

o,7 

.00680 

•99999 

0,3 

.83227 

6390,0 

89  36  38.16 

1.565 

0.90998 

0,6 

+0.00580 

100,0 

9.99999 

o,3 

7.76315 

7492,5 

89  40  04.42 

.566 

.99999 

o,5 

.00480 

o.ooooo 

0,2 

.68091 

9054,7 

89  43  30.69 

.567 

.99999 

0,4 

.00380 

.00000 

0,2 

.57936 

11439,8 

89  46  56.95 

.568 

I.OOOOO 

o,3 

.00280 

.00000 

0,1 

.44659 

15530,9 

89  50  23.22 

.569 

I.  00000 

0,2 

.00180 

.00000 

0,1 

.25438 

24176,8 

89  53  49.48 

1.570 

I.OOOOO 

0,1 

+0.00080 

100,0 

0.00000 

0,0 

6.90109 

54537,4 

89  57  15-75 

•  571  . 

.00000 

0,0 

—  .00020 

.00000 

0,0 

6.3089471 

213228,5 

90  oo  42.01 

.572 

.00000 

0,1 

.00120 

.00000 

0,1 

7.08051 

36080,7 

oo  04  08.28 

•  573 

.00000 

0,2 

.00220 

.00000 

0,1 

.34315 

19707,7 

90  07  34.54 

•  574 

0.99999 

0,3 

.00320 

.00000 

0,1 

.50565 

13556,1 

90  II  00.81 

1.575 

0.99999 

0,4 

—  0.00420 

100,0 

0.00000 

0,2 

7.6236371 

10331,2 

90  14  27.07 

.576 

.99999 

o,5 

.00520 

9-99999 

0,2 

.71631 

8345,8 

90  17  53-33 

.577 

.99998 

0,6 

.00620 

•99999 

0,3 

.79265 

7000,5 

90  21  19.60 

.578 

.99997 

o,7 

.00720 

•99999 

o,3 

.85755 

6028,6 

90  24  45-86 

•  579 

•99997 

0,8 

.00820 

•99999 

0,4 

.91400 

5293,8 

90  28  12.13 

1.580 

0.99996 

0,9 

—0.00920 

100,0 

9.99998 

0,4 

7.96~396n 

47i8,6 

90  31  38.39 

.581 

•99995 

1,0 

.01020 

•99998 

0,4 

8.00875 

4256,1 

90  35  04.66 

.582 

.99994 

1,1 

.OII2O 

.99997 

0,5 

•04935 

3876,2 

90  38  30.92 

.583 

-99993 

1,2 

.01220 

-99997 

o,5 

.08648 

3558,5 

oo  41  57.19 

.584 

.99991 

i,3 

.01320 

.99996 

0,6 

.12068 

3289,0 

90  45  23.45 

1.585 

0.09990 

1,4 

—  0.01420 

100,0 

9.90996 

0,6 

8.15239" 

3057,4 

oo  48  49.72 

.586 

.99988 

i,5 

.01520 

-99995 

o,7 

•  18193 

2856,3 

90  52  15-98 

.587 

.99987 

1,6 

.01620 

-99994 

o,7 

.20959 

2680,0 

go  55  42.25 

.588 

.99985 

i,7 

.01720 

•99994 

0,7 

.23560 

2524,2 

90  59  08.51 

.589 

.99983 

1,8 

.01820 

•99993 

0,8 

.26014 

2385,5 

91  02  34.78 

1.590 

0.99982 

i,9 

—0.01920 

100,0 

9-99992 

0,8 

8.28336* 

2261,2 

91  06  01.04 

.591 

.99980 

2,0 

.02020 

.99991 

0,9 

.30540 

2149,3 

91  09  27.31 

.592 

.99978 

2,1 

.02120 

.99990 

0,9 

.32638 

2047,9 

91  12  53-57 

.593 

.99975 

2,2 

.02220 

.99989 

1,0 

.34639 

1955,6 

91  16  19.84 

•  594 

•99973 

2,3 

.02320 

.99988 

1,0 

•36552 

1871,3 

91  19  46.10 

1.595 

0.09971 

2,4 

—  0.02420 

100,0 

9.99987 

i 

8.383&4n 

1794,0 

91  23  12.37 

.596 

.99968 

2,5 

.02520 

-99986 

i 

.40142 

1722,8 

91  26  38.63 

•  597 

.99966 

2,6 

.02620 

.99985 

i 

-41831 

1657,0 

91  30  04-90 

.598 

.99963 

2,7 

.02720 

-99984 

2 

•43457 

I596,i 

91  33  31-16 

.599 

.99960 

2,8 

.02820 

.99983 

2 

.45025 

1539,4 

91  36  57-43 

1.  600 

0.99957 

2,9 

—  0.02920 

100,0 

9.99981 

1,3 

8.46538, 

1486,7 

91  40  23-69 

—  i  c:nu  :, 

wFr/ 

cosh  ill 

wFo' 

.     sinh  iu 

<ii  P  ' 

. 

w  F,)' 

ii 

I  sinn  11 

w  •  0 

log     . 

w  ro 

loo  cosh  iu 

SMITHSONIAN  TABLES 


223 


TABLE  IV 


THE  ASCENDING  AND  DESCENDING  EXPONENTIAL  AND 

Log)0(eu) 


NOTE. — In  Table  IV,  for  u  greater  than  2.302,  the  tabulated  values  of 
the  ascending  exponential  may  sometimes  be  erroneous  to  one  unit  in  the 
last  place. 

225 


The  Exponential. 


u 

IOQio(eu) 

eu 

e~u 

u 

loj>io(en) 

en 

e- 

o.ooo 
.001 
.002 

.003 

.004 

0.000  0000 
.000  4343 
.000  8686 
.001  3029 

.001  7372 

I.  000  000 
.001  OOI 
.OO2  OO2 

.003  005 
.004  008 

1.  000  0000 

0.099  0005 

.998  0020 

.997  0045 
.996  0080 

0.050 
.051 
.052 
.053 
.054 

O.O2I  7147 
.022  I4OO 
.022  5833 
.023  0176 
.023  4519 

I.05I  271 
.052  323 
.053  376 
.054  430 
•055  485 

0.951  2294 
•950  2787 
•949  3^*9 
.948  3800 
•947  4321 

0.005 
.006 
.007 
.008 
.009 

0.002  1715 
.OO2  6058 
.OO3  O40I 
.003  4744 
.003  9087 

1.005  013 
.006  018 
.007  025 
.008  032 
.009  041 

0.095  0125 
.094  0180 
.993  0244 
.992  0319 
.991  0404 

0.055 
.056 
.057 
.058 
.059 

O.O23  8862 
.024  3205 
.024  7548 
.025  1891 
.025  6234 

1.056  541 
.057  598 
.058  656 
•059  715 
.060  775 

0.946  4851 

•945  5391 
.944  5941 

.943  6499 
.942  7068 

O.OIO 
.Oil 

.012 

.013 

.014 

0.004  3429 
.004  7772 
.005  2115 
.005  6458 
.006  0801 

i.  oio  050 
.on  06  1 

.012  O72 

.013  085 
.014  098 

0.990  0498 
.989  0603 

.988  0717 
.087  0841 
•986  0975 

0.060 
.061 
.062 
•063 
.064 

0.026  0577 
.026  492O 
.026  9263 
.027  3606 
.027  7948 

1.061  837 
.062  899 
.063  062 
.065  027 
.066  092 

0.041  7645 
.940  8232 
.939  8829 
.938  9435 
.938  0050 

0.015 
.016 

.017 
.018 
.019 

0.006  5144 
.006  9487 
.007  3830 
.007  8173 
.008  2516 

1.015  113 
.016  129 

.017  145 

.018  163 
.019  182 

0.085  1119 
.984  1273 
.983  1437 
.982  1610 
.981  1794 

0.065 
.066 
.067 
.068 
.069 

O.O28  2291 
.028  6634 

.029  0977 
.029  5320 
.029  9663 

1.067  159 
.068  227 
.069  295 
.070  365 
.071  436 

0.937  0675 
.936  1309 
.935  1952 
.934  2605 
•933  3267 

O.O20 
.021 
.022 

.023 

.024 

0.008  6859 
.009  I2O2 

.009  5545 
.009  9888 
.010  4231 

1.020  201 
.021  222 
.022  244 
.023  267 
.024  200 

0.080  1987 
.979  2190 

.978  2402 
.977  2625 
.976  2857 

0.070 
.071 
.072 
.073 
.074 

0.030  4006 
.030  8349 
.031  2692 
.031  7035 
.032  1378 

1.072  508 
.073  58i 
.074  655 
.075  73i 
.076  807 

0.932  3938 
.931  4619 
•930  5309 
.929  6008 
.928  6717 

0.025 
.026 

.027 

.028 
.029 

o.oio  8574 
.011  2917 
.011  7260 
.012  1602 
.012  5945 

1.025  315 
.026  341 
.027  368 
.028  306 
.029  425 

0.975  3099 
•974  3351 
.973  3612 
.972  3884 
.971  4165 

0.075 
.076 
.077 
.078 
.079 

0.032  5721 
.033  0064 
.033  4407 
•033  8750 
.034  3093 

1.077  884 
.078  063 
.080  042 
.081  123 
.082  204 

0.927  7435 
.926  8162 
.925  8899 
.924  9644 
.924  0399 

0.030 
.031 
.032 

.033 
.034 

0.013  0288 
.013  4631 
.013  8974 
.014  3317 
.014  7660 

1.030  455 
.031  486 
.032  518 
.033  551 
•034  585 

0.970  4455 
.969  4756 
.968  5066 
.067  5386 
.966  5715 

0.080 

.081 
.082 
.083 
.084 

0.034  7436 
.035  1779 
.035  6121 
.036  0464 
.036  4807 

1.083  287 
.084  371 
.085  456 
.086  542 
.087  629 

0.923  1163 
.922  1937 
.921  2720 
.920  3511 
.919  4313 

0.035 
.036 
.037 
.038 
.039 

0.015  2003 
.015  6346 
.016  0689 
.016  5032 
.016  9375 

1.035  620 
.036  656 
.037  693 
.038  731 
.039  770 

0.065  6054 
.064  6403 
.063  6761 
.962  7129 
.961  7507 

0.085 
.086 
.087 
.088 
.089 

0.036  9150 
.037  3493 
•037  7836 
.038  2179 
.038  6522 

i.  088  717 
.089  806 
.000  897 

.091  988 

.093  081 

0.918  5123 
.917  5942 
.916  6771 
.915  7609 
.914  8456 

0.040 
.041 
.042 
.043 
.044 

0.017  3718 
.017  8061 
.018  2404 
.018  6747 
.019  1090 

1.040  811 
.041  852 
.042  894 
•043  938 
.044  982 

0.060  7894 
.959  8291 
.9588698 
.957  9114 
.956  9540 

0.000 

.091 
.092 

.093 
.094 

0.039  0865 
.039  5208 
.039  9551 
.040  3894 
.040  8237 

1.094  174 
.095  269 
.096  365 
.097  462 
.098  560 

0.913  9312 
.913  0177 
.912  1051 

.911  1935 
.910  2828 

0.045 
.046 

•  047 
.048 
.049 

0.019  5433 
.019  9775 
.020  4118 
.020  8461 
.021  2804 

1.046  028 
.047  074 

.048  122 
.049  171 
.O5O  22O 

0.955  9975 
.955  0420 
.954  0874 
.953  1338 
.952  1811 

0.095 
.006 
.097 
.098 
.099 

0.041  2580 
.041  6923 
.042  1266 
.042  5609 
.042  9952 

1.009  659 
.  loo  759 
.101  860 
.102  063 
.104  066 

0.909  3729 
.908  4640 
.007  5500 
.906  6489 
.905  7427 

0.050 

0.021  7147 

I.05I  271 

0.951  2294 

O.IOO 

0.043  4294 

i.  105  171 

0.904  8374 

log.V; 

lofli,Xeu) 

eu 

a'" 

logt!(eu) 

,.„*-, 

eu 

e-° 

SMITHSONIAN  TABLES 


The  Exponential. 


u 

logio(eu) 

eu 

.- 

u 

logio(eu) 

eu 

.- 

O.IOO 

0.043  4294 

1.105  171 

0.904  8374 

O.I5O 

0.065  1442 

1.161  834 

0.860  7080 

.101 

.043  8637 

.106  277 

.903  9330 

.151 

.065  5785 

.162  997 

.859  8477 

.102 

.044  2980 

.107  383 

.903  0296 

.152 

.066  0128 

.164  160 

.858  9883 

.103 

.044  7323 

.  108  491 

.902  1270 

.153 

.066  4471 

.165  325 

.858  1297 

.IO4 

.045  1666 

.109  600 

.901  2253 

.154 

.0668814 

.166  491 

.857  2720 

0.105 

0.045  6009 

i.  no  711 

0.900  3245 

0.155 

0.067  3156 

1.167  658 

0.856  4152 

.105 

.046  0352 

.in  822 

.899  4246 

.156 

.067  7499 

.168  826 

.855  5592 

.107 

.046  4695 

.112  934 

.898  5257 

.157 

.068  1842 

.169  996 

.854  7041 

.108 

.046  9038 

.114  048 

.897  6276 

.158 

.068  6185 

.171  166 

.853  8498 

.109 

.047  338i 

.115  162 

.896  7304 

.159 

.069  0528 

.172  338 

.852  9964 

O.IIO 

0.047  7724 

1.116  278 

0.895  8341 

0.160 

0.069  4871 

i.  173  5ii 

0.852  1438 

.III 

.048  2067 

.117  395 

.894  9387 

.161 

.069  9214 

.174  685 

.851  2921 

.112 

.048  6410 

.118  513 

.894  0443 

.162 

.070  3557 

.175  860 

.850  4412 

.113 

•049  0753 

.119  632 

.893  1507 

.163 

.070  7900 

'.177  037 

.849  5912 

.114 

.049  5096 

.120  752 

.892  2580 

.164 

.071  2243 

.178  214 

.848  7420 

1  O.H5 

0.049  9439 

i.  121  873 

0.891  3661 

0.165 

0.071  6586 

1.  179  393 

0.847  8937 

.116 

.050  3782 

.122  996 

.890  4752 

.166 

.072  0929 

.180  573 

.847  0462 

.117 

.050  8125 

.124  119 

.889  5852 

.167 

.072  5272 

.181  754 

.846  1996 

.118 

.051  2467 

.125  244 

.8886961 

.168 

.072  9615 

.182  937 

.845  3538 

.119 

.051  6810 

.126  370 

.887  8078 

.169 

.073  3958 

.184  120 

.844  5089 

0.120 

0.052  1153 

1.127  497 

0.886  9204 

0.170 

0.073  8301 

1.185  305 

0.843  6648 

.121 

.052  5496 

.128  625 

.886  0340 

.171 

.074  2644' 

.186  491 

.842  8216 

.122 

.052  9839 

.129  754 

.885  1484 

.172 

.074  6987 

.187  678 

.841  9792 

.123 

.053  4182 

.130  884 

.884  2637 

.173 

.075  1329 

.188866 

.841  1376 

.124 

.053  8525 

.132  016 

.883  3798 

.174 

.075  5672 

.190  056 

.840  2969 

0.125 

0.054  2868 

I.I33  148 

0.882  4969 

0.175 

0.076  0015 

1.191  246 

0.839  4570 

.126 

.054  72ii 

.134  282 

.881  6148 

.176 

.076  4358 

.192  438 

.838  6180 

.127 

•055  1554 

.135  417 

.880  7337 

.177 

.076  8701 

.193  631 

.837  7798 

.128 

.055  5897 

.136  553 

.879  8534 

.178 

.077  3044 

.  194  825 

.836  9424 

.129 

.056  0240 

.137  690 

.878  9740 

.179 

.077  7387 

.196  O2I 

.836  1059 

0.130 

0.056  4583 

1.138  828 

0.878  0954 

0.180 

0.078  1730 

i.  197  217 

0.835  2702 

.131 

.056  8926 

.139968 

.877  2178 

.181 

.078  6073 

.198  415 

.834  4354 

.132 

.057  3269 

.141  108 

.876  3410 

.182 

.079  0416 

.  199  6l4 

.833  6013 

•133 

.057  7612 

.142  250 

.875  4651 

.183 

.079  4759 

.2OO  8l4 

.832  7682 

.1.34 

.058  1955 

.143  393 

.874  5901 

.184 

.079  9102 

.202  016 

.831  9358 

0.135 

0.058  6298 

1.144  537 

0.873  7159 

0.185 

0.080  3445 

1.203  218 

0.831  1043 

.136 

.059  0640 

.145  682 

.872  8426 

.186 

.080  7788 

.204  422 

.830  2736 

.137 

.059  4983 

.  146  828 

.871  9702 

.187 

.081  2131 

.205  627 

.829  4437 

.138 

.059  9326 

.  147  976 

.871  0987 

.188 

.081  6474 

.206  834 

.828  6147 

.139 

.060  3669 

.149  124 

.870  2280 

.189 

.082  0817 

.208  041 

.827  7865 

0.140 

0.060  8012 

i  .  150  274 

0.869  3582 

0.190 

0.082  5160 

1.209  250 

0.826  9591 

.141 

.061  2355 

.151  425 

.868  4893 

.191 

.082  9502 

.210  459 

.826  1326 

.142 

.061  6698 

.152  577 

.867  6213 

.192 

.083  3845 

.211  671 

.825  3069 

.143 

.062  1041 

.153  730 

.866  7541 

.193 

.083  8188 

.212  883 

.824  4820 

.144 

.062  5384 

.154884 

.865  8877 

.194 

.084  2531 

.214  O06 

.823  6579 

0.145 

0.062  9727 

1.156  040 

0.865  0223 

0.195 

0.084  6874 

I.  215  311 

0.822  8347 

.146 

.063  4070 

.157  196 

.864  1577 

.196 

.085  1217 

.216  527 

.822  OI22 

.147 

.063  8413 

.158  354 

.863  2940 

.197 

.085  5560 

.217  744 

.821  1905 

.148 

.064  2756 

.159  513 

.862  4311 

.198 

.085  9903 

.218  962 

.820  3699 

.149 

.064  7099 

.160  673 

.861  5691 

.199 

.086  4246 

.220  182 

.819  5499 

0.150 

0.065  1442 

1.161  834 

o.86b  7080 

0.200 

0.086  8589 

I.  22  I  403 

0.818  7308 

lofle(eu) 

logio(eu) 

eu 

e~u 

loge(eu) 

logio(eu) 

e" 

.- 

WITHSONIAN  TABLES 


227 


The  Exponential. 


u 

looio(eu) 

eu 

e- 

u 

logio(en) 

eu 

e~u 

O.20O 

0.086  8589 

I.  221  403 

0.818  7308 

0.250 

0.108  5736' 

1.284  025 

0.778  8008 

.201 

.087  2932 

.222  625 

.817  9124 

.251 

.109  0079 

.285  310 

.778  0224 

.202 

.087  7275 

.223  848 

.817  0949 

.252 

.  roo  4422 

.286  596 

.777  2447 

.203 

.088  1618 

.225  072 

.816  2782 

.253 

.  109  8765 

.287  883 

.776  4679 

.204 

.088  5961 

.226  298 

.815  4624 

.254 

.no  3108 

.289  172 

•775  6918 

O.2O5 

0.089  0304 

1.227  525 

0.814  6473 

0.255 

o.i  10  7451 

I.  2OO  462 

0.774  9165 

.206 

.089  4647 

.228  753 

.813  8331 

.256 

.III  1794 

.291  753 

.774  1420 

.207 

.089  8990 

.229  983 

.813  0196 

•  257 

.III  6137 

.293  045 

•773  3682 

.208 

.000  3333 

.231  213 

.812  2070 

.258 

.112  0480 

.294  339 

.772  5952- 

.209 

.090  7675 

.232  445 

.811  3952 

.259 

.112  4823 

.295  634 

.771  8230 

O.2IO 

0.091  2018 

1.233  678 

0.810  5842 

0.260 

O.II2  9166 

1.296  930 

0.771  0516 

.211 

.091  6361 

.234  912 

.809  7741 

.261 

•113  3509 

.298  228 

.770  2809 

.212 

.092  0704 

.236  148 

.8089647 

.262 

.113  7852 

.299  527 

.769  5110 

.213 

.092  5047 

•237  385 

.808  1561 

.263 

.  114  2194 

.300  827 

.768  7419 

.214 

.092  9390 

.238-623 

.807  3484 

.264 

.114  6537 

.302  128 

.767  9735 

0.215 

0.093  3733 

1.239  862 

0.806  5414 

0.265 

0.115  0880 

1-303  431 

0.767  2059 

.216 

.093  8076 

.241  IO2 

.805  7353 

.266 

.115  5-223 

.304  735 

.766  4391 

.217 

.094  2419 

.242  344 

.804  9300 

.267 

.115  9566 

.306  040 

.765  6731 

.218 

.004  6762 

.243  587 

.804  1254 

.268 

.116  3909 

.307  347 

.764  9078 

.219 

.095  1  105 

.244  831 

.803  3217 

.269 

.116  8252 

.308  655 

.764  1433 

O.22O 

0.095  5448 

1.246  077 

0.802  5188 

0.270 

0.117  2595 

1.309  964 

0.763  3795 

.221 

.095  9791 

.247  323 

.801  7167 

.271 

.117  6938 

•311  275 

.762  6165 

.222 

.006  4134 

.248  571 

.800  9154 

.272 

.118  1281 

.312  587 

.761  8543 

.223 

.006  8477 

.249  821 

.800  1148 

.273 

.118  5624 

.313  900 

.761  0528 

.224 

.097  2820 

.251  071 

•799  3i5i 

.274 

.118  9967 

•315  215 

.760  3321 

0.225 

0.097  7163 

1.252  323 

0.798  5162 

0.275 

0.119  4310 

1.316  531 

0.759  5721 

.226 

.098  1506 

.253  576 

.797  7181 

.276 

.119  8653 

.317  848 

.758  8129 

.227 

.098  5848 

.254  830 

.796  9208 

.277 

.120  2996 

.319  166 

.758  0545 

.228 

.009  0191 

.256  085 

.796  1243 

.278 

.120  7339 

.320  486 

.757  2968 

.229 

.099  4534 

.257  342 

.795  5285 

.279 

.121  1682 

.321  807 

.756  5399 

0.230 

0.099  8877 

1.258  600 

0.794  '5336 

0.280 

O.I2I  6O25 

1.323  130 

0.755  7837 

.231 

.100  3220 

.259  859 

•793  7395 

.281 

.122  0367 

.324  454 

•755  0283 

.232 

.100  7563 

.26l  I2O 

.792  9461 

.282 

.122  47IO 

.325  779 

•754  2737 

•233 

.101  1006 

.262  381 

.792  1536 

.283 

.  122  0053 

.327  105 

.753  5198 

•234 

.101  6249 

.263  644 

.791  3618 

.284 

.123  3396 

.328  433 

.752  7666 

0.235 

O.IO2  O592 

1.264  909 

0.790  57o8 

0.285 

0.123  7739 

1.329  762 

0.752  0143 

.236 

.  102  4935 

.266  174 

.789  7807 

.286 

.124  2O82 

•331  092 

.751  2626 

•237 

.102  9278 

.267  441 

.788  9913 

.287 

.  t24  6425 

•332  424 

•  750  5H7 

.238 

.103  3621 

.268  709 

.788  2027 

.288 

.125  0768 

•333  757 

.749  7616 

.239 

.103  7964 

•269  979 

.787  4H9 

.289 

.125  5III 

•335  092 

.749  0122 

0.240 

0.104  2307 

1.271  249 

0.786  6279 

0.290 

0.125  9454 

1.336427 

0.748  2636 

.241 

.104  6650 

.272  521 

.785  8416 

.291 

.126  3797 

.337  765 

.747  5'i57 

.242 

.105  0093 

•273  794 

.785  0562 

.292 

.126  8140 

.339  103 

.746  7685 

•243 

•105  5336 

.275  069 

.784  2715 

.293 

.127  2483 

•340  443 

.746  0221 

.244 

.  105  9679 

.276  344 

.783  4876 

.294 

.127  6826 

.341  784 

.745  2765 

0.245 

0.106  4021 

1.277  621 

0.782  7045 

0.295 

0.128  1169 

1.343  126 

0.744  53i6 

.246 

.  106  8364 

.278  900 

.781  9222 

.296 

.128  5512 

.344  470 

•743  7874 

.247 

.107  2707 

.280  179 

.781  1407 

.297 

.1289855 

•345  815 

.743  0440 

.248 

.107  7050 

.281  460 

.780  3599 

.298 

.  129  4198 

•347  162 

.742  3013 

.249 

.108  1393 

.282  742 

.779  58oo 

.299 

.1298541 

.348  510 

•741  5594 

0.250 

0.108  5736 

1.284  025 

0.778  8008 

0.300 

0.130  2883 

1.349  859 

0.740  8182 

looe(eu) 

Iog10(eu) 

eu 

a- 

lofle(eu) 

log,o(eu) 

eu 

6-" 

SMITHSONIAN  TABLES 


228 


The  Exponential. 


u 

logio(eu) 

eu 

e~u 

u 

looio(eu) 

eu 

e~u 

0.300 

0.130  2883 

1.349  859 

0.740  8182 

0.350 

0.152  0031 

1.419  068 

0.704  6881 

.301 

.130  7226 

•351  209 

.740  0778 

•  351 

.  152  4374 

.420  487 

.703  9838 

.302 

.131  1569 

.352  56i 

.739  338i 

•352 

.152  8717 

.421  909 

.703  2801 

.303 

.131  5912 

•353  914 

.738  5991 

•  353 

.153  3o6o 

.423  331 

.702  5772 

.304 

.132  0255 

•355  269 

.7378609 

•  354 

.153  7402 

.424  755 

.701  8750 

0.305 

0.132  4598 

1.356  625 

0.737  1234 

0.355 

0.154  1745 

1.426  181 

0.701  1734 

.306 

.  132  8941 

•357  982 

.736  3866 

.356 

.154  6088 

.427  608 

.700  4726 

.307 

•133  3284 

•359  341 

•735  6506 

.357 

.155  O43'i 

.429  036 

.699  7725 

.308 

.133  7627 

.360  701 

.734  9153 

.358 

.155  4774 

.430  466 

.699  0731 

.309 

.134  1970 

.362  062 

.734  1808 

.359 

•  155  9H7 

.431  897 

.6983744 

0.310 

0.134  6313 

1.363  425 

0.733  4470 

0.360 

0.156  3460 

1.433  329 

0.697  6763 

.311 

.135  0656 

.364  789 

•732  7139 

.361 

.  156  7803 

•434  763 

.696  9790 

.312 

.135  4999 

.366  155 

.731  98i5 

.362 

.157  2146 

.436  199 

.696  2824 

.313 

•135  9342 

.367  522 

.731  2499 

.363 

.  157  6489 

.437  636 

.695  5864 

•314 

.136  3685 

.368890 

•730  5190 

•364 

.  158  0832 

.439  074 

.694  8912 

0.315 

0.136  8028 

1.370  259 

0.729  7889 

0.365 

0.158  5175 

1.440  514 

0.694  1967 

.316 

.137  2371 

.371  630 

.729  0595 

.366 

.158  95i8 

•441  955 

.693  5028 

.317 

.137  6714 

•373  003 

.728  3308 

.367 

.  159  3861 

•443  398 

.692  8096 

.318 

.138  1056 

•374  376 

.727  6028 

.368 

.  159  8204 

.444  843 

.692  1172 

.319 

.138  5399 

•375  751 

.726  8755 

.369 

.  160  2547 

.446  288 

.691  4254 

0.320 

0.138  9742 

1.377  128 

0.726  1490 

0.370 

0.160  6890 

1.447  735 

0.690  7343 

.321 

.  139  4085 

.378  506 

.725  4233 

.371 

.161  1233, 

•449  183 

.690  0439 

.322 

.  139  8428 

•379  885 

.724  6982 

•  372 

.161  5575 

•450  633 

.689  3542 

.323 

.  140  2771 

.381  265 

.723  9739 

•373 

.161  9918 

.452  084 

.688  6652 

.324 

.140  7H4 

.382  647 

.723  ^502 

•  374 

.162  4261 

•453  537 

.687  9769 

0.325 

0.141  1457 

1.384  031 

0.722  5274 

0.375 

0.162  8604 

1.454  991 

0.687  2893 

.326 

.141  5800 

.385  415 

.721  8052 

.376 

.163  2947 

.456  447 

.6866023 

.327 

.  142  0143 

.386  801 

.721  0837 

•  377 

.163  7290 

.457  904 

.685  9161 

.328 

.142  4486 

.388  189 

.720  3630 

.378 

.164  1633 

.459  363 

.685  2305 

.329 

.142  8829 

.389  578 

.719  6430 

.379 

.  164  5976 

.460  823 

.684  5456 

0.330 

0.143  3172 

1.390  968 

0.718  9237 

0.380 

0.165  0319 

1.462  285 

0.683  8614 

.331 

.143  7515 

.392  360 

.718  2052 

.381 

.165  4662 

.463  748 

.683  1779 

.332 

.144  1858 

.393  753 

.717  4873 

.382 

.  165  9005 

.465  212 

.682  4951 

•  333 

.144  6201 

•395  147 

.716  7702 

.383' 

.166  3348 

.466  678 

.681  8129 

•  334 

.145  0544 

.396  543 

.716  0538 

.384 

.166  7691 

.468  145 

.681  1314 

0.335 

0.145  4887 

1-397  940 

0.715  338i 

0.385 

o.  167  2034 

1.469  614 

0.680  4506 

.336 

.145  9229 

.399  339 

.714  6231 

.386 

.  167  6377 

.471  085 

.679  7705 

•  337 

.  146  3572 

.400  739 

.713  9088 

.387 

.  168  0720 

.472  556 

.679  0911 

.338 

.146  7915 

.402  141 

.713  1953 

.388 

.168  5063 

.474  030 

.678  4123 

•  339 

.147  2258 

•403  543 

.712  4824 

.389 

.  168  9406 

•475  505 

.677  7343 

0.340 

0.147  6601 

1.404  948 

0.711  7703 

0.390 

0.169  3748 

1.476  981 

0.677  0569 

•  341 

.  148  0944 

.406  353 

.711  0589 

•  391 

.169  8091 

.478  459 

.676  3802 

•  342 

.148  5287 

.407  760 

.710  3482 

•  392 

.170  2434 

.479  938 

.675  7041 

•  343 

.  148  9630 

.409  169 

.709  6382 

•  393 

.170  6777 

.481  418 

.675  0287 

•  344 

•149  3973 

.410  579 

.708  9289 

•  394 

.171  II2O 

.482  901 

.674  3541 

0.345 

0.149  8316 

1.411  990 

0.708  2204 

0.395 

O.I7I  5463 

1.484  384 

0.673  6800 

.346 

.150  2659 

.413  403 

•707  5125 

.396 

.171  9806 

.485  869 

.673  0067 

.347 

.150  7002 

.414  817 

.706  8053 

.397 

.172  4149 

.487  356 

.672  3340 

.348 

•  I5'i  U45 

.416  232 

.706  0989 

.398 

.172  8492 

.488844 

.671  6620 

•  349 

.151  5688 

.417  649 

•70S  3931 

•  399 

.173  2835 

.490  334 

.670  9907 

0.350 

0.152  0031 

1.419  068 

0.704  6881 

0.400 

0.173'  7178 

1.491  825 

0.670  3200 

lofle(ej) 

loaio(eu) 

eu 

e-tt 

loge(en) 

looio(en) 

eu 

e"* 

SMITHSONIAN  TABLES 


229 


The  Exponential. 


u 

logio(eu) 

en 

e-° 

u 

logio(en) 

en 

•- 

0.400 

0.173  7178 

1.491  825 

0.670  3200 

0.450 

0.195  4325 

1.568  312 

0.637  6282! 

.401 

.174  1521 

•493  317 

.669  6501 

•  451 

.  195  8668 

.569  881 

.636  ogoS1 

.402 

•174  5864 

.494  811 

.668  9807 

•  452 

.196  3011 

•571  452 

.636  3542 

.403 

.175  0-207 

.496  307 

.668  3121 

•453 

.196  7354 

.573  024 

.635  7181 

.404 

•175  4550 

•497  804 

.667  6441 

•  454 

.197  1697 

.574  598 

.635  082; 

0.405 

o.  175  8893 

1.499  303 

0.666  9768 

0.455 

o.  197  6040 

1.576  173 

0.634  448o 

.406 

.  176  3236 

.500  803 

.666  3102 

.456 

.  198  0383 

.577  750 

.633  8138 

.407 

.  176  7579 

.502  304 

.665  6442 

.457 

.  198  4726 

.579  329 

.633  1803 

.408 

.177  1921 

•503  867 

.664  9789 

.458 

.108  0069 

.580  909 

.632  5475 

.409 

.177  6264 

.505  312 

.664  3142 

•  459 

.199  3412 

.582  491 

.631  9152 

0.410 

0.178  0607 

1.506  818 

0.663  6503 

0.460 

o.  199  7755 

1.584  074 

0.631  2836 

.411 

.178  4950 

.508  325 

.662  9869 

.461 

.200  2098 

.585  659 

.630  6527 

.412 

.  178  9293 

.509  834 

.662  3243 

.462 

.200  6441 

.587  245 

.630  0223 

.413 

.179  3636 

•511  345 

.661  6623 

.463 

.201  0783 

•588  833 

.629  3926 

.414 

.179  7979 

•512  857 

.661  ooio 

.464 

.201  5126 

.590  423 

.628  7636 

0.415 

0.180  2322 

I.5I4  371 

0.660  3403 

0.465 

0.201  9469 

1.592  014 

0.628  1351 

.416 

.180  6665 

.515886 

.659  6803 

.466 

.202  38l2 

•593  607 

.627  5073 

.417 

.181  1008 

.517  403 

.659  0209 

.467 

.202  8l55 

.595  201 

.626  8801 

.4*18 

.181  5351 

.518  921 

.658  3622 

.468 

.203  2408 

•596  797 

.626  2535 

.419 

.181  9694 

.520  440 

.657  7042 

.469 

.203  6841 

•598  395 

.625  6276 

0.420 

0.182  4037 

1.521  962 

0.657  0468 

0.470 

O.2O4  Il84 

1.599  994 

0.625  0023 

.421 

.182  8380 

.523  484 

.656  3901 

.471 

.204  5527 

.601  595 

.624  3776 

.422 

.183  2723 

.525  009 

.655  7340 

.472 

.2O4  9870 

.603  197 

.623  7535 

.423 

.183  7066 

.526  534 

.655  0786 

•  473' 

.205  4213 

.604  801 

.623  1301 

.424 

.184  1409 

.528  062 

.654  4239 

•  474 

.205  8556 

.606  407 

.622  5073 

0.425 

o.  184  5752 

1.529  590 

0.653  7698 

0.475 

0.206  2899 

i.  608  014 

0.621  8851 

.426 

.185  0094 

.531  121 

.653  1163 

.476 

.206  7242 

.609  623 

.621  2635 

.427 

.185  4437 

.532  653 

.652  4636 

.477 

.207  1585 

.611  233 

.620  6425 

.428 

.185  8780 

.534  187 

.651  8114 

.478 

.207  5928 

.612  845 

.620  O222 

.429 

.186  3123 

.535  721 

.651  1599 

.479 

.208  0271 

.614  459 

.619  4O25 

0.430 

0.186  7466 

1.537  258 

0.650  5091 

0.480 

0.208  4614 

1.616  074 

0.618  7834 

.431 

.187  1809 

.538  796 

.649  8589 

.481 

.208  8956 

.617  691 

.618  1649 

.432 

.  187  6152 

.540  335 

.649  2094 

.482 

.209  3299 

.619  310 

.617  547i 

•  433 

.188  0495 

.541  876 

.648  5605 

.483 

.209  7642 

.620  930 

.616  9298 

•434 

.  188  4838 

•543  419 

.647  9123 

.484 

.210  1985 

.622  552 

.616  3*32 

0.435 

0.188  9181 

1.544  963 

0.647  2647 

0.485 

0.210  6328 

1.624  175 

0.615  6972 

.436 

.189  3524 

.546  509 

.646  6177 

.486 

.211  0671 

.625  800 

.615  0818 

•437 

.189  7867 

.548  056 

.645  97H 

.487 

.211  5014 

.627  427 

.614  4670 

.438 

.I9O  22IO 

.549  605 

.645  3258 

.488 

•2ii  9357 

.629  055 

.613  8529 

•  439 

.  190  6553 

•551  155 

.644  6808 

.489 

.212  3700 

.630  685 

-613  2393 

0.440 

O.I9I  0896 

i.'552  707 

0.644  0364 

0.490 

0.212  8043 

1.632  316 

0.612  6264 

.441 

.191  5239 

.554  261 

.643  3927 

.491 

.213  2386 

.633  949 

.612  0141 

.442 

.191  9582 

•555  816 

.642  7496 

.492 

.213  6729 

.635  584 

.611  4024 

•443 

.192  3925 

•557  372 

.642  1072 

.493 

.214  1072 

.637  221 

.610  7913 

.-444 

.192  8267 

.558  930 

.641  4654 

•  494 

.214  5415 

.638  859 

.610  1808 

O.445 

O.I93  26lO 

1.560  490 

0.640  8243 

0.495 

0.214  9758 

I.O4O  408 

0.609  5709 

-TT..J 
.446 

.  193  0953 

.562  051 

.640  1838 

.496 

.215  4101 

.642  I4O 

.608  0616 

•447 

.194  1296 

.563  614 

.639  5439 

•  497 

•215  8444 

•  <M3  783 

.608  3530 

.448 

.194  5639 

.565  179 

.638  0047 

.498 

.216  2787 

.645  427 

.607  7449 

.449 

.194  9982 

.566  745 

.638  2661 

.499 

.216  7129 

.047  073 

.607  1375 

0.450 

0.195  4325 

1.568  312 

0.637  6282 

0.500 

0.217  1472 

1.648  721 

0.6o6  5307 

looe(en) 

looio(eu) 

en 

«-" 

looc(eu)    looio(en) 

e" 

e~u 

SMITHSONIAN  TABLES 


230 


The  Exponential. 


u 

looio(eu) 

eu 

e~tt 

u 

loaio(eu) 

eu 

e~° 

0.500 
.501 
.502 
.503 
.504 

0.217  1472 
.217  5815 
.218  0158 
.218  4501 
.218  8844 

1.648  721 
.650  371 
.652  O22 
.653  675 
.655  329 

0.6o6  5307 
.605  9244 
.605  3188 
.604  7138 
.604  1094 

0.550 
.551 

.552 
•  553 
.554 

0.238  8620 
.239  2963 
.239  7306 
.240  1648 
.240  5991 

1-733  253 
•734  987 
.736  723 
.738  461 
.740  200 

0.576  9498 
.576  3731 
.575  7971 
.575  2216 
.574  6466 

0.505 

'  .506 

.507 

.508 

.509 

0.219  3187 
.219  7530 

.220  1873 
.220  O2l6 

.221  0559 

1.656  986 
.658  643 
.660  3O3 
.66l  964 
.663  627 

0.603  5056 
.602  9024 
.602  2998 
.601  6978 
.601  0964 

0.555 
.556 
•  557 
.558 
.559 

0.241  0334 
.241  4677 
.241  9020 
.242  3363 
.242  7706 

1.741  941 
.743  684 
.745  428 
.747  175 
.748  923 

0.574  0723 
.573  4985 
.572  9253 
•572  3526 
.571  7806 

0.510 

.511 
.512 
.513 
.514 

O.22I  49O2 
.221  9245 
.222  3588 
.222  7931! 
.223  2274 

1.665  291 
.666957 
.668625 
.670  295 
,671  966 

O.6oo  4956 
•599  8954 
.599  2958 
.5986968 
.5980984 

0.560 
.561 
.562 
.563 
.564 

0.243  2049 
.243  6392 
.244  0735 
.244  5078 
.244  9421 

1.750  673 
.752  424 
.754  177 
•755  932 
.757  689 

0.571  2091 
.570  6381 
.570  0678 
.569  498o 
.568  9288 

0.515 
.516 
.517 

.518 
.519 

0.223  66l7 
.224  0960 
.224  5302 
.224  9645 
.225  3988 

1.673  639 
.675  3U 
.676  989 
.678  667 
.680  346 

0.597  5006 
•596  9034 
.596  3068 
.595  7io8 
.595  H54 

0.565 
.566 
.567 
.568 
.569 

0.245  3764 
.245  8107 
.246  2450 
.246  6793 
.247  1136 

1.759  448 
.761  208 
.762  970 
.764  734 
.766  500 

0.568  3601 
.567  7921 
.567  2246 
.566  6576 
.566  0912 

0.520 

.521 
.522 
.523 
.524 

0.225  8331 
.226  2674 
.226  7OI7 
.227  1360 
•227  5703 

1.682  028 

.683  711 
.685  395 
.687  081 
.688  769 

0.594  5205 
.593  9263 
•593  3327 
.592  7397 
.592  1472 

0.570 

•  571 
.572 
.573 
.574 

0.247  5479 
.247  9821 
.248  4164 
.248  8507 
.249  2850 

1.768  267 
.770  036 
•771  807 
•773  58o 
•775  354 

0.565  5254 
.564  9602 

.564  3955 
.563  8314 
.563  2679 

0.525 

.526 

.527 

.528 

.529 

O.228  OO46 
.228  4389 
.228  8732 
.229  3075 
.229  7418 

1.690  459 
.692  150 
.693  843 
.695  538 
.697  234 

0.591  5554 
.590.9641 
.590  3734 
.589  7834 
.589  1939 

0.575 
.576 
.577 
.578 
•  579 

0.249  7193 
.250  1536 
.250  5879 

.251  O222 
.251  4565 

1.777  131 
.778  909 
.780  688 
.782  470 
•784  253 

0.562  7049 
.562  1424 
.561  5806 
.561  0193 
.560  4585 

0.530 
.531 

.532 

.533 
•  534 

0.230  I76l 
.230  6lO4 

.231  0447 
.231  4790 
.231  9133 

1.698  932 
.700  632 
•702  334 
.704  037 
.705  742 

0.588  6050 
.588  0167 
.587  4289 
.586  8418 
.586  2553 

0.580 
.581 
.582 
.583 
.584 

0.251  8908 
.252  3251 

.252  7594 
.253  1937 
.253  6280 

1.786  038 
.787  825 
.789  614 
•791  405 
•793  197 

0.559  8984 
•559  3387 
.558  7797 

.558  2212 

.557  6632 

0.535 
.536 
•  537 
.538 
•  539 

0.232  3475 
.232  7818 
.233  2161 
.233  6504 
.234  0847 

1.707  448 
.709  157 
.710  867 
.712  578 
.714  292 

0.585  6693 
.585  0839 
.584  4991 
.583  9149 
.583  3313 

0.585 

.586 
.587 
.588 
.589 

0.254  0623 
.254  4966 
.254  9309 
•255  3652 
.255  7994 

1.794  991 
.796  787 
.798  585 
.800  384 
.802  185 

0.557  1059 
.556  5490 
.555  9928 
.555  4370 
.554  8819 

0.540 
.541 

•  542 
•  543 
•  544 

0.234  5190 
.234  9533 
.235  3876 
.235  8219 
.236  2562 

1.716  007 
.717  724 
.719  442 
.721  163 
.722  885 

0.582  7483 
.582  1658 
.581  5839 
.581  0026 
.580  4219 

0.590 
.591 
.592 
•  593 
•  594 

0.256  2337 
.256  6680 
.257  1023 
.257  5366 
.257  9709 

1.803  988 
.805  793 
.807  600 
.809  409 
.811  219 

0.554  3273 
•553  7732 
•553  2197 
.552  6668 
.552  1144 

0.545 
.546 
.riff 

.648 
•  549 

0.236  6905 
.237  1248 
.237  5591 
.237  9934 
.238  4277 

1.724  608 
.726  334 
.728  061 
.729  790 

•731  521 

0.579  8418 
.579  2622 
.578  6833 
.578  1049 
•  .577  5270 

0.595 
.596 
.597 
.598 
•  599 

0.258  4052 
.258  8395 
.259  2738 
.259  7081 
.260  1424 

1.813  031 
.814  845 
.816  661 
.818  478 
.820  298 

0.551  5626 
•551  0113 
.550  4605 
.549  9104 
.549  3607 

0.550 

0.238  8620 

1.733  253 

0.576  9498 

0.600 

0.200  5767 

1.822  119 

0.548  8116 

loge(ea) 

looio(eu) 

eu 

e-° 

lofle(eu) 

lonio(en) 

eu 

e~u 

SMITHSONIAN  TABLES 


231 


The  Exponential. 


u 

looio(en) 

eu 

e  u 

u 

IOQio(eu) 

e° 

e  u 

0.600 

0.260  5767 

1.822  119 

0.548  8116 

0.650 

0.282  2914 

1.915  541 

0.522  0458 

.601 

.261  ouo 

.823  942 

.548  2631 

.651 

.282  7257 

.917  457 

.521  5240 

.602 

.261  4453 

.825  767 

•547  7i5i 

.652 

.283  1600 

.919  376 

.521  0027 

.603 

.261  8796 

•827  593 

•547  i677 

-653 

.283  5943 

.921  296 

.520  4820 

.604 

.262  3139 

.829  422 

.546  6208 

.654 

.284  0286 

.923  218 

.519  9618 

0.605 

0.262  7482 

1.831  252 

0.546  0744 

0.655 

0.284  4629 

1.925  143 

0.519  4421 

.606 

.263  1825 

.833  084 

.545  5286 

.656 

.284  8972 

.927  069 

.518  9229 

.607 

.263  6168 

.834  918 

•544  9834 

.657 

.285  3315 

.928  997 

.518  4042 

.608 

.264  0510 

.836  754 

.544  4387 

.658 

.285  7658 

.930  927 

.517  8861 

.609 

.264  4853 

.838  592 

•543  8945 

.659 

.286  2OOI 

•932  859 

.517  3684 

0.610 

0.264  9196 

1.840  431 

0.543  3509 

0.660 

0.286  6344 

1-934  792 

0.516  8513 

.611 

.265  3539 

.842  273 

.542  8078 

.661 

.287  0687 

.936  728 

.5i6  3347 

.612 

.265  7882 

.844  116 

.542  2653 

.662 

.287  5O29 

.938  666 

•515  8187 

.613 

.266  2225 

.84*5  96i 

•541  7233 

.663 

.287  9372 

.940  605 

.515  3031 

.614 

.266  6568 

.847  808 

.541  1818 

.664 

.288  3715 

•942  547 

.514  788i 

0.615 

0.267  0911 

1.849  657 

0.540  6409 

0.665 

0.288  8058 

1.944  491 

0.514  2735 

.616 

.267  5254 

.851  507 

.540  1005 

.666 

.289  2401 

.946  436 

.513  7595 

.617 

.267  9597 

.853  360 

.539  5607 

.667 

.289  6744 

.948  383 

.513  2460 

.618 

.268  3940 

.855  214 

.539  0214 

.668 

.200  IO87 

•950  333 

.512  7330 

.619 

.268  8283 

.857  070 

.538  4827 

.669 

.200  5430 

.952  284 

.512  2205 

0.620 

0.269  2626 

1.858  928 

0.537  9444 

0.670 

0.290  9773 

1.954  237 

0.511  7086 

.621 

.269  6969 

.860788 

.537  4068 

.671 

.291  4116 

.956  193 

.511  1971 

.622 

.270  1312 

.862  650 

.5368696 

.6712 

.291  8459 

.958  ISO 

.510  6862 

.623 

•270  5655 

.864  513 

.536  3330 

.673 

.292  2802 

.960  109 

.510  1758 

.624 

.270  9998 

.866379 

•535  7970 

.674 

.292  7145 

.962  070 

.509  6658 

0.625 

0.271  434'! 

1.868246 

0.535  2614 

0.675 

0.293  1488 

1.964  033 

0.509  1564 

.626 

.271  8683 

.870  115 

.534  7264 

.676 

.293  5831 

.965  998 

.508  6475 

.627 

.272  3026 

.871  986 

.534  1920 

.677 

.294  0174 

.967  965 

.508  1391 

.628 

.272  7369 

.873  859 

.533  6581 

.678 

.294  4517 

•969  934 

.507  6312 

.629 

.273  1712 

.875  734 

•533  1247 

.679 

.294  8860 

.971  90S 

.507  1239 

0.630 

0.273  6055 

1.877  611 

0.532  59i8 

0.680 

0.295  3202 

1-973  878 

0.506  6170 

.631 

.274  0398 

.879  489 

.532  0595 

.681 

.295  7545 

•975  853 

.506  1106 

.632 

.274  4741 

.881  370 

•531  5277 

.682 

.296  1888 

.977  829 

.505  6048 

•633 

.274  9084 

.883  252 

.530  9964 

.683 

.296  6231 

.979  808 

.505  0994 

•634 

.275  3427 

.885  136 

•530  4657 

.684 

.297  0574 

.981  789 

.504  5946 

0.635 

0.275  7770 

1.887  022 

0.529  9355 

0.685 

0.297  4917 

1.983  772 

0.504  0902 

.636 

.276  2113 

.888  910 

.529  4058 

.686 

.297  9260 

.985  757 

.503  5864 

.637 

.276  6456 

.890  800 

.528  8767 

.687 

.208  3603 

.987  743 

.503  0831 

.638 

.277  0799 

.892  692 

.528  3481 

.688 

.298  7046 

.989  732 

.502  5802 

.639 

.277  5142 

.894  585 

.527  8200 

.689 

.299  2289 

.991  723 

.502  0779 

0.640 

0.277  9485 

1.896  481 

0.527  2924 

0.690 

0.299  6632 

1.993  7i6 

0.501  5761 

.641 

.278  3828 

.898  378 

.526  7654 

.691 

.300  0975 

•995  7io 

.501  0747 

.642 

.278  8171 

.900  278 

.526  2389 

.692 

.300  5318 

•997  707 

•500  5739 

.643 

.279  2514 

.902  179 

.525  7129 

.693 

.300  9661 

.099  706 

.500  0736 

.644 

.279  6856 

.904  082 

.525  i875 

.694 

.301  4004 

2.001  706 

•499  5738 

0.645 

0.280  1199 

1.905  987 

0.524  6625 

0.695 

0.301  8347 

2.003  709 

0.499  0744 

.646 

.280  5542 

.907  894 

.524  1381 

.696 

.302  2690 

.005  714 

.498  5756 

.647 

.2800885 

.909  803 

.523  6143 

.697 

.302  7033 

.007  720 

.498,0773 

.648 

.281  4228 

.911  714 

.523  0909 

.698 

.303  1375 

.009  729 

•497  5795 

.649 

.281  8571 

.913  626 

.522  5681 

.699 

.303  57i8 

.011  740 

.497  0821 

0.650 

0.282  2914 

I.9IS  541 

0.522  0458 

0.700 

0.304  0061 

2.013  753 

0.496  5853 

looe(e°) 

looitXe0) 

e° 

t— 

looe(eu) 

log^e") 

eu 

e~° 

SMITHSONIAN  TABLCS 


232 


The  Exponential. 


u 

looio(eu) 

en 

e-u 

u 

looio(en) 

eu 

e  u 

0.700 

0.304  0061 

2.013  753 

0.496  5853 

0.750 

0.325  7209 

2.117  ooo 

0.472  366^ 

.701 

.304  4404 

.015  767 

.496  0890 

•  751 

.326  1552 

.119  118 

.471  894^ 

.702 

.304  8747 

.017  784 

.495  5931 

.752 

.326  5895 

.121  238 

.471  422* 

.703 

.305  3090 

.019  803 

•495  0978 

•753 

.327  0237 

.123  36l 

.470  95  rt 

.70-4 

.305  7433 

.021  824 

.494  6029 

•754 

.327  458o 

.125  485 

.470  48oc 

0.705 

0.306  1776 

2.023  847 

0.494  1086 

0.755 

0.327  8923 

2.127  612 

0.470  oiot 

.70J 

.306  6119 

'  .025  872 

.493  6147 

.756 

.328  3266 

.129  740 

.469  540* 

.707 

.307  0462 

.027  898 

.493  1213 

•  757 

.328  7609 

.131  871 

.469  071  J 

.708 

.307  4805 

.029  927 

.492  6285 

.758 

.329  1952 

.134  004 

.468  602; 

.709 

.307  9U8 

.031  958 

.492  1361 

•  759 

.329  6295 

.136  139 

.468  134: 

0.710 

0.308  3491 

2.033  991 

0.491  6442 

0.760 

0.330  0638 

2.  138  276 

0.467  666/ 

.711 

.308  7834 

.036  026 

.491  1528 

.761 

•330  498i 

.140  416 

.467  I99C 

.712 

.309  2177 

.038  063 

.490  6619 

.762 

•330  9324 

.142  557 

.466  732( 

.713 

.309  6520 

.O4O  IO2 

.450  1715 

.763 

•331  3667 

.144  70i 

.466  265. 

.714 

.310  0863 

.042  144 

.489  6815 

.764 

.331  8010 

.  146  846 

.465  799. 

0.715 

0.310  5206 

2.044  187 

0.489  1921 

0.765 

0.332  2353 

2.148  994 

0.465  333< 

.716 

.310  9548 

.046  23'2 

.488  70312 

.766 

.3326696 

.151  144 

.464  858£ 

.717 

•311  3891 

.048  279 

.488  2147 

.767 

•333  1039 

.153  297 

.464  404^ 

.718 

.311  8234 

.050  328 

.487  7267 

.768 

•333  5382 

.155  451 

.463  94CK 

.719 

.312  2577 

.052  380 

•487  2393 

.769 

•333  9725 

.157  608 

.463  476: 

0.720 

0.3-12  6920 

2.054  433 

0.486  7523 

0.770 

0.334  4068 

2.  159  766 

0.463  0131 

.721 

.313  1263 

.056  489 

.486  2657 

•  771 

.334  8410 

.161  927 

.462  550: 

.722 

.313  5606 

.058  546 

.485  7797 

.772 

.335  2753 

.164  090 

.462  o88( 

.723 

.313  9949 

.060  606 

.485  2942 

.773 

.335  7096 

.  166  255 

.461  626 

.724 

.314  4292 

.062  667 

.484  8091 

•  774 

.336  1439 

.168  423 

.461  164; 

0.^25 

0.314  8635 

2.064  73*1 

0.484  3246 

0.775 

0.336  5782 

2.170  592 

0.460  703$ 

.726 

.315  2978 

.066  797 

.483  8405 

.776 

•337  0125 

.172  764 

.460  243. 

.727 

.315  7321 

.068  865 

.483  3569 

•  777 

.337  4468 

.174  938 

.459  783* 

.728 

.316  1664 

.070  935 

.482  8738 

.778 

.337-88ii 

.177  H4 

•459  323; 

.729 

.316  6007 

.073  007 

.482  3911 

.779 

.338  3154 

.179  292 

.458  864< 

0.730 

0.317  0350 

2.075  081 

0.481  9090 

0.780 

0.338  7497 

2.181  472 

0.458  4o6( 

•  731 

.317  4093 

•077  157 

.481  4273 

.781 

•339  1840 

.183  655 

•457  947* 

•  732 

.317  9036 

.079  235 

.480  9461 

.782 

.339  6183 

.185  840 

.457  490 

•  733 

.318  3379 

.081  315 

.480  4654 

.783 

.340  0526 

.188  027 

•457  032? 

.734 

.318  7721 

.083  398 

.479  9852 

.784 

.340  4869 

.190  216 

.456  5T& 

0.735 

0.319  2064 

2.085  482 

0.479  5055 

0.785 

0.340  9212 

2.192  407 

0.456  119 

.736 

.319  6407 

.087  569 

.479  0262 

.786 

•341  3555 

.194  600 

.455  663< 

•  737 

.320  0750 

.089  657 

.478  5474 

.787 

.341  7898 

.196  796 

.455  208 

.738 
•  739 

.320  5093 
.320  9436 

.091  748 
.093  841 

.478  0691 
•477  5913 

.788 
.789 

.342  2241 
•  342  6583 

.198  994 
.201  194 

.454  753- 
.454  298* 

0.740 

0.321  3779 

2.095  936 

0.477  H39 

0.790 

0.343  0926 

2.203  396 

0.453  844* 

.741 

.321  8122 

.098  032 

.476  6370 

.791 

.343  5269 

.205  601 

•453  391 

.742 

.322  2465 

.100  132 

.476  1606 

•  792 

.343  9612 

.207  808 

.452  938- 

•  743 

.322  6808 

.  102  233 

.475  6847 

•  793 

•344  3955 

.210  017 

.452  485 

-744 

.323  1151 

.104  336 

.475  2093 

.794 

.344  8298 

.212  228 

.452  033< 

0.745 

0.323  5494 

2.106  441 

0.474  7343 

0.795 

0.345  2641 

2.214  441 

0.451  58i 

.746 

.323  9837 

.108  549 

.474  2598 

.796 

•345  6984 

.216  657 

.4-51  I29< 

->  -747 

.324  4180 

.no  659 

•473  7858 

•  797 

.346  1327 

.218  874 

.450  679) 

"  .748 

.324  8523 

.112  770 

.473  3122 

.798 

.346  5670 

.221  094 

.450  228 

•  749 

.325  2866 

.114  884 

.472  8392 

•  799 

•347  0013 

.223  3l6 

.449  778 

0.750 

0.325  7209 

2.117  ooo 

0.472  3666 

0.800 

0.347  4356 

2.225  541 

0.449  329< 

lofle(eu) 

loflio(eu) 

en 

e~u 

looe(eu) 

logio(eu) 

eu 

e-n 

SMITHSONIAN  TABLES 


233 


The  Exponential. 


•J 

loflW(eu) 

eu 

e~u 

u 

looio(eu) 

eu 

e  u 

0.800 

0.347  4356 

2.225  541 

0.449  3290 

0.850 

0.369  1503 

2-339  647 

0.427  4149 

.801 

•347  8609 

.227  768 

.448  8799 

.851 

.369  5846 

-341  988 

.4(26  9877 

.802 

.348  3042 

.229  096 

.448  4312 

.852 

.370  0189 

•344  331 

.426  5610 

.803 

.348  7385 

.232  228 

447  9830 

.853 

•370  4532 

.346  676 

.426  1346 

.804 

.349  1728 

.234  461 

.447  5352 

.854 

•370  8875 

.349  024 

.425  7087 

0.805 

0.349  6071 

2.236  696 

0.447  0879 

0.855 

0.371  3218 

2.351  374 

0.425  2832 

.806 

.350  0414 

.238  934 

.446  6411 

.856 

•371  756i 

•353  727 

.424  8581 

.807 

•350  4756 

.241  174 

.446  1946 

.857 

.372  1904 

.356  082 

.424  4335 

.808 

•350  9009 

.243  417 

.445  7487 

.858 

.372  6247 

.358  439 

.424  0093 

.809 

.351  3442 

.245  66l 

.445  3031 

.859 

•373  0590 

.360  799 

.423  5855 

0.810 

0.3SI  7785 

2.247  90S 

0.444  8581 

0.860 

0-373  4933 

2.363  161 

0.423  1621 

.811 

.352  2128 

.250  157 

.444  4134 

.861 

•373  9275 

.365  525 

.422  7391 

.812 

.352  6471 

.252  408 

•  443  0692 

.862 

.374  3618 

.367  892 

.422  3166 

.813 

.353  0814 

.254  662 

.443  5255 

.863 

•374  7961 

.370  261 

.421  8945 

.814 

•353  5157 

.256  918 

.443  0822 

.864 

•375  2304 

•372  632 

.421  4728 

0.815 

0.353  9500 

2.259  176 

0.4412  6393 

0.865 

0.375  6647 

2.375  006 

0.421  0516 

.816 

•354  3843 

.261  436 

.442  1969 

.866 

.376  0990 

•377  382 

.420  6307 

.817 

.354  8186 

.263  699 

.441  7549 

.867 

.376  5333 

.379  76i 

.420  2103 

.818 

•355  2529 

.265  963 

.441  3134 

.868 

.376  9676 

.382  142 

.419  7903 

.819 

.355  6872 

.268  230 

.440  8723 

.869 

.377  4019 

.384  525 

.419  3707 

0.820 

0.356  1215 

2.270  500 

0.440  4317 

0.870 

0.377  8362 

2.386  911 

0.418  9515 

.821 

.356  5558 

.272  771 

.439  9914 

.871 

.378  2705 

.389  299 

.418  5328 

.822 

•356  9901 

.275  045 

.439  5517 

.872 

.378  7048 

.391  689 

.418  1145 

.823 

.357  4244 

.277  322 

.439  1123 

.873 

.379  1391 

.394  082 

.417  6966 

.824 

.357  8587 

.279  600 

.438  6734 

.874 

.379  5734 

.396  478 

.417  2791 

0.825 

0.358  2929 

2.281  881 

0.438  2350 

0.875 

0.380  0077 

2.398  875 

0.416  8620 

.826 

.358  7272 

.284  164 

•437  7970 

.876 

.380  4420 

.401  275 

.416  4454 

.827 

•359  1615 

.286  449 

•437  3594 

.877 

.380  8763 

.403  678 

.416  0291 

.828 

•359  5958 

.288  737 

.436  9223 

.878 

.381  3106 

.406  083 

.415  6133 

.829 

.360  0301 

.291  027 

.436  4856 

.879 

.381  7448 

.408  490 

.415  1979 

0.830 

0.360  4644 

2.293  319 

0.436  0493 

0.880 

0.382  1791 

2.410  900 

0.414  7829 

.831 

.3608987 

.295  613 

•435  6135 

.881 

.382  6134 

.413  312 

.414  3683 

.832 

.361  3330 

.297  910 

•435  1781 

.882 

.383  0477 

.415  726 

.413  9542 

.833 

.834 

.361  7673 
.362  2016 

.300  209 
.302  510 

•434  7431 
.434  3086 

.883 
.884 

.383  4820 
.383  9163 

.418  143 
.420  563 

.413  5404 
.413  1271 

0.835 

0.362  6359 

2.304  814 

0.433  8745 

0.885 

0.384  3506 

2.422  984 

0.412  7142 

.836 

.363  0702 

.307  I2O 

.433  4408 

.886 

.384  T&49 

.425  409 

.412  3017 

.837 

.363  5045 

.309  428 

•433  0076 

.887 

.385  2192 

•427  835 

.411  8896 

.838 

.363  9388 

.311  739 

.432  5748 

.888 

.385  653-S 

.430  264 

.411  4779 

.839 

.364  373'i 

.314  052 

.432  1424 

.889 

.3860878 

.432  696 

.411  0666 

0.840 

0.364  8074 

2.316  367 

0.431  7105 

0.890 

0.386  5'22I 

2.435  130 

0.410  6558 

.841 

.365  24-17 

.318  685 

.431  2790 

.891 

.386  9564 

•437  566 

.410  2453 

.842 

.365  6760 

.321  004 

.430  8480 

.892 

.387  3907 

.440  005 

.409  8353 

.843 

.844 

.366  IIO2 

.366  5445 

.323  327 
.325  651 

.430  4173 
.429  9871 

.893 
.894 

.387  8250 

.388  2593 

.442  446 
.444  890 

.409  4256 
.409  0164 

0.845 

0.366  9788 

2.327  978 

0.429  5574 

0.895 

0.388  6936 

2.447  336 

0.408  6076 

.846 
.847 

.367  4UI 
.367  8474 

•330  307 
.332  638 

.429  1280 
.428  6991 

.896 
.897 

.389  1279 
.389  5622 

•449  784 

•  45-'  235 

.408  1992 
.407  7?'i2 

.848 

.368  2817 

•334  972 

.428  2706 

.858 

.389  9964 

-454  689 

.407  3836 

.849 

.368  7160 

•337  308 

.427  8426 

.899 

•390  4307 

•457  145 

.406  9764 

0.850 

0.369  1503 

2.339  647 

0.427  4149 

0.900 

0.390  8650 

2.459  603 

0.406  5697 

loo-V; 

loouXe") 

e" 

e~~u 

loflc(eu) 

loQio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


The  Exponential. 


u 

looio(eu) 

eu 

e-n 

u 

logio(en) 

en 

e~u 

0.900 

0.390  8650 

2.459  603 

0.406  5697 

0.950 

0.412  5798 

2.585  710 

0.386  7410 

.901 

.391  2993 

.462  064 

.406  1633 

.951 

.413  0141 

.588  297 

.386  3545 

.902 

•391  7336 

.464  527 

.405  7573 

.952 

.413  4483 

.590  886 

.385  9683 

•903 

.392  1679 

.466  993 

.405  35i8 

•  953 

.413  8826 

•593  478 

.385  5825 

.904 

.392  6022 

.469  461 

.404  9466 

•  954 

.414  3l69 

•595  073 

.385  1971 

0.905 

0.393  0365 

2.471  932 

0.404  5419 

0.955 

0.414  7512 

2.508  671 

0.384  8121 

.906 

•393  47O8 

.474  405 

.404  1375 

.956 

.415  1855 

.601  271 

.384  427= 

.CO7 

•393  9051 

.476  88  i 

.403  7336 

•  957 

.415  6198 

.603  873 

.384  0431 

•y/ 

.908 

.909 

•394  3394 
•394  7737 

•479  359 
.481  839 

.403  3301 
.402  9269 

.958 
•959 

.416  0541 
.416  4884 

.606  478 
.609086 

.383  6504 
.383  2760 

0.910 

0.395  2080 

2.484  323 

0.402  5242 

0.960 

0.416  9227 

2.611  696 

0.382  8925 

.911 

.395  6423 

.486  808 

.402  1219 

.961 

.417  3570 

.614  309 

.382  5102 

.912 

.396  0766 

.489  296 

.401  7200 

.962 

.417  7913 

.616  925 

.382  1275 

.913 

.396  5109 

.491  787 

.401  3185 

.963 

.418  2256 

.619  543 

.381  745£ 

.914 

.396  9452 

.494  280 

.400  9173 

.964 

.418  6599 

.622  164 

.381  364-1 

0.915 

0.397  3795 

2.496  775 

0.400  5166 

0.965 

0.419  0942 

2.624  788 

0.380  983:2 

.916 

•397  8137 

•499  273 

.400  1163 

.956 

.419  5285 

.627  414 

.380  6024 

.917 

.398  2480 

•501  774 

.399  7164 

.967 

.419  9628 

.630  042 

.380  222C 

.918 

.398  6823 

.504  277 

.399  3169 

.968 

.420  3971 

.632  674 

.379  &42C 

.919 

.399  "66 

.506  782 

.398  9178 

.969 

.420  8314 

.635  308 

.379  462: 

0.920 

0.399  5509 

2.509  290 

0.398  5190 

0.970 

0.421  2656 

2.637  944 

0.379  o83C 

.921 

•399  9852 

.511  801 

.398  1207 

•971 

.421  6999 

.640  584 

.378  7041 

.922 

.400  4195 

.514  314 

•397  7228 

.972 

.422  1342 

.643  226 

.378  ysst 

.923 

.400  8538 

.516  830 

•397  3253 

•973 

.422  5685 

.645  870 

.377  947^ 

.924 

.401  2881 

.519  348 

.396  9281 

•974 

.423  0028 

•648  517 

•377  569; 

0.925 

0.401  7224 

2.521  868 

0.396  53H 

0.975 

0.423  4371 

2.651  167 

0.377  192^ 

.926 

.402  1567 

.524  39i 

.396  1351 

.976 

.423  8714 

.653  820 

.376  815: 

.927 

.402  5910 

.526  917 

•395  7391 

.977 

.424  3057 

.656  475 

.376  438; 

.928 

.403  0253 

.529  445 

.395  3436 

.978 

.424  7400 

.659  133 

.376  062. 

.929 

.403  4596 

•531  976 

•394  9485 

•  979 

.425  1743 

.661  793 

.375686* 

0.930 

0.403  8939 

2.534  509 

0.394  5537 

0.980 

0.425  6086 

2.664  456 

0.375  3" 

•931 

.404  31282 

•537  045 

•394  1594 

.981 

.426  0429 

.667  122 

•  374  936c 

.932 

.404  7625 

•  539  583 

.393  7654 

.982 

.426  4772 

.669  790 

•  374  56i; 

•  933 

.405  1068 

.542  124 

.393  37i8 

.983 

.426  9115 

.672  462 

.374  i86< 

•  934 

.405  6310 

.544668 

.392  9786 

.984 

.427  3458 

.675  135 

.373  8i2< 

0.935 

0.406  0653 

2.547  213 

0.392  5859 

0.985 

0.427  7801 

2.677  812 

0.373  439- 

.936 

.406  4996 

.549  762 

•392  1935 

.986 

.428  2144 

.680  491 

•373  066 

•  937 

.406  9339 

•552  313 

.391  8015 

.987 

.428  6487 

.683  173 

•372  693 

.938 

.407  3682 

.554  867 

.391  4099 

.988 

.429  0829 

.685  857 

•  372  320< 

•  939 

.407  8025 

.557  4*3 

.391  0187 

.989 

.429  5172 

.688545 

•371  948 

0.94P 

0.408  2368 

2.559  98i 

0.390  6278 

0.990 

0.429  9515 

2.691  234 

0.371  576, 

.941 

.408  6711 

.562  543 

.390  2374 

.991 

.430  3858 

.693  927 

•371  205 

.942 

.409  1054 

•565  107 

.3898474 

.992 

.430  8201 

.696  622 

•370  834 

•  943 

.409  5397 

.567  673 

.389  4577 

•  993 

.431  2544 

.699  320 

•  370  463* 

•944 

.409  9740 

.570  242 

.3890684 

.994 

•431  6887 

.702  021 

•  370  093' 

0.945 

0.410  4083 

2.572  813 

0.388  6796 

0.995 

0.432  1230 

2.704  724 

0.369  723- 

.946 

.410  8426 

•575  387 

.388  2911 

.996 

•432  5573 

.707  430 

.369  353 

•947 

.411  2769 

•577  964 

.387  9030 

•  997 

.432  9916 

.710  139 

.368984 

.948 

.411  7H2 

.580  543 

.387  5153 

.998 

•433  4259 

.712  851 

.368  615 

•  949 

.412  1455 

.583  125 

.387  1280 

.999 

.433  8602 

.715  565 

.368  247 

0.950 

0.412  5798 

2.585  710 

0.386  7410 

1.  000 

0.434  2945 

2.718  282 

0.367  879- 

lofle(eu) 

logio(eu) 

eu 

e-n 

loge(eu) 

Iog10(eu) 

eu 

e-u 

SMITHSONIAN  TABLES 


235 


The  Exponential. 


u 

logio(eu) 

eu 

.- 

u 

logio(en) 

en 

e- 

1.  000 

0.434  2945 

2.718  282 

0-367  8794 

1.050 

0.456  0092 

2.857  651 

0-349  9377 

.OOI 

.434  7288 

.721  ooi 

.367  5H7 

.051 

.456  4435 

.860  510 

•349  5880 

.002 

.435  1631 

.723  724 

.367  1444 

.052 

.456  8778 

.863  372 

•349  2386 

.003 

•435  5974 

.726  449 

•366  7775 

.053 

•457  3121 

.866237 

.348  8895 

.004 

.436  0317 

.729  177 

.366  4109 

.054 

.457  7464 

.869  105 

.348  5408 

1.005 

0.436  4660 

2.731  907 

0.366  0446 

^1.055 

0.458  1807 

2.871  975 

0.348  1924 

.006 

.436  9002 

.734  641 

.365  6788 

.056 

.458  6150 

.874  849 

.347  8444 

.007 

•437  3345 

.737  377 

.365  3133 

•  057 

•459  0493 

.877  725 

•347  4967 

.008 

.437  7688 

•740  115 

.364  9481 

.058 

.459  4836 

.880604 

•347  1494 

.009 

.438  2031 

•742  857 

.364  5834 

.059 

•459  9179 

.883  486 

.346  8024 

1.  010 

0.438  6374 

2.745  601 

0.364  2190 

i.  060 

0.460  3522 

2.886  371 

0.346  4558 

.on 
.012 

•439  0717 
.439  5060 

•748  348 
.751  098 

.363  8549 
.363  4913 

.061 
.062 

.460  7864 
.461  2207 

.889  259 
.892  150 

.346  1095 
•345  7636 

.013 

.439  9403 

•753  850 

.363  1280 

.063 

.461  6550 

•895  043 

.345  4180 

.014 

.440  3746 

.756  605 

.362  7650 

.064 

.462  0893 

.897  940 

•345  0728 

1.015 

0.440  8089 

2.759  363 

0.362  4024 

1.065 

0.462  5236 

2.900  839 

0.344  7279 

.016 

.441  2432 

.762  124 

.362  0402 

.066 

.462  9579 

.903  741 

•344  3833 

.0*17 

.441  6775 

.764  888 

.361  6783 

.067 

.463  3922 

.906  646 

•344  0391 

.018 

.442  I  I  18 

.767  654 

.361  3169 

.068 

.463  8265 

.909  555 

•343  6952 

.019 

.442  5461 

.770  423 

.360  9557 

.069 

.464  2608 

.912  466 

•343  3517 

i.  020 

0.442  9804 

2.773  195 

0.360  5949 

•  1.070 

0.464  6951 

2.915  379 

0.343  0085 

.021 

.443  4147 

•775  969 

.360  2345 

.071 

.465  1294 

.918  296 

.342  6657 

.022 

.443  8490 

•778  747 

.359  8745 

.072 

•465  5637 

.921  216 

.342  3232 

.023 

.444  2833 

•781  527 

•359  5148 

.073 

.465  998o 

.924  139 

.341  9810 

.024 

.444  7175 

.784  3io 

.359  1554 

.074 

.466  4323 

.927  064 

.341  6392 

1.025 

0.445  I5i8 

2.787  095 

0.358  7965 

1.075 

0.466  8666 

2.929  993 

0.341  2978 

.026 

.445  586i 

.789884 

•358  4378 

.076 

.467  3009 

.932  924 

.340  9566 

.027 

.446  0204 

.792  675 

.358  0796 

.077 

•467  7352 

•935  859 

.340  6158 

.028 

.446  4547 

•795  469 

•357  7217 

.078 

.468  1695 

.938  796 

.340  2754 

.029 

.446  8890 

.798  266 

•357  3641 

.079 

.468  6037 

.941  736 

•339  9353 

I.O30 

0.447  3233 

2.801  066 

0.357  0070 

1.080 

0.469  0380 

2.944  680 

0.339  5955 

.031 

.447  7576 

.803  868 

.356  6501 

.081 

.469  4723 

.947  626 

•339  2561 

.032 

.448  1919 

.806  674 

.356  2937 

.082 

.469  9066 

•950  575 

.338  9170 

•033 

.448  6262 

.809  482 

•355  9375 

.083 

.470  3409 

•953  527 

.338  5783 

.034 

.449  0605 

.812  293 

.355  58i8 

.084 

.470  7752 

.956  482 

.338  2399 

1.035 

0.449  4948 

2.815  106 

0.355  2264 

1.085 

0.471  2095 

2.959  440 

0.337  0018 

.036 

.449  9291 

.817  923 

.354  8713 

.086 

.471  6438 

.962  401 

.337  5641 

.037 

•450  3634 

.820  742 

•354  5i66 

.087 

.472  0781 

.965  365 

•337  2267 

.038 

•450  7977 

.823  564 

•354  1623  ~ 

.088 

.472  5124 

.968  331 

.3368896 

.039 

.451  2320 

.826  389 

•353  8083 

.089 

.472  9467 

.971  301 

.336  5529 

1.040 

0.451  6663 

2.829  217 

0-353  4547 

1.090 

0.473  3810 

2.974  274 

0.336  2165 

.041 

.452  1006 

.832  048 

.353  1014 

.091 

•473  8153 

•  977  250   .335  8804 

.042 

•452  5349 

.834  881 

•352  7485 

.092 

.474  2406 

.980  229   .335  5447 

.043 

.452  9691 

•837  717 

•352  3959 

.093 

.474  6839 

.983  210   .335  2094 

.044 

•453  4034 

.840  557 

.352  0437 

.094 

.475  1182 

.986  195   .334  8743 

1.045 

0.453  8377 

2.843  399 

0.351  6918 

1.095 

0.475  5525 

2.989  183  0.334  5396 

.046 

.454  2720 

.846  243 

•351  3403 

.096 

.475  9868 

.992  173 

•334  2052 

.047 

.454  7063 

.849  091 

•350  0891 

.097 

.476  4210 

•333  8712 

.048 

.455  1406 

.851  942 

•350  6383 

.098 

•476  8553 

.998  164 

•333  5375 

.049 

•455  5749 

.854  795 

•350  2879 

.099 

.477  2896 

3.001  163 

•333  2041 

1.050 

0.456  0092 

2.857  651 

0.349  9377 

1.  100 

0.477  7239 

3.004  166 

0.332  8711 

loge(e°) 

lofllo(eu) 

eu 

e~u 

logc(eu) 

log,,,(eu) 

en 

e— 

SMITHSONIAN  TABLES 


236 


The  Exponential. 


u 

looio(eu) 

eu 

e-u 

u 

logio(eu) 

eu 

e~u 

I.IOO 

0.477  7239 

3.004  166 

0.332  8711 

I.I5O 

0.499  4387 

3.158  193 

0.316  636 

.101 

.478  1582 

.007  172 

.332  5384 

.151 

.499  8729 

.161  353 

.316  320 

.102 

.478  5925 

.010  180 

.332  2060 

.152 

-500  3072 

.164  516 

.316  004 

.103 

.479  0268 

.013  192 

.331  8740 

•153 

.500  7415 

.  167  682 

.315688 

.104 

.479  4611 

.016  207 

•331  5423 

.154 

.501  1758 

.170  851 

.315  372 

1.105 

0.479  8954 

3.019  224 

0.331  2109 

1.  155 

0.501  6101 

3.174  023 

0.315  057 

.106 

.480  3297 

.022  245 

•330  8798 

.156 

.502  0444 

.177  199 

.314  742 

.107 

.480  7640 

.025  269 

•330  5491 

.157 

.502  4787 

.  180  378 

.3U  428 

.108 

.481  1983 

.028  296 

-330  2187 

.158 

.502  9130 

.183  560 

.3H  ii3 

.109 

.481  6326 

.031  326 

.329  8887 

•  159 

.503  3473 

.186  745 

.313  799 

1.  1  10 

0.482  0669 

3-034  358 

0.329  5590 

1.160 

0.503  7816 

3-189  933 

0.313  486 

.in 

.482  5012 

.037  394 

.329  2296 

.161 

.504  2159 

.193  125 

.313  172 

.112 

.482  9355 

.040  433 

.328  9005 

.162 

.504  6502 

.196  320 

.312  859 

•113 

.483  3698 

.043  475 

.328  57i8 

.163 

.505  0845 

.199  517 

.312  547 

.114 

.483  8041 

.046  520 

.328  2434 

.164 

.505  5i88 

,.202  719 

.312  234 

I.H5 

0.484  2383 

3.049  568 

0.327  9153 

1.165 

0.505  9531 

3.205  923 

0.311  922 

.116 

.484  6726 

.052  619 

.327  5875 

.166 

.506  3874 

.209  130 

.311  610 

.117 

.485  1069 

.055  673 

.327  2601 

.!67 

.506  8217 

.212  341 

.311  295 

.118 

.485  5412 

.058  731 

.326  9330 

.168 

.507  2560 

.215  555 

.310  988 

.119 

.485  9755 

.061  791 

.326  6062 

.169 

.507  6902 

.218  772 

.310  677 

I.I2O 

0.486  4098 

3.064  854 

0.326  2798 

1.170 

0.508  1245 

3.221  993 

0.310  366 

.121 

.486  8441 

.067  921 

.325  9537 

.171 

.508  5588 

.225  216 

.310  056 

.122 

.487  2784 

.070  990 

.325  6279 

.172 

.508  9931 

.228  443 

.309  746 

.123 

.487  7127 

.074  063 

.325  3024 

.173 

.509  4274 

.231  673 

.309  437 

.124 

.488  1470 

.077  138 

.324  9773 

.174 

.509  8617 

.234  906 

.309  128 

1.  125 

0.488  5813 

3.080  217 

0.324  6525 

I.I75 

0.510  2960 

3-238  143 

0.308  819 

.126 

.489  0156 

.083  209 

.324  3280 

.176 

•510  7303 

.241  383 

.308  510 

.127 

.489  4499 

.086  383 

.324  0038 

.177 

.511  1646 

.244  626 

.308  202 

.128 

.489  8842 

.089  47i 

.323  6800 

.178 

.511  5989 

.247  872 

•307  893 

.129 

.490  3185 

.092  562 

.323  3565 

.179 

.512  0332 

.251  121 

.307  585 

I.I30 

0.490  7528 

3.095  657 

0.323  0333 

1.180 

0.512  4675 

3.254  374 

0.307  278 

.131 

.491  1871 

.098  754 

.322  7104 

.181 

.512  9018 

.257  630 

.306  971 

.132 

.491  6214 

.101  854 

.322  3878 

.182 

.513  336i 

.260  889 

.306  664 

•133 

.492  0556 

.104  957 

.322  0656 

.183 

.513  7704 

.264  152 

.306  358 

•134 

.492  4899 

.108  064 

.321  7437 

.184 

.514  2047 

.267  418 

.306  052 

1.  135 

0.492  9242 

3.  i  n  174 

0.321  4221 

1.185 

0.514  6300 

3.270  687 

0.305  746 

.136 

•493  3585 

.114  286 

.321  1009 

.186 

.515  0733 

•273  959 

.305  440 

•137 

•493  7928 

.117  402 

.320  7799 

.187 

.515  5075 

.277  235 

.305  135 

.138 

.494  2271 

.120  521 

•320  4593 

.188 

.515  9418 

.280  514 

.304  830 

•139 

.494  6614 

.123  643 

.320  1390 

.189 

.516  3761 

.283  796 

.304  525 

I.I40 

0.495  0957 

3.126  768 

0.319  8190 

1.190 

0.516  8104 

3.287  081 

0.304  221 

.141 

•495  5300 

.  129  897 

.319  4994 

.  .191 

.517  2447 

.290  370 

.303  917 

.142 

.495  9643 

.133  028 

.319  1800 

.192: 

.517  6790 

.293  662 

.303  613. 

•143 

.496  3986 

.136  163 

.318  8610 

.193 

.5i8  1133 

.296  957 

.  .303  310 

.144 

.496  8329 

.139  300 

.318  5423 

.194 

•5i8  5476 

.300  256 

.303  006 

1.  145 

0.497  2672 

3.142  441 

0.318  2239 

1.  195 

0.518  9819 

3.303  558 

0.302  704 

.146 

.497  7015 

.145  585 

.317  9059 

.196 

.519  4162 

.306  863 

.302  401 

.147 

.498  1358 

•148  733 

.317  588i 

.197 

.519  8505 

.310  172 

.302  009 

.148 

.498  5701 

.151  883 

.317  2707 

.198 

.520  2848 

.313  483 

•301  797 

.149 

.499  0044 

.155  036 

•316  9536 

.199 

.520  7191 

.316  798 

.301  493 

I.I5O 

0.499  4387 

3.158  193 

0.316  6368 

1.200 

0.521  1534 

3.320  117 

0.301  194 

looe(eu) 

Iofl10(eu) 

eu 

e-u 

looe(eu) 

looio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


237 


The  Exponential. 


u 

looio(eu) 

en 

e- 

u 

logio(eu) 

eu 

e~u 

I.2OO 
.201 
.202 
.203 
.204 

0.521  1534 

.521  5877 

.522  0220 
.522  4563 
.522  8906 

3.320  117 
.323  439 
.326  764 
.330  092 
•333  424 

0.301  1942 
•300  8932 
.300  5924 
.300  2920 
.299  99i8 

I.25O 
.251 
.252 
.253 
•  254 

0.542  8681 
•543  3024 
.543  7367 
.544  1710 
.544  6053 

3-490  343 
•493  835 
•497  331 
.500  830 
•504  332 

0.286  5048 
.286  2184 
.285  9324 
.285  6466 
.285  3611 

1.205 

.206 

.207 

.208 

.209 

0.523  3249 
.523  7591 
•524  1934 
.524  6277 
.525  O62O 

3.336  759 
.340  098 
•343  439 
.346  784 
•350  133 

0.299  6920 
.299  3925 
.299  0932 
.298  7943 
.298  4956 

1.255 
.256 

.257 
.258 
.259 

0.545  0396 

.545  4739 
•545  9082 
.546  3425 
.546  7768 

3.507  838 
.5ii  348 
.514  85i 
.518  378 
.521  898 

0.285  0758 
.284  7909 
.284  5063 
.284  2219 
.283  9378 

1.  210 
.211 
.212 
.213 

.214 

0.525  4963 
.525  9306 
.526  3649 
.526  7992 
.527  2335 

3-353  485 
.356  840 
.360  198 
.363  56o 
.366  925 

0.298  1973 
.297  8992 
.297  6015 
.297  3040 
.297  0069 

1.260 
.261 
.262 
.263 
.264 

0.547  21  IO 
•547  6453 
.548  0796 
.548  5139 
.548  9482 

3.525  421 
.528  949 
.532  479 
.536  014 
.539  551 

0.283  6540 
.283  3705 
.283  0873 
.282  8043 
.282  5217 

1.  215 
.216 
.217 
.218 
.219 

0.527  6678 
.528  102  I 
.528  5364 
.528  9/07 
.529  4050 

3.370  294 
.373  666 
.377  041 
.380  420 
.383  802 

0.296  7100 
.296  4135 
.296  1772 
.295  8212 
.295  5255 

1.265 
.266 
.267 
.268 
.269 

0.549  3825 

.549  8168 
•550  2511 
•550  6854 
•  551  H97 

3-543  093 
.546  638 
.550  186 

•553  738 
.557  293 

0.282  2393 
.281  9572 
.281  6754 
.281  3938 
.281  1126 

I.22O 
.221 
.222 
.223 

.224 

0.529  8393 
•530  2736 
•530  7079 
.531  1422 
•531  5764 

3.387  188 
.390  577 
.393  969 
•397  365 
.400  764 

0.295  2302 
•294  9351 
.294  6403 
.294  3458 
.294  0516 

1.270 
.271 
.272 
.273 
.274 

0.551  5540 
•551  9883 
.552  4226 
.552  8569 
•553  2912 

3.56o  853 
.564  415 
.567  981 
.571  55i 
•575  124 

0.280  8316 
.280  5509 
.280  2705 
.279  9904 
.279  7105 

1.225 

.226 
.227 
.228 
.229 

0.532  0107 

.532  4450 
•532  8793 
•533  3136 
.533  7479 

3.404  166 
.407  572 
.410  981 
.414  394 
.417  810 

0.293  7577 
.293  4641 
.293  1708 
.292  8777 
.292  5850 

1.275 
.276 
.277 
.278 
.279 

0.553  7255 
•554  1598 
•554  5941 
•555  0283 
•555  4626 

3.578  701 
.582  282 
.585866 
.589  454 
.593  045 

0.279  4310 
.279  1517 
.278  8727 
.2/8  5939 
.278  3155 

1.230 
.231 
.232 
•233 
.234 

0.534  1822 
.534  6165 
•535  0508 
•535  4851 
.535  9194 

3.421  230 
.424  652 
.428  079 
.431  509 
.434  942 

0.292  2926 
.292  0004 
.291  7086 
.291  4170 
.291  1257 

1.280 

[282 
.283 
.284 

0.555  8969 
.556  3312 
.556  7655 
•557  1998 
•557  6341 

3.596  640 
.600  238 
.603  840 
.607  446 
.611  055 

0.278  0373 
.277  7594 
.277  4818 
.277  2044 
.276  9274 

1.235 
.236 
.237 
.238 
.239 

0.536  3537 
.536  7880 
.537  2223 
•537  6566 
.538  0909 

3.438  379 
.441  819 
.445  262 
.448  709 
.452  160 

0.290  8348 
.290  5441 
.290  2537 
.289  9636 
.289  6737 

1.285 
.286 
.287 
.288 
.289 

0.558  0684 
.558  5027 
.558  9370 
.559  3713 
•559  8056 

3.614  668 
.618  284 
.621  905 
.625  528 
.629  156 

0.276  6506 
.276  3741 
.276  0978 
.275  8219 
.275  5462 

I.24O 
.241 
.242 

.243 
•  244 

0.538  5252 
.538  9595 
•539  3937 
.539  8280 
.540  2623 

3.455  613 
•459  071 
.462  532 
.465  996 
.469  464 

0.289  3842 
.289  0950 
.288  8060 
.288  5174 
.288  2290 

1.290 
.291 
292 
293 
.294 

0.560  2399 
.560  6742 
.561  1085 
.561  5428 
.561  9771 

3.632  787 
.636  421 
.640  059 
.643  70i 
.647  347 

0.275  2708 
•274  9956 
.274  7208 
.274  4462 
.J74  1/19 

1.245 
.246 
.247 
.248 
.249 

0.540  6066 
.541  1309 
.541  5652 
•541  9995 
.542  4338 

3.472  935 

.179  888 
.483  369 
.486  854 

0.287  9409 
.287  6531 
.287  3656 
.287  0784 
.286  79U 

1.295 
.296 
.297 
.298 
.299 

0.562  4114 
.562  8456 
.563  2709 
.563  7142 
.564  1485 

3,650  996 
.654  <>49 
.658  305 
.661  065 
.665  629 

0.273  fy/9 

.273  35o6 
._>;:,  0774 
.272  8045 

1.250 

0.542  8681 

3-490  343 

0.286  5048 

1.300 

0.564  5828 

3.6Y*; 

0.272  5318 

,.*(.•> 

looio(eu) 

e" 

e- 

loo«,(ea) 

loo,o(eu) 

eu 

e~"u 

SMITHSONIAN  TABLCS 


238 


The  Exponential. 


u 

U>Qio(eu) 

eu 

e~u 

u 

logio(en) 

eu 

e~u 

1.300 

0.564  5828 

3.669  297 

0.272  53l8 

1-350 

0.586  2976 

3.857  426 

0.259  2403 

.301 

.565  0171    .672  9<38 

.272  2594 

.351 

.586  73i8 

.861  285 

.258  9811 

.302 

.565  4514 

.676  643 

.271  9873 

•  352 

.587  1661 

.865  148 

.258  7223 

.303 

.565  8857 

.680  321 

.271  7154 

.353 

.587  6004 

.869  015 

.258  4637 

.304 

.566  3200 

.684  003 

.271  4438 

•  354 

.588  0347 

.872  886 

.258  2054 

1.305 

0.566  7543 

3-687689 

0.271  1725 

1.355 

0.588  4600 

3.876  761 

0.257  9473 

.306 

.567  1886 

.691  379 

.270  9015 

•  356 

.588  0033 

.880  640 

.257  6895 

.307 

.567  6229 

.695  072 

.270  6307 

•  357 

.589  3376 

.884  522 

.257  4319 

.308 

.568  0572 

.698  769 

.270  3602 

.358 

•589  7719 

.888409 

.257  1746 

.309 

.568  4915 

.702  469 

.270  0900 

.359 

.590  2062 

.892  299 

.256  9176 

1.310 

0.568  9258 

3.706  174 

0.269  8201 

1.360 

0.590  6405 

3-806  193 

0.256  6608 

.311 

.569  3601 

.709  882 

.269  5504 

.361 

.591  0748 

.900  091 

.256  4042 

.312 

.569  7944 

.713  593 

.269  2810 

.362 

•591  5091 

.903  993 

.256  1480 

.313 

.570  2287 

.717  309 

.269  0118 

.363 

.591  9434 

.907  899 

.255  8919 

.314 

.570  6629 

.721  028 

.268  7429 

.364 

•592  3777 

.911  809 

.255  6362 

1.315 

0.571  0972 

3.724  751 

0.268  4743 

1.365 

0.592  8120 

3.915  723 

0.255  3807 

.316 

.571  5315 

.728  478 

.268  2060 

.366 

.593  2463 

.919  641 

.255  1254 

.317 

.571  9658 

.732  208 

.267  9379 

.367 

.593  6806 

.923  562 

.254  8704 

.318 

.572  4001 

•735  942 

.267  6701 

.368 

.594  1149 

.927  488 

.254  6157 

.319 

.572  8344 

.739  680 

.267  4026 

.369 

•594  5491 

•931  417 

.254  3612 

1.320 

0.573  2687 

3-743  421 

0.267  1353 

1.370 

0.594  9834 

3-935  351 

0.254  1070 

.321 

•573  7030 

•747  167 

.266  8683 

•  371 

.595  4177 

.939  288 

.253  8530 

.322 

-574  1373 

.750  916 

.266  6016 

•  372 

•595  8520 

.943  229 

.253  5993 

.323 

•574  57i6 

.754  669 

.266  3351 

•  373 

.596  2863 

•947  174 

.253  3458 

.324 

•575  0059 

.758  425 

.266  0689 

•  374 

.596  7206 

•951  124 

.253  0926 

1.325 

0.575  4402 

3.762  185 

0.265  8030 

1-375 

0.597  1549 

3.955  077 

0.252  8306 

.326 

.575  8745 

.765  949 

.265  5373 

.376 

•597  5892 

•959  034 

.252  5869 

.327 

.576  3088 

.769  717 

.265  2719 

•  377 

.598  0235 

.062  995 

.252  3344 

.328 

.576  7431 

•773  489 

.265  0067 

.378 

.598  4578 

.966  960 

.252  0822 

.329 

•577  1774 

.777  264 

.264  7419 

•  379 

.598  8921 

.970  929 

.251  8303 

1.330 

0.577  6117 

3.781  043 

0.264  4773 

1.380 

0.599  3264 

3.974  902 

0.251  5786 

•  331 

.578  0460 

.784  826 

.264  2129 

.381 

.599  7607 

.978  879 

.251  3271 

.332 

.578  4802 

.788  613 

.263  9488 

.382 

.600  1950 

.982  859 

.251  0759 

•333 

.578  9M5 

.792  404 

.263  6850 

.383 

.600  6293 

.986844 

.250  8249 

•  334 

•579  3488 

.795  198 

.263  4215 

.384 

.601  0636 

.990  833 

.250  5742 

1-335 

0-579  7831 

3.799  996 

0.263  1582 

1.385 

0.601  4979 

3.994  826 

0.250  3238 

-336 

.580  2174 

.803  798 

.262  8951 

.386 

.601  9322 

.998823 

.250  0736 

•  337 

.580  6517 

.807  604 

.262  6324 

.387 

.602  3664 

4.002  824 

.249  8237 

.338 

.581  0860 

.811  413 

.262  3699 

.388 

.602  8007 

.006  828 

.249  5740 

•  339 

.581  5203 

.815  226 

.262  1076 

.389 

.603  2350 

.010  837 

.249  3245 

1.340 

0.581  9546 

3.819  044 

0.261  8457 

1.390 

0.603  6693 

4.014  850 

0.249  0753 

.341 

.582  3889 

.822  864 

.261  5840 

•  391 

.604  1036 

.018  867 

.248  8264 

•342 

.582  8232 

.826  689 

.261  3225 

•  392 

.604  5379 

.022  888 

.248  5777 

•343 

•583  2575 

.830  518 

.261  0613 

•  393 

.604  9722 

.026  913 

.248  3292 

•  344 

.583  6918 

.834  350 

.260  8004 

.394 

.605  4065 

.030  942 

.248  0810 

1.345 

0.584  1261 

3.838  187 

0.260  5397 

1.395 

0.605  8408 

4.034  975 

0.247  8330 

.346 

.584  5604 

.842  027 

.260  2793 

.396 

.606  2751 

.039  012 

.247  5853 

.347 

.584  9947 

.845  871 

.260  0191 

•  397 

.606  7094 

.043  053 

.247  3379 

.348 

.585  4290 

.849  718 

.259  7593 

.398 

.607  1437 

.047  098 

.247  0907 

•  349 

.585  8633 

•853  570 

.259  4996 

•  399 

.607  578o 

.051  147 

.246  8437 

1-350 

0.586  2976 

3.857  426 

0.259  2403 

1.400 

0.608  0123 

4.055  200 

0.246  5970 

lofle(eu) 

logio(en) 

eu 

e~u 

Io0e(eu) 

looio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


239 


The  Exponential. 


u 

loflio(eu) 

eu 

.- 

u 

looio(en) 

eu 

e~u 

1.400 
.401 
.402 
.403 
.404 

0.608  0123 
.608  4466 
.608  8809 
.609  3152 
.609  7495 

4.O55  2OO 

•059  257 
.063  318 
.067  384 
.071  453- 

0.246  5970 
.246  3505 
.246  1043 
.245  8583 
.245  6125 

1.450 
•  451 
•  452 

•  453 
.454 

0.629  7270 
.630  1613 
•630  5956 
.631  0299 
.631  4642 

4-263  115 
.267  380 
.271  649 
•275  923 
.280  201 

0.234  5703 
.234  3358 
.234  1016 
.233  8676 
•233  6339 

1.405 

.406 

.407 

.408 

.409 

0.610  1837 
.610  6180 
.611  0523 
.611  4866 
.611  9209 

4.075  527 
.079  604 
.083  686 
.087  772 
.091  861 

0.245  36/1 
.245  1218 
.244  8768 
.244  6321 
.244  3875 

1-455 
.456 
•457 
•  458 
•  459 

0.631  8985 
.632  3328 
.632  7671 
.633  2014 
.633  6356 

4.284  483 
.288  770 
.293  06  1 
.297  356 
.301  656 

0.233  4004 
.233  1671 
.232  9340 
.232  7012 
.232  4686 

1.410 

.411 
.412 
.413 
.414 

0.612  3552 
.612  7895 
.613  2238 
.613  6581 
.614  0924 

4.095  955 

.  100  053 

.104  156 
.108  262 

.112  372 

0.244  1433 
.243  8993 
.243  6555 
.243  4120 
.243  1687 

1.460 
.461 
.462 
•463 
•464 

0.634  0609 
.634  5042 
•634  9385 
.635  3728 
•635  8071 

4.305  960 
.310  268 
.314  580 
.318  897 
.323  218 

0.232  2363 
.232  0042 
.231  7723 
.231  5406 
.231  3092 

1.415 
.416 

.417 
.418 
.419 

0.614  5267 
.614  9610 
•615  3953 
.615  8296 
.616  2639 

4.116  486 

.120  605 

.124  728 
.  128  854 
.  132  985 

0.242  9256 
.242  6828 
.242  4402 
.242  1979 
.241  9559 

1.465 
.466 
•  467 
.468 
•  469 

0.636  2414 
.636  6757 
.637  i  zoo 
.637  5443 
.637  9786 

4.327  543 
•331  873 
.336  207 
•340  545 
.344  888 

0.231  0780 
.230  8470 
.230  6163 
.230  3858 
.230  1555 

1.420 

.421 
.422 
.423 
.424 

0.616  6982 
.617  1325 
.617  5668 
.618  ooio 
.618  4353 

4-137  120 
.141  260 

.145  403 
.149  550 
.153  702 

0.241  7140 
.241  4724 
.241  2311 
.240  9900 
.240  7491 

1.470 
.471 
•472 
•473 
.474 

0.638  4129 
•638  8472 
.639  2815 
•639  7158 
.640  1501 

4-349  235 
•353  587 
.357  942 
.362  302 
.366667 

0.229  9255 
.229  6957 
.229  4661 
.229  2367 
.229  0076 

1.425 
.426 

.427 
.428 

.429 

0.618  8696 
.619  3039 
.619  7382 
.620  1725 
.620  6068 

4-157  858 
.162  018 
.166  182 
.170  350 
.174  523 

0.240  5085 
.240  2681 
.240  0279 
.239  788o 
.239  5484 

1.475 
.476 
•  477 
.478 
•  479 

0.640  5844 
.641  0187 
.641  4529 
.641  8872 
.642  3215 

4-371  036 
.375  409 
•379  787 
.384  169 
.388  555 

0.2!28  7787 

.228  5501 
.228  3216 
.228  0934 
.227  8654 

1.430 
.431 
.432 
.433 

.434 

0.621  0411 
.621  4754 
.621  0097 
.622  3440 
.622  7783 

4.178  609 
.182  880 
.187  065 
.191  254 
.195  447 

0.239  3089 
.239  0697 
.238  8308 
.238  5921 
.238  3536 

1.480 
.481 
.482 
.483 
.484 

0.642  7558 
.643  1901 
.643  6244 
.644  0587 
.644  4930 

4.392  946 
•397  34i 
.401  740 
.406  144 
.410  553 

0.227  6377 
.227  4102 
.227  1829 
.226  9558 
.226  7290 

1.435 
.436 
•437 
.438 
•  439 

0.623  2126 
.623  6469 
.624  0812 
.624  5155 
.624  9498 

4.199  645 
.203  847 
.208  053 

.212  263 

.216  477 

0.238  1154 
.237  8774 
.237  6396 
.237  4021 
.237  1648 

1.485 
.486 
.487 
.488 
.489 

0.644  92-73 
.645  3616 
•045  7959 
.646  2302 
.646  6645 

4.414  965 
.419  383 
.423  804 
.428  230 
.432  661 

0.226  5023 
.226  2760 
.226  0498 
.225  8239 

.225  5981 

1.440 
•441 
.442 
•443 
•444 

0.625  3841 
.625  8183 
.626  2526 
.626  6869 

.627  1212 

4.220  696 
.224  919 
.229  146 
.233  377 
.237  612 

0.236  9278 
.236  6909 
.236  4544 
.236  2180 
.235  98i9 

1.490 
.491 
.492 
•493 
•  494 

0.647  0088 
•647  5331 
.647  9674 
.648  4017 
.648  8360 

4.437  096 

•441  535 
•445  979 
.450  427 
•454  879 

0.225  3727 
.225  1474 
.224  9224 
.224  6976 

.224  4730 

1.445 
.446 
•  447 
•  448 
•  449 

0.627  5555 

.628  4241 
.6288584 
.629  2927 

4.241  852 
.246  096 
.250  344 
.254  597 
.258  854 

0.235  7461 
.235  5104 
.235  2751 
.235  0399 
.234  8050 

1.495 
.496 
.497 
.498 
.499 

0.649  2703 
.649  7045 
.650  1388 
.650  5731 
.651  0074 

4.459  337 
.463  798 
.468  J  :>4 
.472  735 
.477  210 

0.224  2486 
.224  0245 
.223  8006 
.223  5769 
•-'-'3  3534 

1.450 

0.629  7270 

4.263  US 

0.234  5703 

1.500 

0.651  4417 

4.481  689 

0.223  1302 

looete") 

M£ 

e° 

.- 

loo«(«u) 

loguXe0) 

'" 

e~n 

SMITHSONIAN  TABLES 


240 


The  Exponential. 


u 

loflio(e") 

eu 

e  u 

u 

looio(en) 

eu 

e~u 

1.500 

0.651  4417 

4.481  689 

0.223  1302 

1.550 

0.673  1564 

4.7H  470 

O.2I2  2480 

.501 

.651  8760 

•486  173 

.222  9O7I 

•551 

.673  5907 

.716  184 

.212  0358 

.502 

.652  3103 

.490  661 

.222  6843 

•  552 

.674  0250 

.720  903 

.211  8239 

.503 

.652  7446 

•495  154 

.222  4618 

•  553 

.674  4593 

.725  626 

.211  6l22 

.504 

.653  1789 

.499  652 

.222  2394 

•  554 

.674  8936 

.730  354 

.211  4007 

1.505 

0.653  6132 

4.504  154 

O.222  OI73 

1.555 

0.675  3279 

4-735  087 

O.2II  1894 

.506 

.654  0475 

.508  660 

.221  7954 

.556 

.675  7622 

.739  824 

.210  9783 

.507 

.654  48i8 

.513  I7i 

.221  5737 

.557 

.676  1905 

.744  566 

.210  7674 

.508 

.654  9161 

.517686 

.221  3522 

.558 

.676  6308 

•749  313 

.210  5568 

.509 

.655  3504 

.522  206 

.221  I3IO 

.559 

.677  0651 

•754  065 

.210  3463 

1.510 

0.655  7847 

4.526  731 

0.220  9100 

1.560 

0.677  4994 

4.758  821 

O.2IO  1361 

.511 

.656  2190 

.531  260 

.220  6892 

.561 

.677  9337 

.763  582 

.209  926O 

.512 

•656  6533 

•  535  793' 

.220  4686 

.562 

.678  3680 

.768  348 

.2O9  7l62 

.513 

.657  0876 

•540  33i 

.220  2482 

.563 

.678  8023 

•  773  H9 

.209  5066 

.514 

.657  5218 

.544  874 

.220  O28l 

.564 

.679  2366 

.777  895 

.209  2972 

1.515 

0.657  9561 

4.549  421 

O.2I9  8082 

1.565 

0.679  6709 

4-782  675 

O.2O9  0880 

.516 

.658  3904 

.553  973 

.219  5885 

.566 

.680  1052 

.787  460 

.208  8790 

.517 

.658  8247 

.558  529 

.219  3690 

.567 

.680  5395 

.792  250 

.2O8  6703 

.518 

.659  2590 

.563  090 

.219  1497 

.568 

.680  9737 

•797  045 

.208  4617 

.519 

.659  6933 

.567  655 

.218  9307 

.569 

.681  4080 

.801  844 

.208  2533 

1.520 

o.65o  1276 

4.572  225 

0.218  7119 

1.570 

0.681  8423 

4.806  648 

O.2O8  O452 

.521 

.660  5619 

.576  8bo 

.218  4933 

•  571 

.682  2766 

.811  457 

.207  8372 

.522 

.660  9962 

.581  379 

.218  2749 

•  572 

.682  7109 

.816  271 

.207  6295 

.523 

.661  4305 

.585  962 

.218  0567 

•  573 

.683  1452 

.821  090 

.207  4220 

.524 

.661  8648 

.590  551 

.217  8388 

•  574 

.683  5795 

.825  913 

.207  2147 

1.525 

0.662  2991 

4.595  144 

0.217  6211 

1-575 

0.684  0138 

4.830  742 

0.207  0076 

.526 

.662  7334 

.599  741 

.217  4035 

.576 

.684  4481 

.835  575 

.206  8006 

.527 

.663  1677 

.604  343 

.217  1862 

•  577 

.684  8824 

.840  413 

.206  5940 

.528 

.663  6020 

.608  950 

.216  9692 

.578 

.685  3167 

.845  256 

.206  3875 

.529 

.664  0363 

.613  561 

.216  7523 

•  579 

.685  75io 

.850  103 

.206  1812 

1.530 

0.664  4706 

4.618  177 

0.216  5357 

1.580 

0.686  1853 

4.854  956 

0.205  9751 

.531 

.664  9049 

.622  797 

.216  3192 

.581 

.686  6196 

.859  813 

.205  7692 

.532 

.665  3391 

.627  422 

.216  1030 

.582 

.687  0539 

.864  675 

.205  5636 

•533 

.665  7734 

.632  052 

.215  8870 

.583 

.687  4882 

.869  543 

.205  358i 

•534 

.666  2077 

.636  687 

.215  6713 

.584 

.687  9225 

.874  415 

.205  1528 

1.535 

0.666  6420 

4.641  326 

0.215  4557 

1.585 

0.688  3568 

4.879  291 

0.204  9478 

.536 

.667  0763 

.645  969 

.215  2403 

.586 

.688  7910 

.884  173 

.204  7429 

•  537 

.667  5106 

.650  617 

.215  02.52 

.587 

.689  2253 

.889  060 

.204  5383 

.538 

.667  9449 

.655  270 

.214  8103 

.588 

.689  6596 

.893  951 

.204  3339 

.539 

.668  3792 

.659  928 

.214  5956 

.589 

.690  0939 

.898  848 

.204  1296 

1.540 

0.668  8135 

4.664  590 

0.214  3811 

1.590 

0.690  5282 

4.903  749 

0.203  9256 

•  541 

.669  2478 

.669  257 

.214  1668 

•  591 

.690  9625 

.908655 

.203  7218 

.542 

.669  6821 

.673  929 

.213  9528 

.592 

.691  3968 

.913  566 

.203  5182 

.543 

.670  1164 

.678  605 

.213  7389 

.593 

.691  8311 

.918  482 

.203  3148 

.544 

.670  5507 

.683  286 

•213  S253 

•  594 

.692  2654 

.923  403 

.203  1115 

1-545 

0.670  9850 

4.687  972 

0.213  3119 

1-595 

0.692  6997 

4.928  329 

O.2O2  9085 

.546 

.671  4193 

.692  662 

.213  0987 

•  596 

.693  1340 

.933  260 

.202  7057 

.547 

.671  8536 

.697  357 

.212  8857 

•  597 

.693  5683 

.938  196 

.202  5031 

.548 

.672  2879 

.702  057 

.212  6729 

.598 

.694  0026 

•943  136 

.202  3007 

.549 

.672  7222 

.706  761 

.212  4603 

•  599 

.694  4369 

.948  082 

.202  0985 

1-550 

0.673  1564 

4.711  470 

O.2I2  2480 

1.  600 

0.694  8712 

4-953  032 

0.201  8965 

loge(en) 

looio(en) 

eu 

e~u 

looe(eu) 

looio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


241 


The  Exponential. 


u 

Ioo10(eu) 

eu 

e~u 

u 

looio(eu) 

eu 

e~u 

1.  600 

0.694  8712 

4-953  032 

0.201  8965 

1.650 

0.716  5859 

5.206  980 

0.  192  0499 

.601 

.695  3055 

•957  988 

.201  6947 

.651 

.717  O202 

.212  189 

.191  8580 

.602 

.695  7398 

.962  948 

.201  4931 

.652 

.717  4545 

.217  404 

.191  6662 

.603 

.696  1741 

.967  9U 

.201  2917 

.653 

.717  8888 

.222  624 

.191  4746 

.604 

.6966083 

.972  884 

.2OI  O9O5 

.654 

.718  3231 

.227  849 

.191  2832 

1.605 

0,697  0426 

4.977  860 

0.200  8896 

1.655 

0.718  7574 

5.233  080 

0.191  0921 

.606 

.097  4769 

.982  840 

.200  6888 

.656 

.719  1917 

.238  3l6 

.190  9011 

.607 

.697  9H2 

.987  825 

.200  4882 

.657 

.719  6260 

•243  557 

.190  7103 

.608 

.698  3455 

.992  816 

.200  2878 

.658 

.720  0603 

.248  803 

.190  5196 

.609 

.698  7798 

.997  811 

.200  0876 

.659 

.720  4945 

•254  054 

.190  3292 

1.610 

0.699  2141 

5.002  811 

o.  109  8876 

1.660 

0.720  9288 

5-259  3ii 

0.190  1300 

.611 

.6996484 

.007  817 

.  199  6878 

.661 

.721  3631 

.264  573 

.1899489 

.612 

.700  0827 

.012  827 

.  199  4882 

.662 

.721  7974 

.269  840 

.189  7591 

.613 

.700  5170 

.017  842 

.199  2888 

.663 

.722  2317 

.275  112 

.189  5694 

.614 

•700  9513 

.022  863 

.199  0897 

.664 

.722  6660 

.280  39O 

.189  3799 

1.615 

0.701  3856 

5.027  888 

0.198  8907 

1.665 

0.723  1003 

5.285  673 

0.189  1907 

.616 

.701  8199 

.032  918 

.198  6919 

.666 

.723  5346 

.290  962 

.189  0016 

.617 

.702  2542 

.037  954 

.198  4933 

.667 

.723  9689 

.296  255 

.188  8127 

.618 

.702  6885 

.042  994 

.198  2949 

.668 

.724  4032 

.301  554 

.  188  6239 

.619 

.703  1228 

.048  040 

.198  0967 

.669 

.724  8375 

.306858 

.1884354 

1.620 

0.703  5571 

5.053  090 

0.197  8987 

1.670 

0.725  2718 

5.312  168 

o.  188  2471 

.621 

.703  9914 

.058  146 

.197  7009 

.671 

.725  7061 

.317  483 

.188  0589 

.622 

.704  4256 

.063  207 

.197  5033 

.672 

.726  1404 

.322  803 

.  187  8709 

.623 

.704  8599 

.068  272 

.197  3059 

.673 

.726  5747 

.328  128 

.  187  6832 

.624 

.705  2942 

.073  343 

.197  1087 

.674 

.727  0090 

•333  459 

.  187  4956 

1.625 

0.705  7285 

5.078  419 

0.196  9117 

1.675 

0.727  4433 

5.338  795 

0.187  3082 

.626 

.706  1628 

.083  500 

.196  7149 

.676 

.727  8776 

••344  137 

.187  12  IO 

.627 

.706  5971 

.088  586 

.196  5182 

.677 

.728  3118 

.349  483 

.  186  9339 

.628 

.707  0314 

.093  677 

.196  3218 

.678 

.728  7461 

.354  836 

.  186  7471 

.629 

.707  4657 

.098  773 

.196  1256 

.679 

.729  1804 

.360  193 

.186  5604 

1.630 

0.707  9000 

5.103  875 

0.195  9296 

1.680 

0.729  6147 

5.365  556 

0.186  3740 

.631 

•70S  3343 

.108  981 

•195  7337 

.681 

.730  0490 

.370  924 

.186  1877 

.632 

.708  7686 

.114  093 

.195  538i 

.682 

•730  4833 

.376298 

.186  0016 

.633 

.709  2029 

.119  209 

.195  3427 

.683 

.730  9176 

.381  677 

.185  8157 

.634 

.709  6372 

.124  331 

.195  1474 

.684 

.731  3519 

.387  061 

.185  6300 

1.635 

0.710  0715 

5.129  458 

0.194  9524 

1.685 

0.731  7862 

5.392  451 

0.185  4444 

.636 

.710  5058 

.134  590 

.194  7575 

.686 

.732  2205 

.397  846 

.185  2591 

.637 

.710  9401 

.139  727 

.194  5629 

.687 

.732  6548 

.403  247 

•185  0739 

.638 

.711  3744 

.144869 

.  194  3684 

.688 

•733  0891 

.408  653 

.1848889 

.639 

.711  8087 

.150  017 

.194  1741 

.689 

•733  5234 

.414  064 

.184  7041 

1.640 

0.712  2430 

S.IS5  170 

0.193  9800 

1.690 

0.733  9577 

5.419  48i 

0.184  5195 

.641 

.712  6772 

.100  327 

.193  7802 

.691 

•734  3920 

•424  903 

•184  3351 

.642 

.713  IH5 

.165  490 

•193  5925 

.692 

.734  8263 

•430  331 

.184  1509 

.643 

.713  5458 

.170  658 

.193  3990 

.693 

.735  2606 

•435  764 

.183  9668 

.644 

.713  9801 

.175  831 

.193  2057 

.694 

•735  6949 

.441  202 

.183  7829 

i  '645 

0.714  4144 

5.181  oio 

0.193  0126 

1.695 

0.736  1291 

5.446  646 

0.183  5992 

.646 

.714  8487 

.186  194 

.  192  8196 

.(*/> 

•  73<>  5".>l 

•  45^  095 

.183  4157 

.647 

.715  2830 

.191  382 

.192  6269 

.697 

.736  9977 

•457  550 

.183  -'3-'4 

.648 

.715  7173 

.106  576 

.192  4344 

.698 

.737  4320 

.463  oio 

.  18;, 

.649 

.716  1516 

.201  775 

.192  2421 

.699 

•737  8663 

.468  476 

.  182  8663 

1.650 

0.716  5859 

5.206  980 

0.192  0499 

1.700 

0.738  3006 

5-473  947 

0.182  6835 

loo,(eu) 

loQicXe") 

e" 

e~u 

looo(eu) 

loo,,Xeu) 

ett 

e~u 

SMITHSONIAN  TABLES 


242 


The  Exponential. 


u 

looio(eu) 

eu 

e~u 

u 

looio(eu) 

eu 

e~u 

1.700 

0.738  3006 

5-473  947 

0.182  6835 

1-750 

0.760  0153 

5.754  603 

0.173  7739 

.701 

.738  7349 

.479  424 

.182  5009 

•  751 

.760  4496 

.760  360 

.173  6003 

.702 

.739  1692 

.484  906 

.182  3185 

•  752 

.760  8839 

.766  123 

.173  4267 

.703 

.739  6o35 

•490  394 

.182  1363 

•  753 

.761  3182 

.771  892 

.173  2534 

.704 

.740  0378 

-495  887 

.181  9542 

•  754 

.761  7525 

.777  667 

.173  0802 

1.705 

0.740  4721 

5.501  386 

0.181  7724 

1.755 

0.762  1868 

5.783  448 

0.172  9072 

.706 

.740  9064 

.506  890 

.181  5907 

.756 

.762  6211 

.789  234 

.172  7344 

.707 

.741  3407 

.512  399 

.181  4092 

•  757 

.763  0554 

.795  026 

.172  5618 

.708 

.741  7750 

.517  915 

.181  2279 

.758 

.763  4897 

.800  824 

.172  3893 

.709 

.742  2093 

.523  435 

.181  0467 

•  759 

.763  9240 

.806  628 

.172  2170 

I.7IO 

0.742  6436 

5.528  961 

0.180  8658 

1.760 

0.764  3583 

5.812  437 

0.172  0449 

.711 

•743  0779 

.534  493 

.  180  6850 

.761 

.764  7926 

.818  253 

.171  8729 

.712 

.743  5122 

.540  030 

.180  5044 

.762 

.765  2269 

.824  074 

.171  7011 

.713 

•743  9464 

•545  573 

.180  3240 

.763 

.765  6612 

.829  901 

.171  5295 

.714 

.744  3807 

•551  I22 

.180  1438 

.764 

.766  0955 

.835  734 

.171  358i 

I.7I5 

0.744  8150 

5.556  676 

0.179  9637 

1.765 

0.766  5298 

5.841  572 

0.171  1868 

.7J6 

.745  2493 

.562  235 

.179  7838 

.766 

.766  9641 

.847  417 

.171  0157 

.717 

•745  6836 

.567  800 

.179  6042 

.767 

.767  3983 

.853  267 

.170  8448 

.718 

.746  1179 

•573  371 

.  179  4246 

.768 

.767  8326 

.859  123 

.170  6740 

.719 

.746  5522 

.578  947 

.  179  2453 

.769 

.768  2669 

.864  985 

.170  5034 

1.720 

0.746  9865 

5.584  528 

0.179  0661 

1.770 

0.768  7012 

5-870  853 

0.170  3330 

.721 

.747  4208 

.590  116 

.  178  8872 

.771 

.769  1355 

.876  727 

.170  1627 

.722 

.747  8551 

•595  709 

.  178  7084 

.772 

.769  5698 

.882  607 

.  169  0927 

.723 

.748  2894 

.601  307 

.178  5298 

•  773 

.770  0041 

.888  492 

.  169  8228 

.724 

.748  7237 

.606  911 

.178  3513 

.774 

.770  43^4 

.894  384 

.169  6530 

1.725 

0.749  1580 

5.612  521 

0.178  1731 

1.775 

0.770  8727 

5.900  281 

0.169  4834 

.726 

.749  5923 

.618  136 

.177  9950 

•  776 

•771  3070 

.906  184 

.169  3HI 

.727 

.750  0266 

.623  757 

.177  8171 

•  777 

.771  7413 

.912  094 

.169  1448 

.728 

.750  4609 

.629  384 

.  177  6393 

.778 

.772  1756 

.918  009 

.  168  9758 

.729 

•750  8952 

.635  016 

.  177  4618 

•  779 

.772  6099 

.923  930 

.168  8069 

1.730 

0.751  3295 

5.640  654 

o.  177  2844 

1.780 

0.773  0442 

5.929  856 

o.  168  6381 

•  731 

.751  7637 

.646  297 

.177  1072 

.781 

•773  4785 

•935  789 

.168  4696 

•  732' 

.752  1980 

.651  947 

.176  9302 

.782 

.773  9128 

.941  728 

.168  3012 

•  733 

.752  6323 

.657  601 

.176  7534 

.783 

•774  3471 

•947  673 

.168  1330 

•  734 

.753  0666 

.663  262 

.176  5767 

.784 

.774  7814 

•953  623 

.  167  9649 

I  •  735 

0-753  5009 

5,668  928 

0.176  4002 

1.785 

0.775  2157 

5.959  580 

0.167  797i 

.736 

•753  9352 

.674  600 

.176  2239 

.786 

.775  6499 

.965  543 

.107  6293 

.737 

•754  3695 

.680  277 

.176  0478 

.787 

.776  0842 

•971  5ii 

.167  4618 

.738 

.754  8038 

.685  060 

.175  8718 

.788 

.776  5185 

.977  486 

.167  2944 

.739 

.755  2381 

.691  649 

.175  6960 

.789 

.776  9528 

.983466 

.167  1272 

1.740 

0.755  6724 

5.697  343 

0.175  5204 

1.790 

0.777  3871 

5.989  452 

0.166  9602 

.741 

.756  1067 

.703  044 

.175  3450 

.791 

.777  8214 

•995  445 

.166  7933 

.742 

.756  5410 

.708  750 

.175  1697 

.792 

.778  2557 

6.001  443 

.  166  6266 

•  743 

.756  9753 

.714  461 

.174  9946 

.793 

.778  6900 

.007  448 

.166  4600 

•  744 

.757  4096 

.720  178 

.174  8197 

•  794 

.779  1243 

.013  458 

.  166  2937 

1.745 

0.757  8439 

5.725  901 

o.  174  6450 

1.795 

0.779  5586 

6.019  475 

0.166  1275 

.746 

.758  2782 

•731  630 

.174  4704 

.796 

•779  9929 

.025  497 

.165  9614 

*  -747 

.758  7125 

•737  365 

.174  2960 

•  797 

.780  4272 

.031  526 

.165  7955 

^  .748 

.759  1468 

•743  105 

.174  1218 

.798 

.780  8615 

.037  56o 

.165  6298 

.749 

•759  58io 

.748  851 

•173  9478 

•  799 

.781  2958 

.043  601 

.165  4643 

1-750 

0.760  0153 

5.754  603 

0.173  7739 

1.800 

0.781  7301 

6.049  647 

0.165  2989 

loge(eu) 

looio(eu) 

eu 

e~u 

looe(eu) 

logio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


243 


The  Exponential. 


u 

looio(eu) 

e" 

e 

u 

Iog10(ea) 

e° 

e~u 

1.800 

0.781  7301 

6.049  647 

0.165  2989 

1.850 

0.803  4448 

6.359  820 

0.157  2372 

.801 

.782  1644 

.055  700 

.165  1337 

'  .851 

.803  8791 

.366  183 

.157  0800 

.802 

.782  5587 

.061  759 

.164  9686 

.852 

.804  3134 

•372  552 

.156  9230 

.803 

.783  0330 

.067  824 

.  164  8037 

.853 

.804  7477 

.378  928 

.156  7662 

.804 

.783  4672 

.073  895 

.  164  6390 

.854 

.805  1820 

-385  310 

.156  6095 

1.805 

0.783  9015 

6.079  971 

0.  164  4745 

1.855 

0.805  6163 

6.391  698 

0.156  4529 

.806 

.784  3358 

.086  054 

.164  3101 

.856 

.806  0506 

.398  093 

.156  2966 

.807 

.784  7701 

.092  144 

.164  1458 

.857 

.806  4849 

.404  494 

.156  1403 

.808 

.785  2044 

.098  239 

.163  9818 

.858 

.806  9191 

.410  902 

.155  9843 

.809 

.785  6387 

.104  340 

.163  8179 

.859 

.807  3534 

.417  316 

.155  8284 

1.810 

0.786  0730 

6.  I  10  447 

0.163  6541 

1.860 

0.807  7877 

6.423  737 

0.155  6726 

.811 

.786  5073 

.116  561 

.163  4906 

.861 

.808  2220 

.430  164 

.155  5170 

.812 

.786  9416 

.122  68l 

.163  3272 

.862 

.808  6563 

.436  597 

.155  3616 

.813 

.787  3759 

.128  806 

.163  1639 

.863 

.809  0906 

•443  037 

.155  2063 

.814 

.787  8102 

.134  938 

.163  0008 

.864 

.809  5249 

.449  483 

.155  0512 

1.815 

0.788  2445 

6.141  076 

0.162  8379 

1.865 

0.809  9592 

6.455  936 

0.154  8962 

.816 

.788  6788 

.147  220 

.162  6752 

.866 

.810  3935 

•462  395 

.154  7414 

.817 

.789  H3I 

•153  371 

.162  5126 

.867 

.810  8278 

.468  861 

.  154  5867 

.818 

.789  5474 

.159  527 

.162  3501 

.868 

.811  2621 

•475  333 

.  154  4322 

.819 

.789  98i7 

.165  690 

.162  1879 

.869 

.811  6964 

.481  811 

.  154  2779 

1.820 

0.790  4160 

6.171  858 

0.162  0258 

1.870 

0.812  1307 

6.488  296 

0.154  1237 

.821 

.790  8503 

.  178  033 

.161  8638 

..871 

.812  5650 

.494  788 

•153  9696 

.822 

.791  2845 

.184  215 

.161  7020 

.872 

.812  9093 

.501  286 

.153  8157 

.823 

.791  7188 

.190  402 

.161  5404 

.873 

•813  4336 

.507  791 

.153  6620 

.824 

•792  1531 

.196  595 

.161  3789 

.874 

.813  8679 

.514  302 

.153  5084 

1.825 

0.792  5874 

6.  202  795 

0.161  2176 

1.875 

0.814  3022 

6.520  819 

0.153  3550 

.826 

.793  0217 

.209  ooi 

.161  0565 

.876 

.814  7364 

.527  343 

.153  2017 

.827 

•793  4500 

.215  213 

.  160  8955 

.877 

.815  1707 

•533  874 

.153  0486 

.828 

.793  8903 

.221  431 

.160  7347 

.878 

.815  6050 

.540  411 

.152  8956 

.829 

.794  3246 

.227  656 

.160  5741 

.879 

.816  0393 

.546  955 

.152  7428 

1.830 

0.794  7589 

6.233  887 

0.160  4136 

1.880 

0.816  4736 

6.553  505 

0.152  5901 

.831 

•795  1932 

.240  124 

.160  2532 

.881 

.816  9079 

.560  062 

•152  4376 

.832 

.795  6275 

.246  367 

.160  0931 

.882 

.817  3422 

.566  625 

.152  2852 

.833 

.796  0618 

.252  616 

.  159  9330 

.883 

.817  7765 

•  573  195 

.152  1330 

.834 

.796  4961 

.258  872 

.159  7732 

.884 

.818  2108 

•579  771 

.151  9810 

1.835 

0.796  9304 

6.265  134 

o.  159  6135 

1.885 

0.818  6451 

6.586  354 

0.151  8291 

.836 

•797  3647 

.271  402 

.159  4540 

.886 

.819  0794 

.592  944 

.151  677J 

.837 

•797  7990 

.277  677 

.159  2946 

.887 

.819  5137 

•599  540 

•151  5257 

.838 

.798  2333 

.283  958 

.159  1354 

.888 

.819  9480 

.606  143 

.151  3743 

.839 

.798  6676 

.290  245 

.158  9763 

.889 

.820  3823 

.612  753 

.151  2230 

1.840 

0.799  1018 

6.296  538 

0.158  8174 

1.890 

0.820  8166 

6.619  369 

0.151  0718 

.841 

•799  536i 

.302  838 

.158  6587 

.891 

.821  2509 

.625  991 

.150  9208 

.842 

•799  9704 

.309  M4 

.158  5001 

.892 

.821  6852 

.632  621 

.  150  7700 

.843 

.800  J047 

.315  456 

.158  3417 

.893 

.822  1195 

.639  257 

.150  6193 

.844 

.800  8390 

.321  775 

.158  1834 

.894 

.822  5537 

.645  899 

.  150  4687 

1.845 

0.801  2733 

6.328  loo 

0.158  0253 

1.895 

0.822  9880 

6.652  548 

0.150  3183 

.846 

.801  7076 

•334  43i 

.157  8'>74 

.896 

.823  4223 

.659  204 

.150  1681 

.847 

.802  1419 

•340  769 

.157  7096 

.897 

.823  8566 

.665  867 

.150  0180 

.848 

.802  5762 

•  347  H3 

.157  5520 

.898 

.824  2909 

.672  536 

.  149  8681 

.849 

.803  0105 

•353  463 

.157  3945 

.899 

.824  7252 

.679  212 

.149  7183 

1.850 

0.803  4448 

6.359  820 

0.157  2372 

1.900 

0.825  1595 

6.685  804 

0.149  5686 

log.V) 

looir/e0) 

6° 

e-n 

IOQe(eU) 

KxMe") 

eu 

e~u 

SMITHSONIAN  TABLES 


244 


The  Exponential. 


u 

looio(en) 

eu 

e~u 

u 

loaio(e°) 

en 

e~u 

1.900 

0.825  1595 

6.685  894 

0.149  5686 

1.950 

0.846  8742 

7.028688 

0.142  2741 

.001 

•825  5938 

.692  584 

.  149  4191 

•  951 

.847  3085 

.035  720 

.142  1319 

.902 

.826  0281 

.699  280 

.149  2698 

•  952 

.847  7428 

.042  759 

.141  9898 

.003 

.826  4624 

.705  082 

.149  1206 

.953 

.848  1771 

.049  805 

.141  8479 

.004 

.826  8967 

.712  692 

.148  9715 

•954 

.848  6114 

.056  859 

.141  7061 

1.905 

0.827  3310' 

6.719  408 

0.148  8226 

1.955 

0.849  0457 

7.063  919 

0.141  5645 

.906 

.827  7653 

.726  130 

.  148  6739 

.956 

.849  4800 

.070  986 

.141  4230 

.907 

.828  1096 

.732  860 

.  148  5253 

.957 

.849  9143 

.078  061 

.141  2816 

.908 

.828  6339 

•739  596 

•  148  3768 

•  958 

.850  3486 

.085  143 

.141  1404 

.909 

.829  0682 

.746  339 

.148  2285 

•959 

.850  7829 

.092  231 

.140  9993 

I.9IO 

0.829  5025 

6.753  089 

0.148  0804 

1.960 

0.851  2172 

7.099  327 

0.140  8584 

.911 

.829  9368 

•759  845 

.147  9324 

.961 

.851  6515 

.106  430 

.140  7176 

.912 

.830  3710 

.766  608 

.147  7845 

.962 

.852  0858 

.113  540 

.140  5770 

.913 

.830  8053 

.773  378 

.  147  6368 

.963 

.852  5201 

.120  657 

.  140  4365 

.914 

.831  2396 

.780  155 

.147  4892 

.964 

.852  9544 

.127  781 

.140  2961 

I.9I5 

0.831  6739 

6.786  939 

0.147  34l8 

1.965 

0.853  3887 

7.I349I3 

0.140  1559 

.916 

.832  1082 

•793  729 

.147  1946 

.966 

.853  8230 

.142  051 

.140  0158 

.917 

.832  5425 

.800  526 

.147  0474 

.967 

.854  2572 

.149  197 

.139  8759 

.918 

.832  9768 

.807  330 

.146  0005 

.968 

.854  6915 

.156  349 

.139  7300 

.919 

.833  4IH 

.814  141 

.146  7536 

.969 

.855  1258 

.163  509 

.139  596"4 

1.920 

0.833  8454 

6.820  958 

0.146  6070 

1.970 

0.855  5601 

7.170  676 

0.139  4569 

.921 

.834  2797 

.827  783 

.146  4604 

.971 

.855  9944 

•177  851 

.139  3175 

.922 

.834  7140 

.834  614 

.146  3140 

.972 

.856  4287 

.185  032 

.139  1782 

•923 

.835  1483 

.841  452 

.146  1678 

•  973 

.856  8630 

.  192  221 

.  139  0391 

.924 

.835  5826 

.848  297 

.146  0217 

•974 

.857  2973 

.199  417 

.138  9001 

1.925 

0.836  0169 

6.855  149 

0.145  8758 

1.975 

0.857  73l6 

7.206  620 

0.138  7613 

.926 

.836  4512 

.862  007 

.145  7300 

•976 

.858  1659 

.213  830 

.  138  6226 

.927 

.836  8855 

.868  873 

.145  5843 

•977 

.858  6002 

.221  O47 

.  138  4841 

.928 

.837  3198 

.875  745 

.145  4388 

.978 

.859  0345 

.228  272 

.  138  3457 

.929 

•837  7541 

.882  624 

.145  2934 

•  979 

.859  4688 

.235  504 

.138  2074 

1.930 

0.838  1884 

6.889  5io 

0.145  1482 

1.980 

0.859  9031 

7.242  743 

0.  138  0692 

•931 

.838  6226 

.896  403 

.145  0031 

.981 

.860  3374 

.249  989 

.137  9312 

•932 

.839  0569 

.903  303 

.  144  8582 

.982 

.860  7717 

.257  243 

.137  7934 

•933 

.839  4912 

.9IO  2IO 

.144  7134 

.983 

.861  2060 

.264  504 

.137  6557 

•934 

•839  9255 

.917  123 

.144  5688 

.984 

.861  6403 

.271  772 

.137  5i8i 

1-935 

0.840  3598 

6.924  044 

0.  144  4243 

1.985 

0.862  0745 

7.279  047 

0.137  3806 

.936 

.840  7941 

.930  972 

.144  2799 

.986 

.862  5088 

.286  330 

•137  2433 

•937 

.841  2284 

.937  90-5 

.144  1357 

.987 

.862  9431 

.293  620 

.137  1061 

.938 

.841  6627 

.944  847 

.143  99i6 

.988 

•863  3774 

.300  917 

.136  0691 

•  939 

.842  0970 

.951  796 

.143  8477 

.989 

.863  8117 

.308  222 

.  136  8322 

1.940 

0.842  5313 

6.958  751 

0.143  7039 

1.990 

0.864  2460 

7.315  534 

0.136  6954 

.941 

.842  9656 

.965  713 

.143  5603 

.991 

.864  6803 

.322  853 

.136  5588 

.942 

.843  3999 

.972  682 

.143  4168 

•992 

.865  1146 

•330  179 

.  136  4223 

•943 

.843  8342 

•979  659 

.143  2735 

•  993 

.865  5489 

•337  513 

.136  2860 

.944 

.844  2685 

.986  642 

.143  1303 

.994 

.865  9832 

.344  854 

.136  1497 

1.945 

0.844  7028 

6.993  632 

0.142  0872 

1.995 

0.866  4175 

7.352  203 

0.136  0137 

.946 

.845  I371 

7.000  629 

.142  8443 

.996 

.866  8518 

•359  559 

.135  8777 

•947 

.845  5714 

.007  633 

.142  7015 

•  997 

.867  2861 

.366  922 

.135  7419 

.948 

.846  0057 

.014  644 

.142  5589 

.998 

.867  7204 

•374  293 

.135  6062 

.949 

.846  4399 

.021  662 

.142  4164 

.999 

.868  1547 

.381  671 

.135  4707 

1.950 

0.846  8742 

7.028  688 

0.142  2741 

2.OOO 

0.868  5890 

7.389  056 

O.I3S  3353 

loge(eu) 

looio(eu) 

eu 

e~u 

lofle(eu) 

looio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


245 


The  Exponential. 


u 

looio(eu) 

eu 

e-u 

u 

looio(eu) 

eu 

e~u 

2.OOO 

0.868  5890 

7.389  056 

0.135  3353 

2.050 

0.890  3037 

7.767  901 

0.128  7349 

.OOI 

.869  0233 

.396  449 

.135  2000 

.051 

.890  738a 

•775  673 

.128  6062 

.OO2 

.003 

.869  4576 
.8698918 

.403  849 
.411  257 

.135  0649 
.134  9299 

.052 
•053 

•891  1723 
.891  6066 

•783  452 
.791  240 

.  128  4777 
.128  3493 

.004 

.870  3261 

.418  672 

•134  7950 

•054 

.892  0409 

•799  035 

.128  22  10 

2.005 

0.870  7604 

7.426  094 

o.  134  6603 

2.055 

0.892  4752 

7.806  838 

0.128  0928 

.006 

.871  1947 

•433  524 

.134  5257 

.056 

.892  9095 

.814  649 

.127  9648 

.007 

.871  6290 

.440  961 

.134  3912 

•057 

•893  3437 

.822  467 

.127  8369 

.008 

.872  0633 

.448  406 

.134  2569 

.058 

.893  778o 

.830  294 

.127  7091 

.009 

.872  4976 

.455  858 

.134  1227 

.059 

.894  2123 

.838  128 

.127  5815 

2.OIO 
.Oil 

0.872  9319 
.873  3662 

7.463  317 
.470  784 

0.133  9887 
.133  8548 

2.060 
.061 

0.894  6466 
.895  0809 

7.845  970 
.853  820 

0.127  4540 
.127  3266 

.OI2 

.873  8005 

.478  259 

.133  7210 

.062 

.895  5152 

.861  677 

.127  1993 

.013 

.874  2348 

.485  74i 

.133  5873 

.063 

•895  9495 

.869  543 

.127  0722 

.014 

.874  6691 

.493  230 

.133  4538 

.064 

.896  3838 

.877  417 

.  126  9452 

2.015 

0.875  1034 

7.500  727 

0.133  3204 

2.065 

0.896  8181 

7.885  298 

0.126  8183 

.016 

.875  5377 

.508  232 

.133  1871 

.066 

.897  2524 

.893  187 

.126  6915 

.017 

.875  9720 

.515  744 

.133  0540 

.067 

.897  6867 

.901  084 

.126  5649 

.018 

.876  4063 

.523  263 

.132  9210 

.068 

.898  1210 

.908  989 

.126  4384 

.OIp 

.876  8406 

•530  790 

.132  7882 

.069 

'  .898  5553 

.916  902 

.126  3120 

2.020 

0.877  2749 

7.538  325 

o.  132  6555 

2.070 

0.898  9896 

7.924  823 

0.126  1858 

.021 

.877  7091 

.545  867 

.132  5229 

.071 

.899  4239 

•932  752 

.126  0597 

.022 

.878  1434 

•553  417 

.132  3904 

.072 

.899  8582 

.940  689 

.125  9337 

.023 

.878  5777 

.560  974 

.132  2581 

•073 

.900  2925 

•948  633 

.125  8078 

.024 

.879  0120 

.568  539 

.132  1259 

.074 

.900  7268 

.956  586 

.125  6820 

2.O25 

0.879  4463 

7.576  III 

0.131  9938 

2.075 

0.901  1610 

7.964  546 

0.125  5564 

.026    .879  8806 

.583  691 

.131  8619 

.076 

.901  5953 

•972  515 

.125  4309 

.027  |   .880  3M9 

.591  278 

.131  73oi 

•077 

.902  0296 

.980  491 

.125  3056 

.028    .880  7492 

.598  873 

.131  5985 

.078 

.902  4639 

.988476 

.125  1803 

.029 

.881  1835 

.606  476 

.131  4669 

.079 

.902  8982 

.996468 

.125  0552 

2.030 

0.881  6178 

7.614  086 

0.131  3355 

2.080 

0.903  3325 

8.004  469 

0.  124  9302 

.031 

.882  0521 

.621  704 

.131  2043 

.081 

.903  7668 

.012  477 

.  124  8053 

.032 

.882  4864 

.629  330 

.131  0731 

.082 

.904  201  1    .020  494 

.124  6806 

•033 

.882  9207 

.636  963 

.130  9421 

.083 

.904  6354 

.028  518 

.124  5560 

•034 

.883  3550 

.644  604 

.130  8112 

.084 

.905  0697 

.036  551 

.124  4315 

2.035 

0.883  7893 

7.652  252 

0.130  6805 

2.085 

0.905  5040 

8.044  591 

0.124  3071 

.036 

.884  2236 

.659  9o8 

.  130  5499 

.086 

.905  9383 

.052  640 

.124  1829 

•  037 

.884  6579 

.667  572 

.130  4194 

.087 

.906  3726 

.060  697 

.  124  0588 

.038 

.885  0922 

.675  243 

.130  2890 

.088 

.906  8069 

.068  761 

.  123  9348 

•039 

.885  5264 

.682  922 

.130  1588 

.089 

.907  2412 

.076  834 

.123  8109 

2.040 

0.885  96o7 

7.690  609 

0.130  0287 

2.090 

0.907  6755 

8.084  915 

0.123  6871 

.041 

.886  3950 

.698  304 

.1298987 

.091 

.908  1098 

.093  004 

.123  5635 

.042 

.8868293 

.706  006 

.129  7689 

.092 

.908  5441 

.IOI  IOI 

.123  4400 

•043 

.887  2636 

.713  7i6 

.129  6392 

.093 

.908  9784 

.109  206 

.123  3166 

.044 

.887  6979 

.721  433 

.129  5096 

.094 

.909  4126 

.117  320 

.123  1934 

2.045 

0.888  1322 

7.729  159 

0.129  3802 

2.095 

0.909  8469 

8.125  441 

0.123  0702 

.046 

.888  5665 

.736  892 

.  129  2509 

.096 

.910  2812 

•133  570 

.  122  9472 

.047 

.889  0008 

.744  632 

.129  1217 

.097 

.910  7155 

.141  708 

.  122  8243 

.048 

•889  4351 

•752  381 

.128  9926 

.098 

.911  1498 

.  149  854 

.122  7016 

.049 

.8898694 

.760  137 

.1288637 

.099 

.911  5841 

.158  008 

.122  5789 

2.050 

0.890  3037 

7.767  901 

0.128  7349 

2.100 

0.912  0184 

8.166  170 

0.122  4564 

loo,-(eu) 

loo,,Xea) 

6° 

a"" 

log,fe") 

looio(eu) 

ett 

e~u 

SMITHSONIAN  TABLES 


The  Exponential. 


u 

looio(eu) 

eu 

e 

u 

loflio(eu) 

eu 

e-a 

2.IOO 

0.912  0184 

8.166  170 

0.122  4564 

2.150 

0.933  7331 

8.584  858 

0.116  4842 

.IOI 

.912  4527 

.174  340 

.122  3340 

.151 

.934  1674 

•593  448 

.116  3677 

.IO2 

.912  8870 

.182  519 

.122  2Il8 

.152 

.934  6017 

.602  045 

.116  2514 

.103 

.913  3213 

.190  705 

.122  0896 

.153 

.935  0360 

.610  652 

.116  1352 

.104 

.913  7SS6 

.198  900 

.121  9676 

.154 

•935  4703 

.619  267 

.116  0192 

2.105 

0.914  1899 

8.207  103 

O.I2I  8457 

2.155 

0.935  9046 

8.627  890 

0.115  9032 

.106 

.914  6242 

.215  314 

.121  7239 

.156 

.936  3389 

.636  522 

.115  7873 

.107 

.915  0585 

.223  534 

.121  6O22 

•  157 

.936  7732 

.645  163 

.115  6716 

.108 

.915  4928 

.231  761 

.121  4807 

.158 

•937  2075 

.653  813 

.115  556o 

.109 

.915  9271 

.239  997 

.121  3593 

.159 

.937  6418 

.662  471 

.115  4405 

2.  IIO 

0.916  3614 

8.248  241 

O.I2I  2380 

2.160 

0.938  0761 

8.671  138 

0.115  3251 

.III 

.916  7957 

.256  494 

.121  1168 

.161 

.938  5104 

.679  813 

.115  2099 

.112 

.917  2299 

.264  754 

.  120  9957 

.162 

.938  9447 

.688497 

.115  0947 

.113 

.917  6642 

.273  023 

.  120  8748 

.163 

•939  3790 

.697  190 

.114  9797 

.114 

.918  0985 

.281  300 

.120  7540 

.164 

•939  8133 

.705  892 

.114  8647 

2.II5 

0.918  5328 

8.289  586 

0.120  6333 

2.165 

0.940  2476 

8.714  602 

0.114  7499 

.116 

.918  9671 

.297  879 

.120  5127 

.166 

.940  6818 

.723  321 

.114  6352 

.117 

.919  4014 

.306  182 

.120  3923 

.167 

.941  1161 

.732  049 

.114  5207 

.118 

.919  8357 

.314  492 

.120  2719 

.168 

.941  5504 

.740  785 

.114  4062 

.119 

.920  2700 

.322  811 

.120  1517 

.169 

.941  9847 

•749  530 

.114  2919 

2.I2O 

0.920  7043 

8.331  137 

0.120  03l6 

2.170 

0.942  4190 

8.758  284 

0.114  1776 

.121 

.921  1386 

•339  473 

.119  9H7 

.171 

.942  8533 

.767  047 

.114  0635 

.122 

.921  5729 

.347  816 

.119  79l8 

.172 

.943  2876 

.775  818 

.H3  9495 

.123 

.922  0072 

.356  168 

.119  6721 

.173 

.943  7219 

.784  598 

.113  8356 

.124 

.922  4415 

.364  529 

.119  5525 

•  174 

.944  1562 

.793  387 

.113  7218 

2.125 

0.922  8758 

8.372  897 

0.119  4330 

2.175 

0.944  5905 

8.802  185 

0.113  6082 

.126 

.923  3101 

.381  275 

.119  3U6 

.176 

.945  0248 

.810  992 

.113  4046 

.127 

.923  7444 

.389  660 

.119  1943 

.177 

•945  4591 

.819  807 

.113  3812 

.128 

.924  1787 

.398  054 

.119  0752 

.178 

.945  8934 

.828  631 

.113  2678 

.129 

.924  6130 

.406  456 

.118  9562 

.179 

.946  3277 

.837  464 

.113  1546 

2.130 

0.925  0472 

8.414  867 

0.118  8373 

2.180 

0.946  7620 

8.846  306 

0.113  0415 

.131 

.925  4815 

.423  286 

.118  7185 

.181 

.947  1963 

.855  157 

.112  9285 

.132 

.925  9158 

•431  713 

.118  5999 

.182 

.947  6306 

.864  017 

.112  8l57 

.133 

.926  3501 

.440  149 

.118  4813 

.183 

.948  0649 

.872  885 

.112  7029 

.134 

.926  7844 

.448  594 

.118  3629 

.184 

.948  4991 

.881  762 

.112  5903 

2.135 

0.927  2187 

8.457  047 

0.118  2446 

2.185 

0.948  9334 

8.890  649 

0.112  4777 

.136 

.927  6530 

.465  508 

.118  1264 

.186 

•949  3677 

.899  544 

.112  3653 

•  137 

.928  0873 

•473  978 

.118  0083 

.187 

.949  8020 

.908  448 

.112  253O 

.138 

.928  5216 

.482  456 

.117  8904 

.188 

.950  2363 

.917  361 

.112  1408 

.139 

.928  9559 

.490  942 

.117  7726 

.189 

.950  6706 

.926  282 

.112  O287 

2.140 

0.929  3902 

8.499  438 

0.117  6548 

2.190 

0.951  1049 

8.935  213 

o.i  u  9167 

.141 

.929  8245 

.507  941 

.117  5372 

.191 

•951  5392 

•  944  153 

.III  8049 

.142 

.930  2588 

.5i6  454 

.117  4198 

.192 

•951  9735 

•953  ioi 

.III  6931 

•  143 

•930  0931 

.524  974 

.117  3024 

•193 

.952  4078 

.962  059 

.III  5815 

.144 

.93-1  1274 

•533  503 

.117  1852 

.194 

.952  8421 

.971  026 

.III  4700 

2.145 

0.931  S6i7 

8.542  041 

0.117  0680 

2.195 

0.953  2764 

8.080  ooi 

o.in  3586 

.146 

.931  9960 

.550  588 

.116  9510 

.196 

•953  7107 

.988  986 

•III  2473 

.147 

•932  4303 

•559  142 

.116  8341 

.197 

•954  1450 

.997  979 

.III  1361 

.148 

.932  8645 

.567  706 

.116  7174 

.198 

•954  5793 

9.006  982 

.III  O25O 

.149 

.933  2988 

.576  278 

.116  6007 

.199 

•955  0136 

.015  993 

.no  9140 

2.150 

0.933  7331 

8.584  858 

0.116  4842 

2.  2OO 

0.955  4479 

9.025  013 

o.i  10  8032 

loge(eu) 

looioCe11) 

eu 

e-u 

loge(eu) 

Iogi0(eu) 

en 

e~u 

SMITHSONIAN  TABLES 


247 


The  Exponential. 


u 

logio(eu) 

eu 

e~u 

u 

looio(en) 

eu 

e-tt 

2.2OO 

0.955  4479 

9.025  013 

o.i  10  8032 

2.250 

0.977  1626 

9.487  736 

0.105  3992 

.2OI 

.955  8822 

.034  043 

.no  6924 

.251 

•977  5969 

.497  228 

•105  2939 

.202 

.956  3164 

.043  082 

.110  5818 

.252 

.978  0312 

.506  730 

.105  1886 

.203 

.956  7507 

.052  129 

.no  4712 

.253 

.978  4655 

.516  242 

.105  0835 

.204 

•957  1850 

.061  186 

.no  3608 

.254 

.9788998 

.525  763 

.104  9785 

2.2O5 

0.957  6193 

9.070  252 

o.i  10  2505 

2.255 

0.979  3341 

9-535  293 

o.  104  8735 

.206 

.958  0536 

.079  326 

.no  1403 

.256 

.979  7684 

.544  833 

.104  7687 

.207 

.958  4879 

.088  410 

.  1  10  0302 

•  257 

.980  2026 

•554  383 

.104  6640 

.208 

.958  9222 

.097  503 

.109  9203 

•  258 

.980  6369 

.563  942 

.104  5594 

.209 

•959  3565 

.106  605 

.109  8104 

•  259 

.981  0712 

•573  5ii 

.104  4549 

2.2IO 

0.959  7908 

9.H5  7i6 

0.109  7006 

2.260 

0.081  5055 

9-583  089 

0.104  3505 

.211 

.960  2251 

.  124  837 

.109  5910 

.261 

•981  9398 

.592  677 

.104  2462 

.212 
.213 

.960  6594 
.961  0937 

.133  966 
.143  105 

.109  4815 
.  109  3720 

.262 
.263 

.982  3741 
.982  8084 

.602  275 
.611  882 

.104  1420 
.  104  0379 

.214 

.961  5280 

.152  252 

.109  2627 

.264 

.983  2427 

.621  498 

.103  9339 

2.215 

0.961  9623 

9.161  409 

0.109  1535 

2.265 

0.983  6770 

9.631  125 

0.103  8300 

.216 

.962  3966 

.170  575 

.109  0444 

.266 

.984  III3 

.640  761 

.103  7263 

.217 

.962  8309 

.  179  750 

.  108  9354 

.267 

•984  5456 

.650  406 

.103  6226 

.218 

.963  2652 

.188  935 

.  108  8265 

.268 

•984  9799 

.660  061 

.103  5190 

.219 

.963  6995 

.198  128 

.108  7178 

.269 

.985  4142 

.669  726 

.103  4155 

2.22O 

0.964  1337 

9.207  331 

o.loS  6091 

2.270 

0.985  8485 

9.679  401 

0.103  3122 

.221 

.964  5680 

.216  543 

.108  5006 

.271 

.986  2828 

.689085 

.103  2089 

.222 

.965  0023 

.225  764 

.108  3921 

.272 

.986  7171 

.698  779 

.103  1058 

.223 

.965  4366 

.234  994 

.108  2838 

.273 

.987  1514 

.708  483 

.103  0027 

.224 

.965  8709 

.244  234 

.108  1755 

.274 

.987  5857 

.718  106 

.102  8998 

2.225 

0.966  3052 

9.253  483 

0.108  0674 

2.275 

0.988  0199 

9.727  919 

0.102  7969 

.226 

•965  7395 

.262  741 

.107  9594 

.276 

.988  4542 

•737  652 

.102  6942 

.227 

.957  1738 

.272  008 

.107  8515 

.277 

.988  8885 

•747  394 

.102  5915 

.228 

.967  6081 

.281  285 

.107  7437 

.278 

.989  3228 

.757  147 

.IO2  4890 

.229 

.968  0424 

.290  571 

.107  6360 

.279 

•989  757i 

.766  909 

.102  3865 

2.23O 

0.968  4767 

9.299  866 

0.107  5284 

2.280 

0.990  1914 

9.776  680 

0.102  2842 

.231 

.968  9110 

.309  I7i 

.107  4210 

.281 

.990  6257 

.786  462 

.IO2  l82O 

.232 

•969  3453 

^   ^   *J—T*J\J 

.318  484 

.107  3136 

.282 

.991  0600 

.796  253 

.  102  0798 

•233 

.969  7796 

.327  808 

.107  2063 

•  283 

.991  4943 

.806  054 

.101  9778 

.234 

.970  2139 

•  337  UO 

.107  0992 

.284 

.991  9286 

.815  865 

.101  8759 

2.235 

O.970  6482 

9.346  482 

0.106  9921 

2.285 

0.992  3629 

9.825  686 

o.ioi  7741 

£ 

.236 

.971  0825 

•355  833 

.  106  8852 

.286 

.992  7972 

•835  517 

.101  6723 

•  237 

.971  5l68 

•365  194 

.106  7784 

.287 

•993  2315 

•845  357 

.101  5707 

.238 

.971  9511 

•374  563 

.106  6716 

.288 

.993  6658 

.855  208 

.101  4692 

•  239 

•972  3853 

•383  943 

.106  5650 

.289 

.994  looi 

.865  068 

.101  3678 

2.240 

0.972  8l96 

9-393  331 

0.106  4585 

2.290 

0.994  5344 

9.874  938 

o.ioi  2665 

.241 

•973  2539 

.402  729 

.106  3521 

.291 

.994  9687 

.884  818 

.101  1652 

.242 

.973  6882 

.412  137 

.106  2458 

.292 

•995  4030 

.894  707 

.101  0641 

.243 

.974  1225 

.421  554 

.106  1396 

.293 

•995  8372 

.904  607 

.100  9631 

.244 

.974  5568 

.430  980 

.  106  0335 

.294 

.996  2715 

•914  517 

.  IOO  8622 

2.245 

0.974  9911 

9.440  416 

0.105  9275 

2.295 

0.996  7058 

9.924  436 

o.ioo  7614 

.246 

.975  4254 

.449  861 

.105  8217 

.296 

.097  1401 

•934  365 

.100  6607 

•  247 

.975  8597 

•459  315 

.105  7159 

.297 

•997  5744 

.944  305 

.106  5601 

.248 

.976  2940 

.468  779 

.105  6102 

.298 

.9980087 

•954  -'54 

.100  4596 

.249 

.976  7283 

.478  253 

.105  5047 

•  299 

.098  4430 

.964  213 

.  loo  3592 

2.250 

0.977  1626 

9.487  73<5 

0.105  3992 

2.300 

0.098  8773 

9.974  182 

o.ioo  2588 

Io0c(e°) 

looi.Xe°) 

eu 

e-u 

loflc(eu) 

looio(ea) 

eu 

«-" 

SMITHSONIAN  TABLES 


248 


The  Exponential. 


u 

looio(eu) 

eu 

e~u 

u 

logio(en) 

eu 

e~u 

2.300 

0.098  8773 

9.974  182 

o.ioo  2588 

2.350 

I.O20  592O 

10.485  570 

0.095  3692 

.301 

.999  3116 

.984  162 

.100  1586 

.351 

.O2I  0263 

.496  061 

.095  2738 

.302 

•999  7459 

.994  151 

.100  0585 

.352 

.O2I  4606 

.506  562 

.095  1786 

.303 

i.ooo  1802 

10.004  150 

.099  9585 

•  353 

.O2I  8949 

.517  074 

.095  0835 

.304 

.coo  6145 

.014  159 

.0998586 

•  354 

.022  3292 

.527  596 

.094  9884 

2.305 

i.ooi  0488 

10.024  178 

0.099  7588 

2.355 

1.022  7635 

10.538  129 

0.094  8935 

.306 

.001  4831 

.034  207 

.099  6591 

.356 

.023  1978 

.548  672 

.094  7987 

.307 

.001  9174 

.044  247 

.099  5595 

•  357 

.023  6321 

.559  226 

.094  7039 

.308 

.002  3517 

.054  296 

.099  4600 

•  358 

.024  0664 

.569  791 

.094  6093 

.309 

.002  7860 

.064  355 

.099  3606 

•  359 

.024  50O7 

.580366 

.094  5147 

2.310 

1.003  2203 

10.074  425 

0.099  2613 

2.360 

1.024  9350 

10.590  95i 

0.094  4202 

.311 

.003  6545 

.084  504 

.099  1620 

.361 

.025  3693 

.601  548 

.094  3259 

.312 

.004  0888 

.094  594 

.099  0629 

.362 

.025  8036 

.612  155 

.094  2316 

.313 

.004  5231 

.  104  693 

.098  9639 

.363 

.026  2379 

.622  772 

.094  1374 

.314 

.004  9574 

.114  803 

.098  8650 

.364 

.026  6722 

.633  400 

.094  0433 

2.315 

1.005  3917 

10.124  923 

0.098  7662 

2.365 

1.027  1064 

10.644  039 

0.093  9493 

.316 

.005  8260 

.135  053 

.0986675 

.366 

.027  5407 

.654  688 

.093  8554 

.317 

.006  2603 

.145  193 

.098  5688 

.367 

.027  9750 

.665  348 

.093  7616 

.318 

.006  6946 

•155  343 

.098  4703 

.368 

.028  4093 

.676  019 

.093  6679 

.319 

.007  1289 

.165  504 

.098  3719 

.369 

.028  8436 

.686  700 

.093  5743 

2.320 

1.007  5632 

10.175  674 

0.098  2736 

2.370 

1.029  2779 

10.697  392 

0.093  4807 

.321 

.007  9975 

.I&5  855 

.098  1754 

.371 

.029  7122 

.708  095 

.093  3873 

.322 

.008  4318 

.196  046 

.098  0772 

•  372 

.030  1465 

.718  808 

.093  2940 

.323 

.0088661 

.206  247 

.097  9792 

•  373 

.030  5808 

.729  533 

.093  2007 

.324 

.009  3004 

.216  459 

.097  8813 

•  374 

.031  0151 

.740  268 

.093  1076 

2.325 

1.009  7347 

10.226  680 

0.097  7834 

2.375 

1.031  4494 

10.751  013 

0.093  0145 

.326 

.010  1690 

.236  912 

.097  6857 

.376 

.031  8837 

.761  770 

.092  9215 

.327 

.010  6033 

.247  154 

.097  5881 

•  377 

.032  3180 

•772  537 

.092  8286 

.328 

.011  0376 

.257  406 

.097  4905 

.378 

.032  7523 

•783  315 

•092  7359 

.329 

.011  4718 

.267669 

.097  3931 

•  379 

.033  1866 

.794  103 

.092  6432 

2.330 
.331 

i.  on  9061 

.012  3404 

10.277  942 
.288  225 

0.097  2957 
.097  1985 

2.380 
.381 

1.033  6209 
.034  0552 

10.804  903 
.815  713 

0.092  5506 
.092  4581 

.332 

.012  7747 

.298  518 

.097  1014 

.382 

.034  4895 

.826  534 

.092  3657 

.333 

.013  2090 

.308  822 

.097  0043 

.383 

.034  9238 

.837  366 

.092  2733 

.334 

.013  6433 

.319  136 

.096  9073 

.384 

.035  358o 

.848  209 

.092  1811 

2.335 

1.014  0776 

10.329  460 

0.096  8105 

2.385 

1.035  7923 

10.859  063 

0.092  0890 

.336 

.014  5119 

•339  795 

.096  7137 

.386 

.036  2266 

.869927 

.091  9969 

.337 

.014  9462 

.350  140 

.096  6171 

.387 

.036  6609 

.880  803 

.091  0050 

.338 

.015  3805 

.360  495 

.096  5205 

.388 

.037  0952 

.991  689 

.091  8131 

•  339 

.015  8148 

.370861 

.096  4240 

.389 

.037  5295 

.902  586 

.091  7214 

2.340 

1.016  2491 

10.381  237 

0.096  3276 

2.390 

1.037  9638 

10.913  494 

0.091  6297 

•  341 

.  .016  6834 

•391  623 

.096  2314 

•  391 

.038  3981 

.924  413 

.091  538i 

•  342 

.017  ii77 

.402  020 

.096  1352 

.392 

.038  8324 

•935  343 

.091  4466 

•343 

.017  5520 

.412  427 

.096  0391 

•  393 

.039  2667 

.946  284 

.091  3552 

•  344 

.017  9863 

.422  845 

•095  9431 

•  394 

.039  7010 

•957  235 

.091  2639 

2.345 

1.018  4206 

10.433  273 

0.095  8472 

2.395 

1.040  1353 

10.968  198 

0.091  1727 

•  346 

.018  8549 

.443  7ii 

.095  7514 

.396 

.040  5696 

.979  172 

.091  0816 

•  347 

.019  2891 

.454  160 

.095  6557 

•  397 

.041  0039 

.990  156 

.090  9905 

.348 

.019  7234 

.464  620 

.095  5601 

.398 

.041  4382 

II.  001  152 

.090  8996 

•  349 

.020  1577 

.475  089 

.095  4646 

•  399 

.041  8725 

.012  159 

.090  8087 

2-350 

1.020  5920 

10.485  570 

0.095  3692 

2.400 

1.042  3068 

11.023  176 

0.090  7180 

loge(eu) 

logio(eu) 

eu 

e~u 

loge(eu) 

lofllo(eu) 

eu 

e~~u 

SMITHSONIAN  TABLES 


249 


The  Exponential. 


u 

looio(en) 

eu 

e~u 

u 

looio(eu) 

en 

e  u 

2.400 

1.042  3068 

11.023  176 

0.090  7180 

2.450 

1.064  0215 

11.588  347 

0.086  2936 

.401 

.042  7411 

.034  205 

.090  6273 

•  451 

.064  4558 

.599  941 

.086  2073 

.402 

•043  1753 

•045  245 

.090  5367 

•  452 

.064  8001 

.611  547 

.086  1212 

.403 

.043  6006 

.056  296 

.090  4462 

•453 

.065  3244 

.623  164 

.086  0351 

.404 

.044  0439 

•067  357 

.090  3558 

.454 

.065  7587 

•634  793 

.085  9491 

2.405 

1.044  4782 

11.078  430 

o.ooo  2655 

2.455 

I.  066  1930 

11.646  434 

0.085  8632 

.406 

.044  9125 

.089  514 

•000  1753 

.456 

.066  6272 

.658  086 

.085  7774 

.407 

.045  3468 

.100  609 

.000  0851 

•  457 

.067  0615 

.669  750 

.085  6916 

.408 

.045  78ii 

.in  715 

.089  9951 

•  458 

.067  4958 

.681  425 

.085  6060 

.409 

.046  2154 

.122  833 

.089  9052 

•459 

.067  9301 

.693  113 

.085  5204 

2.410 

1.046  6497 

11.133  96l 

0.089  8153 

2.460 

I.  068  3644 

11.704  812 

0.085  4350 

.411 

.047  0840 

.145  101 

.089  7255 

.461 

.068  7987 

.716  522 

.085  3496 

.412 

.047  5183 

.156  251 

.089  6358 

.462 

.069  2330 

.728  245 

.085  2643 

.413 
.414 

.047  9526 
.048  3869 

.167  413 
.178  586 

.089  5463 
.089  4568 

.463 
.464 

.069  66731 
.070  1016 

.739  979 
•751  725 

.085  1790 
.085  0939 

2.415 

1.048  8212 

II.I89  770 

0.089  3673 

2.465 

1.070  5359 

11.763  482 

0.085  0088 

.416 

•049  2555 

.2OO  966 

.089  2780 

.466 

.070  9702 

.775  252 

.084  9239 

.417 

.049  6898 

.212  172 

.089  1888 

.467 

.071  4045 

.787  033 

.084  8390 

.418 

.050  1241 

.223  390 

.089  0006 

.468 

.071  8388 

.708  826 

.084  7542 

.419 

.050  5584 

.234  619 

.089  0106 

.469 

.072  2731 

.810  630 

.0846695 

2.420 

1.050  9926 

11.245  859 

0.088  9216 

2.470 

1.072  7074 

11.822  447 

0.084  5849 

.421 

.051  4269 

.257  III 

.088  8327 

.471 

.073  1417 

.834  275 

.084  5003 

.422 

.051  8612 

.268  374 

.088  7440 

.472 

.073  576o 

.846  115 

.084  4159 

.423 

.052  2955 

.279  648 

.088  6553 

.473 

.074  0103 

.857  967 

.084  3315 

.424 

.052  7298 

.290  933 

.088  5666 

•474 

.074  4445 

.869831 

.084  2472 

2.425 

1.053  1641 

11.302  229 

0.088  4781 

2.475 

1.074  8788 

11.881  707 

0.084  1630 

.426 

.053  5984 

.313  537 

.0883897 

•476 

.075  3i3i 

.893  595 

.084  0789 

.427 

.054  0327 

.324  857 

.088  3013 

.477 

.075  7474 

.905  494 

.083  9948 

.428 

.054  4670 

.336  187 

.088  2131 

•  478 

.076  1817 

.917  406 

.083  9109 

.429 

.054  9013 

•347  529 

.088  1249 

•479 

.076  6160 

.929  329 

.083  8270 

2.430 

1.055  3356 

11.358  882 

0.088  0368 

2.480 

1.077  0503 

11.941  264 

0.083  7432 

.431 

.055  7699 

•370  247 

.087  9488 

.481 

.077  4846 

.953  212 

.083  6595 

.432 

.056  2042 

.381  623 

.087  8609 

.482 

.077  9189 

.965  171 

.083  5759 

•433 

.056  6385 

.393  oio 

.087  7731 

.483 

•078  3532 

•977  H2 

.083  4924 

•434 

.057  0728 

.404  409 

.087  6854 

.484 

.078  7875 

.089  125 

.083  4089 

2.435 

1.057  5071 

11.415  819 

0.087  5977 

2.485 

1.079  2218 

12.001  120 

0.083  3256 

.436 

.057  9414 

.427  240 

.087  5102 

.486 

.079  6561 

.013  127 

.083  2423 

•437 

.058  3757 

.438  673 

.087  4227 

.487 

.080  0004 

.025  147 

.083  1591 

.438 

.0588099 

.450  118 

.087  3353 

.488 

.080  5247 

.037  178 

.083  0760 

•439 

.059  2442 

•461  573 

.087  2481 

.489 

.080  9590 

.049  221 

.082  9929 

2.440 

1.059  6785 

11.473  041 

0.087  1609 

2.490 

1.081  3933 

12.061  276 

0.082  9100 

.441 

.060  1128 

.484  520 

.087  0737 

.491 

.081  8276 

.073  343 

.082  8271 

•442 

.060  5471 

.496  oio 

.086  9867 

.492 

.082  2618 

.085  423 

.082  7443 

•443 

.060  9814 

•507  512 

.086  8998 

•493 

.082  6961 

.097  5U 

.082  6616 

.444 

.061  4157 

.519  025 

.086  8129 

.494 

.083  1304 

.109  618 

.082  5790 

2.445 

1.061  8500 

11.530  550 

0.086  7261 

2.495 

1.083  5647 

12.  121  734 

0.082  4065 

.446  . 

.062  2843 

.542  086 

.086  6395 

.496 

.083  9990 

.133861 

.082  4140 

•  447 

.062  7186 

•553  634 

.086  5529 

•  497 

.084  4333 

.146  ooi 

.082  3316 

.448 

.063  1529 

.565  193 

.0864663 

.498 

.084  8676 

.158  153 

.082  j.j«;.* 

•  449 

.063  5872 

.576  764 

.086  3799 

•499 

.085  3019 

.170  318 

.082  1671 

2.450 

1.064  0215 

n.588  347 

0.086  2936 

2.500 

1.085  7302 

12.182  494 

0.082  0850 

I0fle(e°) 

loouXe") 

eu 

e~u 

IOQe(eD) 

lofllo(eu) 

e" 

e-" 

SMITHSONIAN  TABLES 


250 


The  Exponential. 


u 

loflio(eu) 

eu 

e 

u 

Ioflio(e") 

eu 

e-n 

2.500 

1.085  7362 

12.182  494 

0.082  0850 

2.550 

I.  107  4509 

12.807  IO4 

0.078  0817 

.501 

.086  1705 

.194  683 

.082  0030 

•  551 

.107  8852 

.819  917 

.078  0036 

.502 

.086  6048 

.206  883 

.081  9210 

•  552 

.108  3195 

.832  744 

.077  9257 

.503 

.087  0391 

.219  096 

.081  8391 

•  553 

.108  7538 

.845  583 

.077  8478 

.504 

.087  4734 

.231  322 

.081  7573 

•  554 

.109  1881 

.858  435 

.077  7700 

2.505 

1.087  9077 

12.243  559 

0.081  6756 

2.555 

1.109  6224 

12.871  300 

0.077  6922 

.506 

.088  3420 

.255  809 

.081  5940 

.556 

.no  0567 

.884  177 

.077  6146 

.507 

.088  7763 

.268  071 

.081  5124 

.557 

.no  4910 

.897  068 

.077  5370 

.508 

.089  2106 

.280  345 

.081  4309 

.558 

.110  9253 

.909  972* 

.077  4595 

.509 

.089  6449 

.292  631 

.081  3495 

•  559 

.III  3596 

.922  888 

.077  3821 

2.510 

1.090  0791 

12.304  930 

0.081  2682 

2.560 

i.  in  7939 

12.935  817 

0.077  3047 

.511 

.090  5U4 

.317  241 

.081  1870 

.561 

.112  2282 

.948  760. 

.077  2275 

.512 

.090  9477 

.329  565 

.081  IOS9 

.562 

.112  6625 

.961  715 

•077  1503 

.513 

.091  3820 

.341  900 

.081  0248 

.563 

.113  0968 

.974  683 

.077  0732 

.514 

.091  8163 

•354  248 

.080  9438 

.564 

.113  5311 

.987664 

.076  9961 

2.515 

1.092  2506 

12.366  609 

d  080  8629 

2.565 

I.  113  9653 

13.000  658 

0.076  9192 

.516 

.092  6849 

.378  982 

.c8o  7821 

.566 

.114  3996 

.013  666 

.076  8423 

.517 

.093  1192 

•391  307 

.080  7013 

.567 

.114  8339 

.026  686 

.076  7655 

.518 

.093  5535 

.403  764 

.080  6207 

.568 

.115  2682 

.039  719 

.076  6888 

.519 

.093  9878 

.416  174 

.080  5401 

.569 

.115  7025 

.052  765 

.076  6121 

2.520 

1.094  4221 

12.428  597 

0.080  4596 

2.570 

1.116  1368 

13.065  824 

0.076  5355 

.521 

.094  8564 

.441  032 

.080  3792 

•  571 

.116  5711 

.078  897 

.076  4590 

.522 

.095  2907 

•453  479 

.ofr-  2988 

•  572 

.117  0054 

.091  982 

.076  3826 

.523 

.095  7250 

.465  958 

.080  2186 

.573 

.117  4397 

.105  081 

.076  3063 

.524 

.096  1593 

.478  411 

.080  1384 

•  574 

.117  8740 

.118  192 

.076  2300 

2.525 

1.096  5936 

12.490  895 

0.080  0583 

2.575 

1.118  3083 

13-131  317 

0.076  1538 

.526 

.097  0279 

.503  392 

.079  9783 

.576 

.118  7426 

•  144  455 

.076  0777 

.527 

.097  4622 

.515  902 

.079  8984 

•  577 

.119  1769 

.157  606 

.076  0017 

.528 

.097  8965 

.528  424 

.079  8185 

.578 

.119  6112 

.170  770 

.075  9257 

.529 

.098  3307 

•540  959 

.079  7387 

•  579 

.  120  0455 

.183  948 

.075  8498 

2.530 

1.098  7650 

12.553  5o6 

0.079  6590 

2.580 

I  .  120  4798 

13.197  138 

0.075  7740 

.531 

.099  1993 

.566  066 

•079  5794 

.581 

.120  9141 

.210  342 

.075  6983 

.532 

.099  6336 

.578  638 

.079  4999r 

.582 

.121  3484 

.223  559 

.075  6226 

•  533 

.100  0679 

•591  223 

.079  4204 

.583 

.121  7826 

.236  789 

.075  5470 

•  534 

.100  5022 

.603  821 

.079  3410 

.584 

.122  2l69 

.250  032 

•075  4715 

2.535 

i  .  100  9365 

12.616  431 

0.079  2617 

2.585 

I.  122  6512 

13.263  289 

0.075  396i 

.536 

.101  3708 

.629  054 

.079  1825 

.586 

.123  0855 

.276  559 

.075  3207 

•  537 

.101  8051 

.641  689 

.079  1034 

.587 

.123  5198 

.289  842 

.075  2454 

.538 

.102  2394 

.654  337 

.079  0243 

.588 

.123  9541 

•303  139 

.075  1702 

.539 

.102  6737 

.666998 

.078  9453 

.589 

.124  3884 

.316  449 

•075  0951 

2.540 

1.103  1080 

12.679  671 

0.078  8664 

2.590 

I.I24  8227 

13.329  772 

O.075  O20O 

•  541 

.103  5423 

.692  357 

.078  7876 

•  591 

.125  2570 

•343  108 

.074  9451 

•  542 

.103  9766 

.705  056 

.078  7088 

.592 

.125  6913 

.356  458 

.074  8701 

•  543 

.104  4109 

.717  767 

.078  6302 

•  593 

.126  1256 

.369821 

.074  7953 

•  544 

.  104  8452 

.730  491 

.078  5516 

•  594 

.126  5599 

.383  198 

.074  7206 

2.545 

i.  105  2795 

12.743  228 

0.078  4731 

2.595 

1.126  9942 

13.396  587 

0.074  6459 

.546 

.105  7138 

•755  978 

.078  3946 

.596 

.127  4285 

.409  991 

.074  5713 

•  547 

.106  1480 

.768  740 

.078  3163 

•  597 

.  127  8628 

.423  407 

.074  4967 

.548 

.106  5823 

.781  515 

.078  2380 

.598 

.128  2971 

.436  838 

.074  4223 

•  549 

.107  0166 

•794  30J 

.078  1598 

•  599 

.128  7314 

.450  281 

.074  3479 

2-550 

i.  107  4509 

12.807  104 

0.078  0817 

2.600 

1.129  1657 

13.463  738 

0.074  2736 

Iofle(eu) 

looio(eu) 

eu 

e~u 

looe(eu) 

loflio(en) 

eu 

e_n 

SMITHSONIAN  TABLES 


251 


The  Exponential. 


u 

looio(eu) 

eu 

e-° 

u 

Iog10(eu) 

eu 

e  u 

2.600 

1.129  1657 

13.463  738 

0.074  2736 

2.650 

I.I50  8804 

14.154  039 

0.070  6512 

.601 

.129  5999 

.477  208 

.074  1993 

.651 

.151  3147 

.168  200 

.070  5806 

.602 

.  130  0342 

.490  692 

.074  1252 

.652 

.151  7490 

.182  375 

.070  5101 

.603 

.  130  4685 

.504  190 

.074  0511 

•653 

.152  1833 

.196  565 

.070  4396 

.604 

.130  9028 

.517  701 

.073  9771 

.654 

.152  6176 

.210  768 

.070  3692 

2.605 

I.I3I  3371 

13.531  225 

0.073  9031 

2.655 

I.  153  0518 

14.224  986 

0.070  2988 

.606 

.131  7714 

•  544  763 

.073  8293 

.656 

.153  4861 

.239  218 

.070  2286 

.607 

.132  2057 

.558  315 

.073  7555 

•657 

.153  9204 

.253  464 

.070  1584 

.608 

.132  6400 

.571  880 

.073  6818 

.658 

•154  3547 

.267  725 

.070  0883 

.609 

.  133  0743 

.585  459 

.073  6081 

.659 

.  154  7890 

.282  ooo 

.070  0182 

2.610 

1.133  5086 

13.599  051 

0.073  5345 

2.660 

I.  155  2233 

14.296  289 

0.069  9482 

.611 

.133  9429 

.612  657 

.073  4610 

.661 

•  155  6576 

•310  593 

.069  8783 

.612 

.  134  3772 

.626  276 

.073  3876 

.662 

.156  0919 

.324  910 

.069  8085 

.613 

.1348115 

.639  909 

.073  3143 

.663 

.156  5262 

.339  242 

.069  7387 

.614 

.135  2458 

.653  556 

.073  2410 

.664 

.  156  9605 

.353  589 

.069  6690 

2.615 

1.135  6801 

13.667  216 

0.073  1678 

2.665 

I.  157  3948 

14.367  950 

0.069  5994 

.616 

.136  1144 

.680  890 

.073  0947 

.666 

.  157  8291 

.382  325 

.069  5298 

.617 

.136  5487 

.694  578 

.073  0216 

.667 

.158  2634 

.396  714 

.069  4603 

.618 

.136  9830 

.708  280 

.072  9486 

.668 

.158  6977 

.411  118 

.069  3909 

.619 

.137  4172 

•721  995 

.072  8757 

.669 

.159  1320 

•425  536 

.069  3215 

2.620 

I.  137  8515 

13-735  724 

0.072  8029 

2.670 

I.  159  5663 

14.439  969 

0.069  2522 

.621 

.138  2858 

.749  466 

.072  7301 

.671 

.160  0006 

.454  416 

.069  1830 

.622 

.138  7201 

.763  222 

.072  6574 

.672 

.160  4349 

.468  878 

.069  1139 

.623 

.139  1544 

.776  993 

.072  5848 

.673 

.160  8692 

.483  354 

.069  0448 

.624 

.139  5887 

.790  776 

.072  5122 

.674 

.161  3034 

•497  845 

.0689758 

2.625 

I  .  140  0230 

13-804  574 

0.072  4398 

2.675 

1.161  7377 

14.512  350 

0.068  0068 

.626 

.  140  4572 

.818  386 

.072  3674 

.676 

.162  1720 

.526  869 

.068  8380 

.627 

.  140  8916 

.832  211 

.072  2950 

.677 

.162  6063 

.541  404 

.068  7692 

.628 

.141  3259 

.846  050 

.072  2228 

.678 

.163  0406 

.555  952 

.068  7004 

.629 

.141  7602 

.859  903 

.072  1506 

.679 

.  163  4749 

•570  515 

.068  6318 

2.630 

1.142  I94S 

13.873  770 

0.072  0785 

2.680 

1.163  9092 

14.585  093 

0.068  5632 

.631 

.142  6288 

.887  651 

.072  0064 

.681 

.  164  3435 

.599686 

.068  4946 

.632 

.143  0631 

.001  545 

.071  9344 

.682 

.164  7778 

.614  293 

.068  4262 

.633 

.143  4974 

.915  454 

.071  8626 

.683 

.165  2121 

.628  914 

.068  3578 

.634 

.143  9317 

.929  376 

.071  7907 

.684 

.165  6464 

.643  550 

.068  2894 

2.635 

1.144  3660 

13-943  312 

0.071  7190 

2.685 

1.166  0807 

14.658  201 

0.068  2212 

.636 

.144  8003 

.957  263 

.071  6473 

.686 

.166  5150 

.672  867 

.068  1530 

.637 

.145  2345 

.971  227 

.071  5757 

.687 

.  166  9493 

.687  547 

.068  0849 

.638 

.145  6688 

.985  205 

.071  5041 

.688 

.167  3836 

.702  242 

.068  0168 

.639 

.146  1031 

•999  197 

.071  4327 

.689 

.167  8179 

.716  952 

.067  9489 

2.640 

1.146  5374 

14.013  204 

0.071  3613 

2.690 

1.168  2522 

14.731  676 

0.067  8809 

.641 

.146  9717 

.027  224 

.071  2899 

.691 

.168  6865 

.746  415 

.067  8l3I 

.642 

.147  4060 

.041  258 

.071  2187 

.692 

.169  1207 

.761  169 

.067  7453 

.643 

.  147  8403 

.055  306 

.071  1475 

.693 

.169  5550 

•775  937 

.067  6776 

.644 

.148  2746 

.069  369 

.071  0764 

.694 

.169  9893 

.790  721 

.067  6100 

2.645 

1.148  7089 

14.083  445 

0.071  0054 

2.695 

1.170  4236 

14.805  519 

0.067  5424 

.646 

.149  1432 

.097  536 

.070  9344 

.696 

.  170  8579 

.820  332 

.067  4749 

.647 

.149  5775 

.in  640 

.070  8635 

.697 

.171  2922 

.835  159 

.067  4074 

.648 

.150  01  18 

.125  759 

.070  7927 

.171  7265 

.850  002 

.067  3401 

.649 

.150  4461 

.  139  892 

.070  7219 

.699 

.172  1608 

.864  859 

.067  2728 

2.650 

1.150  8804 

14.154  039 

0.070  6512 

2.700 

I.I72  5951 

14.879  732 

0.067  2055 

looe(e°) 

looicXe") 

en 

e~u 

looe(eu) 

|*£ 

eu 

.- 

SMITHSONIAN  TABLES 


252 


The  Exponential. 


u 

logio(en) 

eu 

e-tt 

u 

logw(eu) 

eu 

e-u 

2.700 

1.172  5951 

14-879  732 

0.067  2055 

2.750 

1.194  3098 

15.642  632 

0.063  9279 

.701 

.173  0294 

.894  619 

.067  1383 

•  751 

.194  7441 

.658  282' 

.063  8640 

.702 

.173  4637 

.909  52i 

.067  0712 

•752 

.195  1784 

.673  948 

.063  8001 

.703 

.173  8980 

.924  438 

.067  0042 

•753 

.195  6127 

.689  630 

.063  7364 

.704 

•174  3323 

.939  370 

.066  9372 

•  754 

.196  0470 

.705  328 

.063  6727 

2.705 

1.174  7666 

14-954  317 

0.066  8703 

2.755 

1.196  4813 

15.721  041 

0.063  6090 

.706 

.175  2009 

.969278 

.066  8035 

.756 

.196  9156 

.736  770 

.063  5454 

.707 

•175  6352 

.984  255 

.066  7367 

•  757 

.197  3499 

•752  514 

.063  4819 

.708 

.  176  0695 

.999  247 

.066  6700 

.758 

.197  7842 

.768  275 

.063  4185 

.709 

•176  5038 

15.014  254 

.066  6039 

.759 

.198  2185 

.784  051 

.063  3551 

2.710 

1.176  9380 

15.029  275 

0.066  5368 

2.760 

1.198  6528 

15.799  843 

0.063  2918 

.711 

.177  3723 

.044  312 

.066  4/03 

.761 

.199  0871 

.815  651 

.063  2285 

.712 

.1778066 

•059  364 

.066  4039 

.762 

.199  5214 

.831  474 

.063  1653 

.713 

.178  2409 

.074  431 

.066  3375 

.763 

.  199  9557 

.847  3H 

.063  1022 

.714 

.178  6752 

.089  513 

.066  2712 

•  764 

.200  3899 

.863  169 

.063  O39I 

2.715 

1.179  1095 

15.104  610 

0.066  2050 

2.765 

1.200  8242 

15.879  040 

0.062  976l 

.716 

.  .179  5438 

.119  722 

.066  1388 

.766 

.201  2585 

.894  927 

.062  9132 

.717 

.  179  978i 

.134  850 

.066  0727 

.767 

.201  6928 

.910  830 

.062  8503 

.718 

.180  4124 

.149  9921 

.066  0066 

.768 

.202  1271 

.926  749 

.062  7875 

.719 

.  180  8467 

.165  149 

.065  9407 

.769 

.202  5614 

.942  683 

.062  7247 

2.720 

1.181  2810 

15.180  322 

0.065  8748 

2.770 

1.202  9957 

15.958  634 

O.O62  662O 

.721 

.181  7153 

.195  5io 

.065  8089 

.771 

.203  4300 

.974  601 

.062  5994 

.722 

.182  1496 

.210  713 

.065  7431 

.772 

.203  8643 

•990  583 

.062  5368 

.723 

.182  5839 

.225  932 

.065  6774 

•  773 

.204  2986 

16.006  582 

.062  4743 

.724 

.  183  0182 

.241  165 

.065  6118 

•  774 

.204  7329 

.022  596 

.062  4119 

2.725 

1.183  4525 

15.256  414 

0.065  5462 

2.775 

1.205  1672 

16.038  627 

0.062  3495 

.726 

.183  8868 

.271  678 

.065  4807 

.776 

.205  6015 

.054  674 

.062  2872 

.727 

.184  3211 

.286  957 

.065  4152 

•  777 

.206  0358 

.070  736 

.062  2249 

.728 

.184  7553 

.302  252 

•065  3499 

.778 

.206  4701 

.086  815 

.062  1627 

.729 

.185  1896 

.317  562 

.065  2845 

.779 

,206  9044 

.102  910 

.062  1006 

2.730 

1.185  6239 

15.332  887 

0.065  2193 

2.780 

1.207  3387 

I6.II9  O2I 

0.062  0385 

.731 

.  186  0582 

.348  228 

.065  1541 

.781 

.207  7730 

.135  148 

.061  9765 

.732 

.186  4925 

•363  583 

.065  0890 

.782 

.208  2072 

.151  291 

.061  9146 

.733 

.  186  9268 

.378  955 

.065  0239 

.783 

.208  6415 

.167  451 

.061  8527 

.734 

.187  3611 

•394  34i 

.064  9589 

.784 

.209  0758 

.183  626 

.061  7908 

2.735 

1.187  7954 

15.409  743 

0.064  8940 

2.785 

1.209  5101 

16.199  818 

0.061  7291 

.736 

.188  2297 

.425  161 

.064  8291 

.786 

.209  9444 

.216  026 

.061  6674 

.737 

.  188  6640 

.440  594 

.064  7643 

.787 

.210  3787 

.232  250 

.061  6058 

.738 

.189  0983 

.456  042 

.064  6006 

.210  8130 

.248  490 

.061  5442 

.739 

.189  5326 

.471  5o6 

.064  6349 

'.& 

.211  2473 

.264  747 

.061  4827 

2.740 

1.189  9669 

15.486  985 

0.064  5703 

2.790 

I.  211  68l6 

16.281  020 

0.061  4212 

.741 

.190  4012 

.502  480 

.064  5058 

.791 

.212  1159 

.297  309 

.061  3598 

.742 

.190  8355 

.517  990 

.064  4413 

.792 

.212  5502 

.313  614 

.061  2985 

.743 

.191  2698 

.533  5i6 

.064  3769 

.793 

.212  9845 

•329  936 

.061  2372 

.744 

.191  7041 

•549  057 

.064  3126 

•  794 

.213  4188 

.346  274 

.061  1760 

2.745 

1.192  1384 

15.564  614 

0.064  2483 

2.795 

I.2I3  8531 

16.362  629 

0.061  1149 

.746 

.192  5726 

.580  186 

.064  1841 

.796 

.214  2874 

.379  ooo 

.061  0538 

.747 

.193  0069 

•595  774 

.064  1199 

.797 

.214  7217 

•395  387 

.060  9928 

.748 

.193  4412 

.611  378 

.064  0558 

.798 

.215  1560 

.411  790 

.060  9318 

.749 

.193  8755 

.626  997 

.063  9918 

.799 

•215  5903 

.428  2IO 

.060  8709 

2.750 

1.194  3098 

15.642  632 

0.063  9279 

2.800 

1.216  0245 

16.444  647 

0.060  8101 

loge(eu) 

looio(en) 

eu 

e~~u 

looe(eu) 

looio(en) 

eu 

e~u 

SMITHSONIAN  TABLES 


253 


The  Exponential. 


u 

logio(eu) 

en 

e  u 

u 

looio(en) 

eu 

e~u 

2.800 

I.  216  0245 

16.444  647 

0.060  8101 

2.850 

1-237  7393 

17.287  782 

0.057  8443 

.801 

.216  4588 

.461  loo   .060  7493 

.851 

.238  1736 

.305  078 

.057  7865 

.802 

.216  8931 

.477  569   -060  6886 

.852 

.238  6079 

.322  392 

.057  7287 

.803 

.217  3274 

.494  055   .060  6279 

.853 

.239  0422 

•339  723 

.057  6710 

.804 

.217  7617 

•510  557 

.060  5673 

•854 

.239  4765 

•357  071 

.057  6134 

2.805 

1.218  1960 

16.527  076 

0.060  5068 

2.855 

1.239  9107 

17.374  437 

0.057  5558 

.806 

.218  6303 

•543  611 

.060  4463 

.856 

.240  3450 

.391  820 

.057  4083 

.807 

.219  0646 

.560  163 

.060  3859 

•  857 

.240  7793 

.409  221 

.057  4408 

.808 

.219  4989 

.576  732 

.060  3255 

.858 

.241  2136 

.426  639 

•057  3834 

.809 

.219  9332 

•593  317 

.060  2652 

.859 

.241  6479 

.444  074 

.057  3261 

2.810 

1.220  3675 

16.609  9i8 

0.060  2050 

2.860 

1.242  0822 

17.461  527 

0.057  2688 

.811 

.220  8018 

.626  536 

.060  1448 

.861 

.242  5165 

.478  997 

.057  2115 

.812 

.221  2361 

.643  I7i 

.060  0847 

.862 

.242  9508 

.496  485 

•057  1543 

.813 

.221  6704 

.659  823 

.060  0246 

.863 

.243  3851 

.513  990 

.057  0972 

.814 

.222  1047 

.676  491 

.059  9047 

.864 

.243  8194 

.531  513 

.057  0401 

2.815 

1.222  5390 

16.693  176 

0.059  9047 

2.865 

1.244  2537 

17.549  053 

0.056  9831 

.816 

.222  9733 

.709  877 

.059  8448 

.866 

.244  6880 

.566  611 

.056  9262 

.817 

.223  4076 

.726  596 

.059  7850 

.857 

.245  1223 

.584  186 

.056  8693 

.818 

.223  8418 

•743  331 

.059  7253 

.868 

.245  5566 

.601  779 

.056  8124 

.819 

.224  2761 

.760  082 

.059  6656 

.869 

.245  9909 

.619  390 

•056  7557 

2.820 

1.224  7104 

16.776  851 

0.059  6059 

2.870 

1.246  4252 

17.637  018 

0.056  6989 

.821 

.225  1447 

.793  636 

•059  5464 

.871 

.246  8595 

.654  664 

.056  6423 

.822 

.225  5790 

.810  438 

.059  4868 

.872 

.247  2938 

.672  328 

•056  5856 

.823 

.824 

.226  0133 
.226  4476 

.827  257 
.844  692 

.059  4274 
.059  3680 

.873 
.874 

.247  7280 
.248  1623 

.690  009 

.707  708 

.056  5291 
.056  4726 

2.825 

1.226  8819 

16.860  945 

0.059  3087 

2.875 

1.248  5966 

17.725  424 

0.056  4161 

.826 

.227  3162 

.877  814 

.059  2494 

.876 

.249  0309 

•743  158 

.056  3598 

.827 

.227  7505 

.894  70i 

.059  1902 

.877 

.249  4652 

.760  910 

.056  3034 

.828 

.228  1848 

.911  604 

.059  1310 

.878 

.249  8995 

.778  680 

.056  2471 

.829 

.228  6191 

.928  524 

.059  0719 

.879 

•250  3338 

.796468 

.056  1909 

2.830 

1.229  0534 

16.945  461 

0.059  0129 

2.880 

1.250  7681 

17.814  273 

0.056  1348 

.831 

.229  4877 

.962  415 

.058  9539 

.881 

.251  2024 

.832  096 

.056  0787 

.832 

.229  9220 

.979  386 

.058  8949 

.882 

.251  6367 

•849  937 

.056  0226 

.833 

.230  3563 

.996  374 

.058  8361 

.883 

.252  0710 

.867  795 

.055  9666 

.834 

.230  7906 

17-013  378 

•058  7773 

.884 

.252  5053 

.885  673 

.055  9107 

2.835 

1.231  2249 

17.030  400 

0.058  7185 

2.885 

1.252  9396 

17.903  568 

0.055  8548 

.836 

.231  6592 

.047  439 

.058  6598 

.886 

.253  3739 

.921  480 

.055  7990 

.837 

.232  0934 

.064  495 

.058  6012 

.887 

.253  8082 

•939  411 

•055  7432 

.838 

.232  5277 

.081  568 

.058  5426 

.888 

.254  2425 

.957  359 

.055  6875 

.839 

.232  9620 

.098658 

.058  4841 

.889 

.254  6768 

•975  325 

.055  6318 

2.840 

1.233  3963 

17.115  766 

0.058  4257 

2.890 

1.255  TIII 

17-993  310 

0.055  5762 

.841 

.233  8306 

.132  890 

•058  3673 

.891 

.255  5453 

18.011  312 

.055  5207 

.842 

.234  2649 

.150  031 

.058  3089 

.892 

.255  9796 

.029  332 

.055  4652 

.843 

.234  6992 

.167  190 

.058  2507 

.893 

.256  4139 

.047  371 

.055  4097 

.844 

•235  1335 

.184  366 

.058  1924 

.894 

.256  8482 

.065  4^7 

.055  3544 

2.845 

1.235  5678 

17.201  559 

0.058  1343 

2.895 

1.257  2825 

18.083  SOT 

0.055  2990 

.846 

.236  0021 

.218  769 

.058  0762 

.896 

.257  7i68 

.101  594 

.055  8438 

.847 

.236  4364 

.235  996 

.058  0181 

.*,; 

.258  1511 

.119  705 

.055  1885 

.848 

.236  8707 

.253  241 

.057  0601 

.898 

.258  5854 

.  137  833 

.055  U34 

.849 

.237  3050 

.270  503 

.057  9022 

.899 

.259  0197 

.155  98o 

•055  0783 

2.850 

1.237  7393 

17.287  782 

0.057  8443 

2.900 

1.259  4540 

18.174  MS 

0.055  0232 

lofe(en) 

Iog10(e0) 

e" 

a— 

1ooc(eu) 

lo0l,Xea) 

a" 

e- 

SMITHSONIAN  TABLES 


254 


The  Exponential. 


1  
u 

logw(eu) 

eu 

e~u 

u 

logio(en) 

en 

e~u 

2.900 

1.259  4540 

18.174  145 

0.055  0232 

2.950 

1.281  1687 

19-105  954 

0.052  3397 

.501 

.259  8883 

.192  329 

.054  9682 

•  951 

.281  6030 

.125  069 

.052  2874 

.902 

.260  3226 

.210  530 

.054  9133 

•  952 

.282  0373 

.144  204 

.052  2351 

.903 

.260  7569 

.228  750 

.054  8584 

•  953 

.282  4716 

•163  358 

.052  1829 

.904 

.261  1912 

.246  988 

.054  8036 

•954 

.282  9059 

.182  531 

.052  1308 

2.905 

1.261  6255 

18.265  244 

0.054  7488 

2.955 

1.283  3402 

19.201  723 

0.052  0787 

.906 

.262  0598 

.283  5l8 

.054  6941 

.956 

.283  7745 

.220  934 

.052  0266 

.907 

.262  4941 

.301  811 

.054  6304 

•957 

.284  2088 

.240  165 

.051  9746 

.908 

.262  9284 

.320  122 

.054  5848 

.958 

.284  6431 

.259  414 

.051  9227 

.909 

.263  3626 

.338  451 

.051  5302 

•959 

.285  0774 

.278  683 

.051  8708 

2.910 

1.263  7969 

18.356"  799 

0.054  4757 

2.060 

1.285  5H7 

19.297  972 

0.051  8189 

.911 

.264  2312 

•375  165 

.054  4213 

.961 

.285  9460 

.317  279 

.051  7671 

.912 

.264  6655 

•393  549 

.054  3669 

.962 

.286  3803 

.336  606 

.051  7154 

.913 

.265  0998 

.411  952 

.054  3125 

.963 

.286  8145 

•355  953 

.051  6637 

.914 

.265  5341 

•430  373 

.054  2583 

.964 

.287  2488 

.375  3i8 

.051  6121 

2.915 

1.265  9684 

18.448  812 

0.054  2040 

2.965 

1.287  6831 

19.394  703 

0.051  5605 

.916 

.266  4027 

.467  270 

.054  1499 

.966 

.288  1174 

.414  108 

.051  5089 

.917 

'  .266  8370 

.485  747 

.054  0957 

.967 

.288  5517 

•433  53i 

.051  4575 

.918 

.267  2713 

.504  242 

.054  0417 

.968 

.2889860 

•452  975 

.051  4060 

.919 

.267  7056 

.522  755 

.053  9876 

.969 

.289  4203 

•472  437 

.051  3546 

2.920 

1.268  1399 

18.541  287 

0.053  9337 

2.970 

1.289  8546 

19.491  920 

0.051  3033 

.921 

.268  5742 

•559  838 

.053  8758 

•971 

.290  2889 

.511  421 

.051  2520 

.922 

.269  0085 

.578  407 

.053  8259 

.972 

.290  7232 

.530  942 

.051  2008 

.923 

.269  4428 

.596  995 

.053  7721 

•  973 

.291  1575 

•550  483 

.051  1496 

.924 

.269  8771 

.615  601 

.053  7184 

•974 

.291  5918 

.570  043 

.051  0985 

2.925 

1.270  3114 

18.634  226 

0.053  6647 

2.975 

1.292  0261 

19.589  623 

0.051  0474 

.926 

.270  7457 

.652  870 

.053  6111 

.976 

.292  4604 

.609  223 

.050  9964 

.927 

.271  1799 

.671  532 

•053  5575 

•977 

.292  8947 

.628  842 

.050  9454 

.928 

.271  6142 

.690  213 

.053  5039 

.978 

.293  3290 

.648  480 

.050  8045 

.929 

.272  0485 

.708  912 

.053  4505 

•979 

.293  7633 

.668  139 

.050  8437 

2.930 

1.272  4828 

18.727  631 

0.053  3970 

2.980 

1.294  1976 

19.687  817 

0.050  7928 

.931 

.272  9171 

.746  368 

.053  3437 

.981 

.294  6319 

.707  5U 

.050  7421 

.932 

.273  3514 

.765  123 

.053  2904 

.982 

.295  0661 

.727  232 

.050  6913 

•  933 

•273  7857 

.783  898 

.053  2371 

.983 

.295  5004 

.746  969 

.050  6407 

•  934 

.274  22OO 

.802  691 

.053  1839 

.984 

.295  9347 

.766  726 

.050  5901 

2.935 

1.274  6543 

18.821  505 

0.053  1307 

2.985 

1.296  3690 

19.786  502 

0.050  5395 

.936 

.275  0886 

.840  334 

.053  0776 

.986 

.296  8033 

.806  299 

.050  4890 

•937 

.275  5229 

.859  184 

.053  0246 

.987 

.297  2376 

.826  115 

.050  4385 

.938 

.275  9572 

.878  052 

.052  9716 

.988 

.297  6719 

.845  951 

.050  3881 

•939 

.276  3915 

.896  940 

.052  9186 

.989 

.298  1062 

.865  807 

.050  3377 

2.940 

1.276  8258 

18.915  846 

0.052  8657 

2.990 

1.298  5405 

19.885  682 

0.050  2874 

.941 

.277  2601 

•934  772 

.052  8129 

.991 

.298  9748 

.905  578 

.050  2372 

.942 

.277  6944 

•953  7i6 

.052  7601 

.992 

.299  4091 

.925  494 

.050  1870 

•943 

.278  1287 

.972  679 

.052  7074 

•993 

.299  8434 

.945  429 

.050  1368 

•944 

.278  5630 

.991  661 

.052  6547 

.994 

.300  2777 

.965  385 

.050  0867 

2.945 

1.278  9972 

19.010  662 

0.052  6021 

2.995 

1.300  7120 

19.985  360 

0.050  0366 

.946 

.279  4315 

.029  683 

.052  5495 

.996 

.301  1463 

20.005  355 

.049  9866 

•  947 

.279  8658 

.048  722 

.052  4970 

•997 

.301  5806 

.025  371 

.049  9367 

.948 

.280  3001 

.067  780 

.052  4445 

.998 

.302  0149 

.045  406 

.049  8867 

•  949 

.280  7344 

.086857 

.052  3921 

•999 

.302  4492 

.065  461 

.049  8369 

2.950 

1.281  1687 

19-105  954 

0.052  3397 

3.000 

1.302  8834 

20.085  537 

0.049  7871 

looe(eu) 

logio(eu) 

eu 

e~u 

lofle(eu) 

logio(eu) 

eu 

e-u 

SMITHSONIAN  TABLES 


255 


The  Exponential. 


u 

looio(eu) 

en 

e  u 

u 

logioCe") 

eu 

•- 

3.00 

.01 

.02 

.03 
.04 

1.302  8834 
.307  2264 
•311  5693 
.315  9123 
.320  2552 

20.085  537 
.287  400 
.491  292 
.697  233 
.905  243 

0.049  7871 
.049  2917 
.048  8012 
.048  3156 
.047  8349 

3-50 

•  51 

•  52 
.53 
•  54 

1.520  0307 
.524  3736 
.528  7166 
.533  0595 
•537  4025 

33-115  452 
.448  268 
.784  429 
34.123  968 
.466  919 

0.030  1974 
.029  8969 
.029  5994 
.029  3049 
.029  0133 

3-05 
.06 
.07 
.08 
.09 

1.324  5982 
.328  9411 
.333  2841 
.337  6270 
.341  9699 

2I.H5  344 
.327  557 
.541  903 
.758  402 
.977  078 

0.047  3589 
.046  8877 
.046  4212 
.045  9593 
.045  5020 

S:S 

:i 

•  59 

1.541  7454 
.546  0884 
•550  4313 
•554  7742 
•  559  H72 

34.813  318 
35.163  197 
.5i6  593 
.873  541 
36.234  076 

0.028  7246 
.028  4388 
.028  1559 
.027  8757 
•027  5983 

3-10 
.11 

.12 

.13 
.14 

1.346  3129 
•350  6558 
.354  9988 
•359  3417 
.363  6847 

22.197  951 
.421  044 
.646  380 
.873  080 
23.103  867 

0.045  0492 
.044  6010 
.044  1572 
.043  7178 
.043  2828 

3.60 

.6l 
.62 
.63 

.64 

1.563  4601 
.567  8031 
.572  1460 
.576  4890 
.580  8319 

36.598  234 
.966  053 
37.337  568 
.712  817 
38.091  837 

0.027  3237 
.027  0518 
.026  7827 
.026  5162 
.026  2523 

3.15 
.16 

is 

.19 

1.368  0276 
•372  3706 
.376  7U5 
.381  0565 
.385  3994 

23.336  065 
.570  596 
.807  484 
24.046  754 
.288  427 

0.042  8521 
.042  4257 
.042  0036 
.041  5857 
.041  1719 

3.65 

.66 
.67 
.68 
.69 

1.585  1749 
089  5178 
•593  8607 
.598  2037 
.602  5466 

38.474  666 
.861  343 
39.251  906 
.646  394 
40.044  847 

0.025  9911 
.025  7325 
.025  4765 
.025  2230 
.024  9720 

3.20 

.21 
.22 
.23 
.24 

1.389  7423 
.394  0853 
.398  4282 
.402  7712 
.407  1141 

24.532  530 
.779086 

25.O28  I2O 
.279  657 

•533  722 

0.040  7622 
.040  3566 
.039  9551 
.039  5575 
.039  1639 

3.70 

.71 
•  72 

•  73 
•  74 

I  .606  8896 
.611  2325 
.615  5755 
.619  9184 
.624  2614 

40.447  304 
.853  807 
41.264  394 
.679  108 
42.097  990 

0.024  7235 
.024  4775 
.024  2340 
.023  9928 
.023  7541 

3.25 
.26 

3 

.29 

1.411  4571 
.415  8000 
.420  1430 
.424  4859 

25.790  340 
26.049  537 
.3H  339 
•575  773 
.842  864 

0.038  7742 
.038  3884 
.038  0064 
.037  6283 
.037  2538 

3:^ 

.77 
•  78 
.79 

1.628  6043 
•632  9473 
.637  2902 
.641  6331 
.645  9761 

42.521  082 
.948  426 
43.380  065 
.816  042 
44.256  400 

0.023  5177 
.023  2837 
.023  0521 
.022  8227 
.022  5956 

3.30 
.31 
•32 
•33 

•  34 

1.433  1718 
•437  5147 
.441  8577 
.446  2006 
.450  5436 

27.112  639 
.385  125 
.660  351 
.938  342- 
28.219  127 

0.036  8832 
.036  5162 
.036  1528 
.035  7931 
.035  4370 

3.8o 
.81 
.82 
.83 
.84 

1.650  3190 
.654  6620 
.659  0049 
.663  3479 
.667  6908 

44.701  184 

45.150  439 
.604  208 
46.062  538 
.525  474 

0.022  3708 
.022  1482 
.O2I  9278 
.O2I  7096 
.O2I  4936 

':S 

3 

.39 

1.454  8865 
.459  2295 
.463  5724 
.467  9153 
.472  2583 

28.502  734 
.789  191 
29.078  527 
.370  771 
.665  952 

0.035  0844 
•034  7353 
.034  3896 
.034  0475 
.033  7087 

':!! 

:! 

.89 

1.672  0338 
.676  3767 
.680  7196 
.685  0626 
.689  4055 

46.093  063 
47.465  351 
•942  386 
48.424  215 
.910  887 

O.02I  2797 
.021  0680 
.020  8584 
.020  6508 

.020  4453 

3.40 

.41 

.42 

•43 
•44 

1.476  6012 
.480  9442 
.485  2871 
.489  6301 
.493  9730 

29.964  100 
30.265  244 
.569  415 
.876  643 
31.186  958 

0.033  3733 
.033  0412 
.032  7124 
.032  3869 
.032  0647 

3-90 
.91 
.92 
•93 
.94 

1.693  7485 
.698  0914 
.702  4344 
.706  7773 
.711  1203 

49.402  449 
.898952 
50.400  445 
.906  978 
51.418  601 

0.020  2419 
.020  O405 
.OI9  8411 
.019  6437 
.OI9  4482 

3-45 
.46 
•  47 
.48 
.49 

1.498  3160 
.502  6589 
.507  0019 
.511  3448 
.515  6877 

31.500  392 
.816  977 
32.136  743 
.459  722 
.785  948 

0.031  7456 
.031  4298 
.031  1170 
.030  8074 
.030  5009 

3'?J 
.96 

.99 

1.715  4632 
.719  8061 
.724  1491 
.728  4920 
•732  8350 

51.935  367 
52.457  326 
.984  53i 
53.517  034 
54.054  889 

0.019  2547 
.019  0631 
.018  8734 
.018  6856 
.018  4997 

3.50 

1.520  0307 

33-II5  452 

0.030  1974 

4.00 

1.737  1779 

54.598  150 

0.018  3156 

loflc(e°) 

looicXe") 

en 

e~u 

looc(en) 

loouXe") 

'" 

e~u 

SMITHSONIAN  TABLCS 


256 


The  Exponential. 


1  
u 

logio(eu) 

eu 

e~u 

u 

loflio(en) 

eu 

e 

4.00 

1-737  1779 

54.598  150 

0.018  3156 

4.50 

1.954  3252 

90.017  131 

o.on  .1090 

.01 

.741  5209 

55.146  871 

.018  1334 

.51 

.958  6681 

.921  819 

.010  9985 

.02 

•745  8638 

.701  106 

.017  9530 

.52 

.963  oni 

91.835  598 

.010  8890 

•03 

.750  2068 

56.260  911 

.017  7743 

•  53 

.967  3540 

92.758  561 

.010  7807 

.04 

•754  5497 

.826  343 

.017  5975 

•  54 

.971  6969 

93.690  800 

.010  6734 

4-05 

1.758  8927 

57-397  457 

0.017  4224 

4-55 

1.976  0399 

94.632  408 

o.oio  5672 

.06 

.763  2356 

.974  3ii 

.017  2490 

.56 

.980  3828 

95.583  480 

.010  4621 

.07 

.767  5785 

58.556  963 

.017  0774 

•  57 

.984  7258 

96.544  no 

.010  3580 

.08 

.771  9215 

59.145  470 

.016  9075 

.58 

.9890687 

97.514  394 

.010  2549 

.09 

.776  2644 

.739  892 

.016  7392 

.59 

•993  4H7 

98.494  430 

.oio  1529 

4.10 

1.780  6074 

60.340  288 

0.016  5727 

4.60 

1.997  7546 

99.484  3i6 

o.oio  0518 

.11 

.784  9503 

.946  718 

.016  4078 

.61 

2.002  0976 

100.484  150 

.009  9518 

.12 

•  .789  2933 

6i.559  242 

.016  2445 

.62 

.006  4405 

101.494  032 

.009  8528 

•13 

.793  6362 

62.177  923 

.016  0829 

.63 

.010  7835 

102.514  064 

.000  7548 

.14 

•797  9792 

.802  821 

.015  9229 

.64 

.015  1264 

103.544  348 

.009  6577 

4-15 

1.802  3221 

63.434  ooo 

0.015  7644 

4.65 

2.019  4693 

104.584  986 

0.009  5616 

.16 

.806  6650 

64.071  523 

.015  6076 

.66 

.023  8123 

105.636  082 

.009  4665 

•  17 

.811  0080 

.715  452 

.015  4523 

.67 

.028  1552 

106.697  743 

.009  3723 

.18 

.815  3509 

65.365  853 

.015  2085 

.68 

.032  4082 

107.770  073 

.009  2790 

.19 

.819  6939 

66.022  791 

.015  1463 

.69 

.036  8411 

108.853  180 

.009  1867 

4.20 

1.824  0368 

66.686  331 

0.014  9956 

4.70 

2.041  1841 

109.947  172 

0.009  0953 

.21 

.828  3798 

67-356  540 

.014  8464 

.71 

.045  5270 

111.052  160 

.009  0048 

.22 

.832  7227 

68.033  484 

.014  6986 

.72 

.049  8700 

112.168  253 

.008  9152 

•23 

.837  0657 

.717  232 

.014  5524 

•  73. 

.054  2129 

113.295  563 

.008  8265 

.24 

.841  4086 

69.407  852 

.014  4076 

•  74 

.058  5558 

114.434  20  J 

.008  7386 

4-25 

1.845  7515 

70.105  412 

0.014  2642 

4.75 

2.062  8o83 

115.584  285 

0.008  6=517 

.26 

.850  0945 

.809983 

.014  1223 

•  76 

.067  2417 

II6.745  926 

.008  5656 

.27 

.854  4374 

71.521  636 

.013  9818 

•  77 

.071  5847 

II7.9I9  242 

.008  4804 

.28 

.858  7804 

72.240  440 

.013  8427 

.   .78 

.075  9276 

II9.I04  351 

.008  3960 

.29 

.863  1233 

.966  468 

.013  7049 

.79 

.080  2706 

120.301  369 

.008  3125 

4.30 

1.867  4663 

73.699  794 

0.013  5686 

4.80 

2.084  6135 

I2I.5IO  418 

0.008  2297 

•31 

.871  8092 

74.440  489 

.013  4335 

.81 

.088  9565 

122.731  61  8 

.008  1479 

•32 

.876  1522 

75.188  628 

.013  2999 

.82 

"  .093  2994 

123.965  091 

.008  0668 

•  33 

.880  4951 

.944  287 

.013  1675 

.83 

.097  6423 

125.210  961 

.007  9865 

•34 

.884  8381 

76.707  539 

.013  0365 

.84 

.101  9853 

126.469  352 

.007  9071 

4-35 

1.889  1810 

77.478  463 

0.012  9068 

4.85 

2.106  3282 

127.740  390 

0.007  8284 

.36 

.893  5239 

78.257  134 

.012  7784 

.86 

.no  6712 

129.024  203 

.007  7505 

•  37 

.897  8669 

79.043  632 

.012  6512 

.87 

.115  0141 

130.320  918 

.007  6734 

.38 

.902  2058 

.838  033 

.012  5254 

.88 

.119  357i 

131.630  665 

.007  5970 

•  39 

.906  5528 

80.640  419 

.012  4007 

.89 

.123  7000 

132.953  575 

.007  5214 

4.40 

1.910  8957 

81.450  869 

O.OI2  2773 

4.90 

2.128  0430 

134.289  780 

0.007  4466 

.41 

.915  2387 

82.269  464 

.012  1552 

.91 

.132  3859 

135.639  415 

.007  3725 

.42 

.919  5816 

83.096  285 

.012  0342 

.92 

.  136  7289 

137.002  613 

.007  2991 

•43 

.923  9246 

.931  417 

.Oil  9U5 

•93 

.141  0718 

138.379  513 

.007  2265 

.44 

.928  2675 

84.774  942 

.011  7959 

.94 

.145  4147 

139.770  250 

.007  1546 

4-45 

1.932  6104 

85.626  944 

o.on  6786 

4.95 

2.149  7577 

141.174  964 

0.007  0834 

.46 

.936  9534 

86.487  509 

.on  5624 

.96 

.154  1006 

142.593  796 

.007  0129 

•47 

.941  2963 

87.356  723 

•oil  4473 

•97 

.158  4436 

144.026  888 

.006  9431 

.48 

•945  6393 

88.234  673 

.oil  3334 

.98 

.162  7865 

145.474  382 

.006  8741 

•49 

.949  9822 

89.121  446 

.on  2206 

•  99 

.167  1295 

146.936  424 

.006  8057 

4-50 

1.954  3252 

90.017  131 

,0.011  1090 

5.00 

2.171  4724 

148.413  159 

0.006  7379 

loge(eu) 

looio(en) 

eu 

e~u 

loge(eu) 

lodio(eu) 

eu 

e~u 

SMITHSONIAN  TABLES 


257 


The  Exponential. 


u 

looio(eu) 

eu 

e~u 

u 

looio(eu) 

eu 

e 

5.00 

2.171  4724 

148.413  159 

0.006  7379 

5.50 

2.388  6197 

244.691  932 

0.004  0868 

.01 

.175  8154 

149.904  736 

.006  6709 

•  51 

.392  9626 

247.151  127 

.004  0461 

.02 

.180  1583 

151.411  304 

.006  6045 

•52 

•397  3055 

249.635  037 

.004  0058 

.03 

.184  5012 

152.933  013 

.006  5388 

•  53 

.401  6485 

252.143  911 

.003  9660 

.04 

.188  8442 

154.470  015 

.006  4737 

•  54 

.405  9914 

254.677  999 

.003  9265 

5-05 

2.193  18/1 

156.022  464 

0.006  4093 

5-55 

2.410  3344 

257.237  556 

0.003  8875 

.06 

.197  5301 

157.590  516 

.006  3456 

.56 

.414  6773 

259.822  836 

.003  8488 

.07 

.201  8730 

159.174  327 

.006  2824 

•  57 

.419  0203 

262.434  099 

.003  8105 

.08 

.206  2l6o 

160.774  056 

.006  2109 

•  58 

.423  3632 

265.071  606 

.003  7726 

.09 

.210  5589 

162.389  862 

.006  1580 

•  59 

.427  7062 

267.735  620 

.003  7350 

5-10 

2.214  9OI9 

164.021  907 

0.006  0967 

5.6o 

2.432  0491 

270.426  407 

0.003  6979 

.11 

.219  2448 

165.670  355 

.006  0361 

.61 

.436  3920 

273.144  238 

.003  6611 

.12 

.223  5877 

167.335  369 

.005  9760 

.62 

•440  7350 

275.889  383 

.003  6246 

•13 

.227  9307 

169.017  118 

.005  9166 

.63 

.445  0779 

278.662  117 

.'003  5886 

.14 

.232  2736 

170.715  768 

•005  8577 

.64 

.449  4209 

281.462  718 

.003  5529 

5.15 

2.236  6l66 

172.431  490 

0.005  7994 

5.65 

2.453  7638 

284.291  466 

0.003  5175 

.16 

.240  9595 

174.164  455 

.005  7417 

.66 

.458  1068 

287.148  642 

.003  4825 

.17 

.245  3025 

175-914  837 

.005  6846 

.67 

.462  4497 

200.034  534 

.003  4479 

.18 

.249  6454 

177.682  811 

.005  6280 

.68 

.466  7927 

292.949  430 

.003  4136 

.19 

.253  9884 

179.468  553 

.005  5720 

.69 

.471  1356 

295.893  620 

.003  3796 

5-20 

2.258  3313 

181.272  242 

0.005  5166 

5-70 

2.475  4785 

298.867  401 

0.003  346o 

.21 

.262  6743 

183.094  058 

.005  4617 

.71 

.479  8215 

301.871  068 

.003  3127 

.22 

.267  0172 

184.934  184 

.005  4073 

.72 

.484  1644 

304.904  923 

.003  2797 

•23 

.271  3601 

186.792  804 

•005  3535 

•  73 

•488  5074 

307.069  268 

.003  2471 

.24 

•275  7031 

188.670  103 

.005  3003 

•74 

•492  8503 

311.064  411 

.003  2148 

5-25 

2.280  0460 

190.566  269 

0.005  2475 

5-75 

2.497  1933 

314.190  660 

0.003  1828 

.26 

.284  3890 

192.481  491 

.005  1953 

.76 

.501  5362 

317.348  329 

.  .003  1511 

.27 

.288  7319 

194.415  963 

.005  1436 

77 

•505  8792 

320.537  733 

.003  1198 

.28 

.293  0749 

196.369  875 

.005  0924 

.78 

.5IO  2221 

323.759  190 

.003  0887 

.29 

.297  4178 

198.343  426 

.005  0418 

•  79 

.514  5651 

327.013  024 

.003  0580 

5.30 

2.301  7608 

200.336  8  10 

0.004  9916" 

5.8o 

2.518  9080 

330.299  560 

0.003  0276 

.31 

.306  1037 

202.350  228 

.004  9419 

.81 

.523  2509 

333.619  126 

.002  9974 

.32 

.310  4466 

204.383  882 

/OO4  8928 

.82 

.527  5939 

336.972  054 

.002  9676 

•33 

.314  7896 

206.437  974 

.004  8441 

.83 

•531  9368 

340.358  679 

.002  9381 

•  34 

.319  1325 

208.512  710 

.004  7959 

.84 

.536  2798 

343-779  341 

.002  9088 

5-35 

2.323  4755 

210.608  298 

0.004  7482 

5.85 

2.540  6227 

347.234  381 

O.OO2  8799 

.36 

.327  8184 

212.724  946 

.004  7009 

.86 

.544  9657 

350.724  144 

.OO2  8512 

•  37 

.332  1614 

214.862  868 

.004  6541 

.87 

.549  3086 

354-248  980 

.002  8229 

.38 

.336  5043 

217.022  275 

.004  6078 

.88 

•553  6516 

357.809  242 

.002  7948 

•  39 

.340  8473 

219.203  386 

.004  5620 

.89 

•557  9945 

361.405  284 

.002  7670 

5.40 

2.345  1902 

221.406  416 

0.004  5i66 

5-90 

2.562  3374 

365.037  468 

0.002  7394 

.41 

•349  5331 

223.631  588 

.004  4716 

.91 

.5666804 

368.706  156 

.002  7122 

.42 

.353  8761 

225.879  122 

.004  4271 

.92 

•571  0233 

372.411  714 

.002  6852 

•43 

.358  2190 

228.149  245 

.004  3831 

•93 

.575  3663 

376.154  5M 

.002  6585 

•  44 

.362  5620 

230.442  183 

•004  3395 

•94 

•579  7092 

379-934  930 

.002  6320 

5-45 

2.366  9049 

232.758  166 

0.004  2963 

5-95 

2.584  0522 

383.753  339 

O.OO2  6058 

.46 

.371  2479 

235.097  424 

.004  2536 

.96 

•688  3951 

387.610  124 

.002  5799 

•47 

.375  59o8 

237.460  193 

.004  21  12 

•97 

•592  738i 

39L505  671 

.002  5542 

.48 

.379  9338 

239.846  707 

.004  1093 

,   -98 

.597  0810 

395.440  368 

.002  5288 

.49 

•384  2767 

242.257  207 

.004  1278 

•99 

.601  4239 

399.414  610 

.002  5037 

5.50 

2.388  6197 

244.691  932 

0.004  0868 

6.00 

2.605  7669 

403.4^8  793 

0.002  4788 

log,(eu) 

100,0(6") 

e" 

e~u 

UMk(e°) 

looi<Xeu) 

eu 

e~a 

SMITHSONIAN  TABLES 


258 


The  Exponential. 


u 

looioCe") 

eu 

e-« 

I 

.43429  44819 

2.71  828      183 

0.367  879  441 

2 

.86858  89638 

7.38  905     610 

0.135  335  283 

3 

1.30288  34457 

20.0  855     369 

(I)       497870684 

4 

I.737I7  79276 

54-5  98i      500 

(I)        183  156  389 

5 

2.17147  24095 

148.  413      159 

(2)       673  794  700 

6 

2.60576  68914 

403.  428     793 

(2)       247  875  218 

7 

3.04006  13733 

109    6.63   316 

(3)       911  88  i  966 

8 

3.47435  58552 

298"  0.95    799 

(3)       335  462  628 

9 

3.90865  03371 

810    3.08  393 

(3)       123  409  804 

10 

4.34294  48190 

220    26.4  658 

(4)       453  999  298 

ii 

4.77723  93009 

598    74-1    417 

(4)       167  017  008 

12 

5-2II53  37828 

162     754.    791 

(5)       614  421  235 

13 

5.64582  82647 

442    413.    392 

(5)       226  032  941 

14 

6.08012  27466 

I2O      260       4.28 

(6)       831  528  719 

15 

6.51441  72285 

326     001       7-37 

(6)      305  902  321 

16 

6.94871   I7I05 

888    611     0.52 

(6)       112  535  175 

17 

7.38300  61924 

241    549     52.8 

(7)       413  993  772 

18 

7.81730  06743 

656    599     69.1 

(7)       152  299  797 

19 

8.25159  51562 

178    482     301  . 

(8)       560  279  644 

20 

8.68588  96381 

485     165      195. 

(8)      206  115  362 

21 

9.12018  41200 

131    881     573 

'.I. 

(9)       758  256  043 

22 

9.55447  86019 

358    49i     285 

X 

(9)       278  946  809 

23 

9.98877  30838 

974    480     345 

'£, 

(9)       102  618  796 

24 

10.42306  75657 

264     891       221 

~2\ 

(10)       377  513  454 

25 

10.85736  20476 

720    048     993 

2 

(10)       138  879  439 

26 

11.29165  65295 

195     729     609 

\3'. 

(ii)       510908903 

27 

H.72595  10114 

532    048     241 

.3. 

(ii)       187  952  882 

28 

12.16024  54933 

144    625     707 

A 

(12)        691  440  Oil 

29 

12.59453  99752 

393     133     430 

(12)         254  366  565 

30 

13.02883  44571 

106    864     746 

[5. 

(13)       935  762  297 

31 

13.46312  89390 

290    488     497 

'.5. 

(13)       344247711 

32 

13.89742  34209 

789    629     602 

'£'. 

(13)       126  641  656 

33 

14.33171  79028 

214    643     58o 

6: 

(14)      465  888  615 

34 

14.76601  23847 

583    461     743 

6; 

(14)       171  390  843 

35 

15.20030  68666 

158    601     345 

'7. 

(15)      630  511  676 

36 

15.63460  13485 

431     123      155 

7] 

(15)      231  952  283 

37 

16.06889  58304 

117     191     424 

8] 

(16)      853  304  763 

38 

16.50319  03123 

3i8    559     3i8      [ 

8] 

(16)      313  9i3  279 

39 

16.93748  47942 

865    934     004       [8; 

(16)       115  482  242 

40 

17.37177  92761 

235    385     267       [9] 

(17)      424  835  426 

41 

17.80607  37580 

639    843     493       I 

(17)       156  288  219 

42 

18.24036  82399 

173    927     494     [10: 

(18)       574  952  227 

43 

18.67466  27218 

472    783     947     [10: 

(18)      211  513  104 

44 

19.10895  72037 

128    516     ooi     [ii] 

(19)         778   113   22J. 

45 

19.54325  16856 

349    342     711     [ii; 

(19)      286  251  858 

46 

19.97754  61675 

949    611     942     [n; 

(19)       105  306  174 

47 

20.41184  06495 

258    131     289     [12; 

(20)       387  399  763 

48 

20.84613  51314 

701    673     59i     [12] 

(20)       142  516  408 

49 

21.28042  96133 

190    734     657     [i 

(21)         524  288   566 

50 

21.71472  40952 

518    470     553     [13] 

(21)          192  874  985 

The  numbers  in  square  brackets  denote  the  numbers  of  figures  between  the 

last  figure  given  and  the  decimal  point  ;  for  example,  the  first  nine  figures  of  e50 

are  518470553,  and  there  are  13  additional  figures  before  the  decimal  point  is 

reached.     The  numbers  in  parentheses  denote  the  numbers  of  ciphers  between 

the  decimal  point  and  the  first  significant  figure  ; 

for  example,  in  e—5°  there  'are 

21  ciphers  between  the  decimal  point  and  the  figures  192874985. 

TABLES 


259 


The  Exponential. 


u 

logio(eu) 

eu 

e-u 

51 

22.14001  85771 

140  934  90S  [14] 

(22)  709  547  416 

52 

22.58331  3^590 

383  loo  800  [14] 

(22)  261  027  907 

53 

23.01700  75409 

104  137   594  [15] 

(23)  960  268  005 

54 

23.45190  20228 

283  075  330  [15] 

(23)  353  262  857 

55 

23.88619  65047 

769  4/8  527  [15] 

(23)    129  958  143 

56 

24.32049  09866 

209  165  950  [16] 

(24)  478  089  288 

57 

24.75478  54685 

568  572  ooo    16] 

(24)    175  879  220 

58 

25.18907  99504 

154  553  894  [17] 

(25)  647  023  493 

59 

25-62337  44323 

420  121  040  [17] 

(25)  238  026  641 

60 

26.05766  89142 

114  200  739  [18] 

(26)  875  651  076 

61 
62 

26.49196  33961 
26.92625  78780 

310  429  794  [18] 
843  835  667  [18] 

(26)  322  134  029 
(26)   118  506  487 

63 

27-36055  23599 

229  378  316  [19] 

(27)  435  961  ooo 

64 

27.79484  68418 

623  514  908  [19] 

(27)   160  381  089 

65 

28.22914  13237 

169  488  924  [20] 

(28)  590  009  054 

66 

28.66343  58056 

460  718  663  [20 

(28)    217  O52  2OI 

67 

29.09773  02875 

125   236    317    [21. 

(29)  798  490  425 

68 

29.53202  47694 

340  427  605  [21 

(29)    293   748  211 

69 

29.96631  92513 

925   378    172    [21. 

(29)  108  063  928 

70 

30.40061  37332 

251  543  867  [22^ 

(30)  397  544  974 

7i 

30.83490  82151 

683   767    123    [22] 

(30)   146  248  623 

72 

31.26920  26970 

185  867     175    [23] 

(3i)  538  018  616 

73 

31.70349  71789 

505   239    363    [23] 

(3-1)   197  925  988 

74 

32.13779  16608 

137  338    298    [24; 

(32)  728  129  018 

75 

32.57208  61427 

373  324  200  [24; 

(32)  267  863  696 

76 

33.00638  06246 

101  480  039  [25" 

(33)  985  415  469 

77 

33.44067  51066 

275  851  346  [25; 

(33)  362  514  092 

78 

33.87496  95885 

749  841   700  [25; 

(33)   133  36i  482 

79 

34.30926  40704 

203  828   107  [26] 

(34)  490  609  473 

80 

34-74355  85523 

554  062  238  [26] 

(34)   180  485  139 

81 

35.17785  30342 

150  609  731   [27] 

(35)  663  967  720 

82 

35.61214-75161 

409  399  696  [27] 

(35)  244  260  074 

83 

36.04644  19980 

in  286  376  [28] 

(36)  898  582  594 

84 

36.48073  64799 

302  507  732  [28] 

(36)  330  570  063    . 

85 

36.91503  09618 

822  301   271   [28 

(36)   121  609  930 

86 

37-34932  54437 

223  524  660  [29; 

(37)  447  377  931 

87 

37.78361  99256 

607  603  023  [29; 

(37)    164  58i  143 

88 

38.21791  44075 

165  163  626  [30" 

(38)  605  460  189 

89 

38.65220  88894 

448  961   282  [30 

(38)    222   736  356 

90 

39.08650  33713 

122  040    329    [31! 

(39)  819  401  262 

9i 

39.52079  78532 

331  740  oio  [31] 

(39)  301  440  879 

92 

39.95509  23351 

ooi  762  841  [31] 

(39)   no  893  902 

93 

40.38938  68170 

245  124  554  [32] 

(40)  407  955  867 

94 

40.82368  12989 

666  317  622  [32] 

(40)   150  078  576 

95 

41.25797  578o8 

181  123  908  [33] 

(41)  552  108  228 

96 

41.69227  02627 

492  345  829  [33] 

(41)  203  109  266 

97 

42.12656  47446 

133  833  472  [34] 

(42)  747  197  234 

98 

42.56085  92265 

363  797  095  [34] 

(42)  274  878  501 

99 

42.99515  37084 

088  903  032  [34] 

(42)    IOI    122   149 

100 

43.42944  81903 

268  811  714  [35] 

(43)  372  007  598 

The  numbers  in  square  brackets  denote  the  numbers  of  figures  between  the 

last  figure  given  and  the  decimal  point  ;  for  example,  the  first  nine  figures  of  e1* 

are  518470553,  and  there  are  13  additional  figures  before  the  decimal  point  is 

reached.     The  numbers  in  parentheses  denote  the  numbers  of  ciphers  between 

the  decimal  point  and  the  first  significant  figure  ;  for  example,  in  e~M  there  are 

2i  ciphers  between  the  decimal  point  and  the  figures  192874985. 

SMITHSONIAN  TABLES 


Auxiliary   laoie  ror  interpolation  01 
(p  =  n  X  43429  44819  .    .    .) 


n 

P 

n 

p 

n 

P 

n 

p 

n 

p 

o.ooo 

OOO 

O.050 

2171 

O.IOO 

4343 

O.I5O 

6514 

0.200 

8686 

.001 

043 

.051 

2215 

.IOI 

4386 

.151 

6558 

.2OI 

8729 

.002 

087 

.052 

2258 

.IO2 

4430 

.152 

6601 

.202 

8773 

.003 

130 

.053 

2302 

.103 

4473 

.153 

6645 

.203 

8816 

.004 

174 

.054 

2345 

.104 

4517 

.154 

6668 

.204 

8860 

0.005 

217 

0.055 

2389 

0.105 

4500 

0.155 

6732 

0.205 

8903 

.006 

26l 

.056 

2432 

.106 

4604 

.156 

6775 

.206 

8946 

.007 

304 

.057 

2475 

.107 

4647 

.157 

6818 

.207 

8990 

.008 

347 

.058 

2519 

.108 

4690 

.r58 

6862 

.208 

9033 

.009 

391 

.059 

2562 

.109 

4734 

.159 

6905 

.209 

9077 

O.OIO 

434 

O.o6o 

2606 

O.I  10 

4777 

0.160 

6949 

O.2IO 

9120 

.on 

478 

.061 

2649 

.III 

4821 

.161 

6992 

.211 

9164 

.012 

521 

.062 

2693 

.112 

4864 

.162 

7036 

.212 

9207 

.013 

565 

.063 

2736 

•113 

4908 

.163 

7079 

.213 

9250 

.014 

608 

.064 

2779 

.114 

4951 

.164 

7122 

.214 

9294 

0.015 

651 

0.065 

2823 

O.II5 

4994 

0.165 

7166 

0.215 

9337 

.016 

695 

.066 

2866 

.116 

5038 

.166 

7209 

.216 

938i 

.017 

738 

.067 

2910 

.117. 

5081 

.167 

7253 

.217 

9424 

.018 

782 

.068 

2953 

.118 

5125 

.168 

7296 

.218 

9468 

.019 

825 

.069 

2997 

.119 

5i68 

.169 

7340 

.219 

95ii 

0.020 

869 

0.070 

3040 

O.I2O 

5212 

0.170 

7383 

O.22O 

9554 

.O2I 

912 

.071 

3083 

.121 

5255 

.171 

7426 

.221 

9598 

.022 

955 

.072 

3127 

.122 

5298 

.172 

7470 

.222 

.023 

999 

.073 

3170 

.123 

5342 

.173 

7513 

.223 

9685 

.024 

1042 

.074 

3214 

.124 

5385 

.174 

7557 

.224 

9728 

0.025 

1086 

0.075 

3257 

0.125 

5429 

0.175 

7600 

0.225 

9772 

.026 

1129 

.076 

3301 

.126 

5472 

.176 

7644 

.226 

9815 

.027 

1  173 

.077 

3344 

.127 

55i6 

.177 

7687 

.227 

9858 

.028 

1216 

.078 

3387 

.128 

5559 

.178 

7730 

.228 

9902 

.029 

1259 

•079 

3431 

.129 

5602 

.179 

7774 

.229 

9945 

0.030 

1303 

0.080 

3474 

O.I30 

5646 

0.180 

7817 

O.230 

9989 

.031 

1346 

.081 

35i8 

.131 

5689 

.181 

7861 

.231 

10032 

.032 

1390 

.082 

356i 

.132 

5733 

.182 

7904 

.232 

10076 

•  033 

1433 

.083 

3605 

.133 

5776 

.183 

7948 

.233 

10119 

.034 

1477 

.084 

3648 

.134 

5820 

.184 

7991 

.234 

10162 

0.035 

1520 

0.085 

3692 

0.135 

5863 

0.185 

8034 

0.235 

10206 

.036 

1563 

.086 

3735 

.  136 

59o6 

.186 

8078 

.236 

10249 

.037 

1607 

.087 

3778 

.137 

5950 

.187 

8121 

.237 

10293 

.038 

1650 

.088 

3822 

.138 

5993 

.188 

8165 

.238 

10336 

.039 

1694 

.089 

3865 

.139 

6037 

.189 

8208 

.239 

10380 

0.040 

1737 

0.000 

3909 

0.140 

6080 

0.190 

8252 

0.240 

10423 

.041 

1781 

.091 

3952 

.141 

6124 

.191 

8295 

.241 

10466 

.042 

1824 

.092 

3996 

.142 

6167 

.192 

8338 

.242 

10510 

.043 

1867 

.093 

4039 

•  143 

6210 

.193 

8382 

.243 

10553 

.044 

1911 

.094 

4082 

.144 

6254 

.194 

8425 

•244 

10597 

0.045 

1954 

0.095 

4126 

0.145 

6297 

0.195 

8469 

0.245 

10640 

.046 

1998 

.096 

2169 

.146 

6341 

.196 

8512 

.246 

10684 

.047 

2041 

.097 

4213 

.147 

6384 

.197 

8556 

.247 

10727 

.048 

2085 

.098 

4256 

.148 

6428 

.198 

8599 

.248 

10771 

.049 

2128 

.099 

4300 

.149 

6471 

.199 

8642 

.249 

10814 

0.050 

2171 

O.IOO 

4343 

0.150 

6514 

O.2OO 

8686 

0.250 

10857 

n 

p 

n 

p 

n 

P 

n 

P 

n 

p 

SMITHSONIAN  TABLES 


26l 


Auxiliary   laoie  tor  interpolation  of 
(p  =  n  X  43429  44819  .   .   . ) 


n 

p 

n 

p 

n 

p 

n 

p 

n 

P 

0.250 

10857 

0.300 

13029 

0.350 

I52OO 

0.400 

17372 

0.450 

19543 

.251 

IOOOI 

.301 

13072 

•351 

15244 

.401 

I74I5 

•451 

19587 

.252 

10944 

•  302 

I3"6 

•352 

15287 

.402 

17459 

•452 

19630 

•  253 

10988 

•  303 

I3I59 

•353 

I533I 

•403 

17502 

-453 

19674 

•  254 

II03I 

.304 

13203 

•  354 

15374 

.404 

17545 

•454 

I97I7 

0.255 

1  1075 

0.305 

13246 

0.355 

I54I7 

0.405 

17589 

0.455 

-T+J+J 

19760 

.256 

11118 

.306 

13289 

.356 

15461 

.406 

17632 

.456 

19804 

.257 

11161 

.307 

13333 

.357 

15504 

.407 

17676 

•457 

19847 

.258 

11205 

.308 

13376 

.358 

15548 

.408 

17719 

.458 

19891 

•  259 

11248 

.309 

13420 

•  359 

I559I 

.409 

17763 

•459 

19934 

0.260 

11292 

0.310 

13463 

0.360 

15635 

0.410 

17806 

0.460 

19978 

.261 

1  1335 

.3" 

13507 

.361 

15678 

.4" 

17850 

.461 

2O02I 

.262 

"379 

.312 

13550 

.362 

I572I 

.412 

17893 

.462 

20064 

.263 

11422 

.313 

13593 

.363 

I'5765 

.413 

17936 

•463 

20108 

.264 

"465 

.314 

13637 

.364 

15808 

.414 

17980 

.464 

20I5I 

0.265 

n-509 

0.315 

13680 

0.365 

15852 

0.415 

18023 

0.465 

20195 

.266 

"552 

.316 

13724 

.366 

15895 

.416 

18067 

.466  20238 

.267 

11596 

.317 

13767 

.367 

15939 

.417 

18110 

.467  20282 

.268 

11639 

.318 

I38II 

.368 

15982 

.418 

18154 

.468  20325 

.269 

11683 

.319 

13854 

.369 

16025 

.419 

18197 

.469 

20368 

0.270 

11726 

0.320 

13897 

0.370 

16069 

0.420 

18240 

0.470 

20412 

.271 

11769 

.321 

I394I 

•  371 

l6lI2 

.421 

18284 

•471 

20455 

.272 

"813 

.322 

13984 

.372 

16156 

.422 

18327 

.472 

20499 

.273 

"856 

.323 

14028 

•  373 

16199 

.423 

18371 

•  473 

20542 

.274 

11900 

.324 

I407I 

•  374 

16243 

.424 

18414 

.474 

20586 

0.275 

"943 

0.325 

I4"5 

0.375 

16286 

0.425 

18458 

0.475 

20629 

.276 

11987 

.326 

14158 

.376 

16329 

.426 

18501 

.476 

20672 

.277 

12030 

.327 

14201 

•  377 

16373 

.427 

18544 

.477 

20716 

.278 

12073 

.328 

14245 

.378 

16416 

.428 

18588 

.478 

20759 

.279 

12117 

.329 

14288 

.379 

16460 

.429 

18631 

.479 

20803 

0.280 

12160 

0.330 

14332 

0.380 

16503 

0.430 

18675 

0.480 

20846 

.281 

12204 

•  331 

H375 

.381 

16547 

•431 

18718 

.481 

20890 

.282 

12247 

.332 

14419 

.382 

16500 

•432 

18762 

.482 

20933 

.283 

12291 

•  333 

14462 

.383 

16633 

•  433 

18805 

.483 

20976 

.284 

12334 

•334 

14505 

.384 

16677 

•434 

18848 

.484 

2IO2O 

0.285 

12377 

0.335 

14549 

0.385 

16720 

0.435 

18892 

0.485 

2IO63 

.286 

12421 

.336 

H592 

.386 

16764 

.436 

18935 

.486 

2IIO7 

.287 

12464 

.337 

14636 

.387 

16807 

•437 

18979 

.487 

2II5O 

.288 

12508 

.338 

14679 

.388 

16851 

.438 

19022 

.488 

2II94 

.289 

I255I 

•  339 

14723 

.389 

16894 

•439 

19066 

.489 

21237 

0.290 

12595 

0.340 

14766 

0.390 

16937 

0.440 

19109 

0.490 

21280 

.291 

12638 

•  341 

14809 

•  391 

16981 

•441 

19152 

.491 

21324 

.292 

12681 

.342 

14853 

•  392 

17024 

.442 

19196 

•493 

21367 

.293 
.294 

12725 
12768 

.343 
•  344 

14896 
14940 

•  393 
•  394 

17068 
I7III 

•  443 
•444 

19239 
19283 

•493 
•494 

21411 

^1454 

0.295 

12812 

0.345 

14983 

0.395 

I7I55 

0.445 

19326 

0.495 

21498 

.296 

12855 

.346 

15027 

.396 

I7I98 

.446 

19370 

.496 

21541 

.297 

12899 

•  347 

15070 

•  397 

17241 

.447 

I94I3 

•497 

21584 

.298 

12942 

.348 

I5"3 

.398 

17285 

.448 

19456 

.498 

21628 

.299 

12985 

•349 

I5I57 

.399 

17328 

.449 

19500 

.499 

21671 

0.300 

13029 

0.350 

15200 

0.400 

17372 

0.450 

19543 

0.500 

21715 

n 

p 

n 

P 

n 

p 

n 

p 

n 

p 

SMITHSONIAN  TABLE* 


262 


TABLE  V 


NATURAL  LOGARITHMS 


NOTE. — In  Table  V,  for  u  greater  than  158,  linear  interpolation  of 
logew  suffices  to  give  a  value  whose  error  is  not  greater  than  one  unit  in 
the  last  place. 

263 


Natural  Logarithms. 


u 

lOQeU 

U.FO' 

u 

lOQ.U 

•  IV 

u 

loo.  u 

*v 

u 

iog.u 

<oF0' 

o 

—  CO 

00 

50 

3.91202 

2OOO 

IOO 

4.60517 

IOOO 

150 

5.01064 

667 

I 

o.ooooo 

IOOOOO 

3.93183 

I96l 

101 

4.6I5I2 

990 

151 

5.01728 

662 

2 

0.69315 

50000 

52 

3.95124 

1923 

IO2 

4.62497 

080 

152 

5.02388 

658 

3 

1.09861 

33333 

53 

3.97029 

1887 

103 

4.63473 

971 

153 

5.03044 

654 

4 

1.38629 

25000 

54 

3.98898 

1852 

104 

4.64439 

962 

154 

5.03695  . 

649 

5 

1.60944 

2OOOO 

55 

4-00733 

1818 

105 

4.65396 

952 

155 

5-04343 

645 

6 

1.79176 

16667 

56 

4.02535 

1786 

106 

4.66344 

943 

156 

5-04086 

64I 

7 

1.94591 

14286 

57 

4.04305 

1754 

107 

4.67283 

935 

157 

5-05625 

637 

8 

2.07944 

12500 

58 

4.06044 

1724 

108 

4.68213 

926 

158 

5.06260 

633 

9 

2.19722 

mil 

59 

4.07754 

1695 

109 

4.69135 

917 

159 

5.06890 

629 

10 

2.30259 

IOOOO 

60 

4-09434 

1667 

1  10 

4.70048 

009 

160 

5.07517 

625 

ii 

2-39790 

9091 

61 

4.II087 

1639 

III 

4.70953 

901 

161 

5.08140 

621 

12 

2.48491 

8333 

62 

4.I27I3 

1613 

112 

4.71850 

893 

162 

5.08760 

617 

13 

2.56495 

7692 

63 

4.I43I3 

1587 

113 

4.72739 

885 

163 

5-09375 

6l3 

14 

2.63906 

7143 

64 

4.15888 

1562 

114 

4.73620 

877 

164 

5.09987 

610 

15 

2.70805 

6667 

6s 

4.17439 

1538 

115 

4-74493 

870 

165 

5.10595 

606 

16 

2.77259 

6250 

66 

4.18965 

1515 

116 

4.75359 

862 

166 

5.III99 

602 

17 

2.83321 

5882 

67 

4.20469 

1493 

117 

4.76217 

855 

167 

5.H799 

599 

18 

2.89037 

5556 

68 

4.2I95I 

1471 

118 

4.77068 

847 

168 

5.12396 

595 

19 

2.94444 

5263 

69 

4.234H 

1449 

119 

4.77912 

840 

169 

5.12990 

592 

20 

2.99573 

5000 

70 

4.24850 

1429 

1  20 

4.78749 

833 

170 

5.13580 

588 

21 

3.04452 

4762 

4.26268 

1408 

121 

4-79579 

826 

171 

5.14166 

585 

22 

3.09104 

4545 

72 

4.27667 

1389 

122 

4.80402 

820 

172 

5-14749 

58i 

23 

3.13549 

4348 

73 

4.20046 

1370 

123 

4.81218 

813 

173 

5.15329 

578 

24 

3.17805 

4167 

74 

4.30407 

1351 

124 

4.82028 

806 

174 

5.15906 

575 

25 

3.21888 

4000 

75 

4.31749 

1333 

125 

4.82831 

800 

175 

5.16479 

571 

26 

3.25810 

3846 

76 

4.33073 

1316 

126 

4.83628 

794 

176 

5.17048 

568 

27 

3  .  29584 

3704 

77 

4.34381 

1299 

127 

4.84419 

787 

177 

5.I76I5 

565 

28 

3.33220 

357i 

78 

4.35671 

1282 

128 

4.85203 

78i 

178 

5.I8I78 

562 

29 

3.36730 

3448 

79 

4.36945 

1266 

129 

4.85981 

775 

179 

5.18739 

559 

30 

3.40120 

3333 

80 

4.38203 

1250 

130 

4.86753 

769 

180 

5.19296 

556 

31 

3-43399 

3226 

81 

4-39445 

1235 

131 

4.87520 

763 

181 

5.19850 

552 

32 

3.46574 

3125 

82 

4.40672 

1  220 

132 

4.88280 

758 

182 

5  .  20401 

549 

33 
34 

3.49651 
3-52636 

3030 
2941 

83 
84 

4.41884 
4.43082 

1205 
iigo 

133 
134 

4.89035 
4.89784 

752 
746 

183 
184 

5.20949 
5.21494 

546 

543 

35 

3.55535 

2857 

85 

4.44265 

1176 

135 

4.90527 

741 

185 

5.22036 

541 

36 

3.58352 

2778 

86 

4-45435 

1163 

136 

4.91265 

735 

186 

5.22575 

538 

37 

3.61092 

2703 

87 

4.46591 

1149 

137 

4.91998 

730 

187 

5-23111 

535 

38 

3.63759 

2632 

88 

4-47734 

1136 

138 

4.92725 

725 

188 

5-23644 

532 

39 

3.66356 

2564 

89 

4.48864 

1124 

139 

4.93447 

719 

189 

5.24175 

529 

40 

3.68888 

2500 

90 

4.49981 

mi 

140 

4.94164 

714 

190 

5.24702 

526 

41 

3.71357 

2439 

4.51086 

1099 

141 

4.94876 

709 

191 

5.25227 

5-'4 

42 
43 
44 

3.73767 
3.76120 
3-78419 

2381 
2326 
2273 

92 
93 
94 

4.52179 
4.53200 
4.54329 

1087 
1075 
1064 

142 

143 
144 

4.95583 
4.96284 
4.96981 

704 
699 
694 

192 
193 

194 

5.25750 
5.26269 
5.26786 

521 
5i8 
515 

45 

3.80666 

2222 

95 

4.55388 

1053 

145 

4.97673 

690 

195 

5.27300 

513 

46 

3.82864 

2174 

96 

T  */*£W 

4.56435 

1042 

146 

4.98361 

196 

5.27811 

510 

47 
48 

3.85015 
3-87120 

2128 
2083 

97 
98 

4.57471 
4.58497 

1031 

IO2O 

147 
148 

4.99043 
4-99721 

sn 
680 

676 

197 
198 

5.28320 
5.28827 

508 
505 

49 

3.89182 

2041 

99 

4.59512 

IOIO 

149 

5-00395 

671 

199 

5.29330 

503 

50 

3.91202 

2000 

TOO 

4.60517 

1000 

ISO 

5.01064 

667 

200 

5.29832 

500 

ex 

X 

.-« 

ex 

X 

e~x 

ex 

X 

•rj 

ex 

X 

e~x 

SMITHSONIAN  TABLES 


264 


Natural  Logarithms. 


u 

lOOell 

«Fo' 

u 

log.u 

«FO' 

u 

logeu 

«F0' 

u 

lOflell 

«FO' 

200 

5.20832 

500 

250 

5.52146 

400 

300 

5.70378 

333 

350 

5.85793 

286 

201 

5.30330 

498 

251 

5.52545 

398 

301 

5.707II 

332 

351 

5.86079 

285 

202 

5.30827 

495 

252 

5.52943 

397 

302 

5.71043 

331 

352 

5.86363 

284 

203 

5.3I32I 

493 

253 

5-53339 

395 

303 

5.71373 

330 

353 

5.86647 

283 

2O4 

5.3I8I2 

490 

254 

5-53733 

394 

304 

5.71703 

329 

354 

5.86930 

282 

205 

5.32301 

488 

255 

5.54126 

392 

305 

5.72031 

328 

355 

5.87212 

282 

206 

5.32788 

485 

256 

5.54518 

39i 

306 

5.72359 

327 

356 

5.87493 

281 

207 

5.33272 

483 

257 

5-54908 

389 

307 

5.72685 

326 

357 

5.87774 

280 

208 

5-33754 

481 

258 

5.55206 

388 

308 

5.73010 

325 

358 

5.88053 

279 

209 

5.34233 

478 

259 

5.55683 

386 

309 

5-73334 

324 

359 

5.88332 

279 

2IO 

5-347II 

476 

260 

5.56068 

385 

310 

5.73657 

323 

360 

5.88610 

278 

211 

5.35186 

474 

261 

5.56452 

383 

3ii 

5-73979 

322 

361 

5.88888 

277 

212 

5.35659 

472 

262 

5.56834 

382 

312 

5.74300 

321 

362 

5.89164 

276 

213 

5.36129 

469 

263 

5.57215 

380 

313 

5.74620 

319 

363 

5.89440 

275 

214 

5.36598 

467 

264 

5-57595 

379 

314 

5-74939 

3l8 

364 

5.89715 

275 

215 

5.37064 

465 

265 

5.57973 

377 

315 

5.75257 

317 

365 

5.89990 

274 

216 

5.37528 

463 

266 

5.58350 

376 

316 

5-75574 

3i6 

366 

5-90263 

273 

217 

5:37990" 

461 

267 

5.58725 

375 

317 

5.75890 

315 

367 

5.90536 

272 

218 

5.38450 

459 

268 

5.59099 

373 

3i8 

5.76205 

314 

368 

5.90808 

272 

219 

5-38007 

457 

269 

5.59471 

372 

319 

5-76519 

313 

369 

5.91080 

271 

22O 

5.39363 

455 

270 

5.59842 

370 

320 

5.76832 

312 

370 

5.91350 

270 

221 

5.398i6 

452 

271 

5.60212 

309 

321 

5.77144 

312 

37i 

5.91620 

270 

222 

5.40268 

450 

272 

5.60580 

368 

322 

5-77455 

311 

372 

5.91889 

269 

223 

5.40717 

448 

273 

5.60947 

366 

323 

5.77765 

310 

373 

5.92158 

268 

224 

5-41165 

446 

274 

5.6I3I3 

365 

324 

5.78074 

309 

374 

5.92426 

267 

225 

5.41610 

444 

275 

5.6l677 

364 

325 

5.78383 

308 

375 

5.92693 

267 

226 

5.42053 

442 

276 

5.62040 

362 

326 

5.78690 

307 

376 

5.92959 

266 

227 

5.42495 

441 

277 

5.62402 

361 

327 

5-78996 

306 

377 

5.93225 

265 

228 

5.42935 

439 

278 

5.62762 

360 

328 

5-79301 

305 

378 

5.93489 

265 

229 

5.43372 

437 

279 

5.63I2I 

358 

329 

5.79606 

304 

379 

5-93754 

264 

230 

5.438o8 

435 

280 

5.63479 

357 

330 

5.79909 

303 

380 

5.94017 

263 

231 

5.44242 

433 

281 

5.63835 

356 

331 

5.80212 

302 

381 

5.94280 

262 

232 

5.44674 

431 

282 

5'.64I9I 

355 

332 

5.80513 

301 

382 

5.94542 

262 

233 

5.45104 

429 

283 

5.64545 

353 

333 

5.80814 

300 

383 

5.94803 

261 

234 

5-45532 

427 

284 

5.64897 

352 

334 

5-81114 

299 

384 

5-95064 

260 

235 

5-45959 

426 

285 

5.65249 

351 

335 

5.8I4I3 

299 

385 

5.95324 

260 

236 

5.46383 

424 

286 

5.65599 

350 

336 

5-81711 

298 

386 

5.95584 

259 

237 

5.46806 

422 

287 

5.65948 

348 

337 

5.82008 

297 

387 

5.95842 

258 

238 

5.47227 

420 

288 

5.66296 

347 

338 

5-82305 

296 

388 

5.96101 

258 

239 

5.47646 

418 

289 

5.66643 

346 

339 

5.82600 

295 

389 

5.96358 

257 

240 

5-48064 

417 

290 

5.66988 

345 

340 

5.82895 

294 

390 

5.96615 

256 

241 

5.48480 

415 

291 

5.67332 

344 

341 

5.83188 

293 

391 

5.96871 

256 

242 

5.48894 

413 

292 

5.67675 

342 

342 

5.83481 

292 

392 

5.97126 

255 

243 

5.49306 

412 

293 

5.68017 

341 

343 

5.83773 

292 

393 

5.9738i 

254 

244 

5.49717 

410 

294 

5.68358 

340 

344 

5-84064 

291 

394 

5.97635 

254 

245 

5.50126 

408 

295 

5.68698 

339 

345 

5.84354 

290 

395 

5.97889 

253 

246 

5.50533 

407 

296 

5.69036 

338 

346 

5.84644 

289 

396 

5.98141 

253 

247 

5.50939 

405 

297 

5.69373 

337 

347 

5.84932 

288 

397 

5.98394 

252 

248 

5.51343 

403 

298 

5.69709 

336 

348 

5.85220 

287 

398 

5-98645 

251 

249 

5.51745 

402 

299 

5.70044 

334 

349 

5.85507 

287 

399 

5.98896 

251 

250 

5.52146 

400 

300 

5.70378 

333 

350 

5.85793 

286 

400 

5.99146 

250 

ex 

X 

e-x 

e* 

X 

e~x 

ex 

X 

e—  x 

ex 

X 

e—  x 

SMITHSONIAN  TABLES 


265 


Natural  Logarithms. 


u 

^ 

«F0' 

u 

lOOeU 

«FO' 

U 

(OQeU 

»F0' 

u 

logeu 

«F0' 

400 

5.99146 

250 

450 

6.10925 

222 

500 

6.2I46I 

2OO 

550 

6.30992 

182 

40  1 

5.99396 

249 

451 

6.  1  1  147 

222 

501 

6.  21661 

200 

55i 

6.31173 

181 

402 

5.99645 

249 

452 

6.11368 

221 

502 

6.21860 

109 

552 

6.31355 

181 

403 

5.99894 

248 

453 

6.11589 

221 

503 

6.22059 

199 

553 

6.31536 

181 

404 

6.00141 

248 

454 

6.  11810 

22O 

504 

6.22258 

198 

554 

6.31716 

181 

405 

6.00389 

247 

455 

6.  12030 

22O 

505 

6.22456 

198 

555 

6.31897 

180 

406 

6.00635 

246 

456 

6.12249 

219 

506 

6.22654 

198 

556 

6.32077 

180 

407 

6.00881 

246 

457 

6.12468 

219 

507 

6.22851 

197 

557 

6.32257 

180 

408 

6.01127 

245 

458 

6.12687 

218 

508 

6.23048 

197 

558 

6.32436 

179 

409 

6.01372 

244 

459 

6.  12905 

218 

509 

6.23245 

196 

559 

6.32615 

179 

410 

6.01616 

244 

460 

6.13123 

217 

5io 

6.23441 

196 

560 

6.32794 

179 

411 

6.01859 

243 

461 

6.13340 

217 

511 

6.23637 

196 

56i 

6.32972 

178 

412 

6.O2IO2 

243 

462 

6.13556 

216 

512 

6.23832 

195 

562 

6.33150 

178 

413 

6.O2345 

242 

463 

6.13773 

216 

6.24028 

195 

563 

6.33328 

178 

414 

6.02587 

242 

464 

6.13988 

216 

5i4 

6.24222 

195 

564 

6.33505 

177 

415 

6.02828 

241 

465 

6.14204 

215 

5i5 

6.24417 

194 

565 

6.33683 

177 

416 

6.03069 

240 

466 

6.14419 

215 

5i6 

6.24611 

194 

566 

6.33859 

177 

417 

6.03309 

240 

467 

6.14633 

214 

5i7 

6.24804 

193 

567 

6.34036 

176 

418 

6.03548 

239 

468 

6.14847 

214 

5i8 

6.24998 

193 

568 

6.34212 

176 

419 

6.03787 

239 

469 

6.15060 

213 

519 

6.25190 

193 

569 

6.34388 

176 

420 

6.O4O25 

238 

470 

6.15273 

213 

520 

6.25383 

192 

570 

6.34564 

175 

421 

6.04263 

238 

47i 

6.15486 

212 

521 

6.25575 

192 

571 

6.34739 

175 

422 

6.O45OI 

237 

472 

6.15698 

212 

522 

6.25767 

192 

572 

6.34914 

175 

423 

6.04737 

236 

473 

6.15910 

211 

523 

6.25958 

191 

573 

6.35089 

175 

424 

6.04973 

236 

474 

6.16121 

211 

524 

6.26149 

191 

574 

6.35263 

174 

425 

6.05209 

235 

475 

6.16331 

211 

525 

6.26340 

190 

575 

6.35437 

174 

426 

6.05444 

235 

476 

6.16542 

210 

526 

6.26530 

190 

576 

6.35611 

174 

427 

6.05678 

234 

477 

6.  16752 

210 

527 

6.26720 

190 

577 

6.35784 

173 

428 

6.05912 

234 

478 

6.16961 

209 

528 

6.26910 

189 

578 

6.35957 

173 

429 

6.06146 

233 

479 

6.17170 

209 

529 

6.27099 

189 

579 

6.36130 

173 

430 

6.06379 

233 

480 

6.17379 

208 

530 

6.27288 

189 

58o 

6.36303 

172 

431 

6.06611 

232 

481 

6.17587 

208 

531 

6.27476 

188 

58i 

6.30475 

172 

432 

6.06843 

231 

482 

6.17794 

207 

532 

6.27664 

188 

582 

6.36647 

172 

433 

6.07074 

231 

483 

6.18002 

207 

533 

6.27852 

188 

583 

6.36819 

172 

434 

6.07304 

230 

484 

6.18208 

207 

534 

6.28040 

187 

584 

6.36990 

171 

435 

6.07535 

230 

485 

6.18415 

206 

535 

6.28227 

187 

585 

6.37161 

171 

436 

6.07764 

229 

486 

6.18621 

206 

536 

6.28413 

187 

586 

6.37332 

171 

437 

6.07993 

229 

487 

6.18826 

205 

537 

6.28600 

186 

587 

6.37502 

170 

438 

6.08222 

228 

488 

6.19032 

205 

538 

6.28786 

186 

588 

6.37673 

170 

439 

6.08450 

228 

489 

6.19236 

204 

539 

6.28972 

186 

589 

6.37843 

170 

440 

6.08677 

227 

490 

6.19441 

204 

540 

6.29157 

185 

590 

6.38012 

169 

441 

6.08904 

227 

491 

6.19644 

204 

54i 

6.2934-' 

185 

591 

6.38182 

169 

442 

6.09131 

226 

492 

6.19848 

203 

542 

6.29527 

185 

592 

6.38351 

169 

443 

6.09357 

226 

493 

6.20051 

203 

543 

6.29711 

184 

593 

6.38519 

169 

444 

6.09582 

225 

494 

6.20254 

202 

544 

6.29895 

184 

594 

(,-.38088 

168 

445 

6.09807 

225 

495 

6.20456 

2O2 

545 

6.30079 

183 

595 

6.38856 

168 

446 

6.10032 

224 

496 

6.20658 

2O2 

546 

6.30262 

183 

596 

6.39024 

168 

447 

6.10256 

224 

497 

6.20859 

201 

547 

6.30445 

183 

597 

6.39192 

168 

448 

6.  10479 

223 

498 

6.21060 

201 

548 

6.30628 

182 

598 

6.39359 

167 

449 

6.10702 

223 

499 

6.21261 

200 

549 

6.30810 

182 

599 

6.395-*> 

167 

450 

6.10925 

222 

500 

6.21461 

2OO 

550 

6.30992 

182 

600 

6.39693 

167 

ex 

x 

e~x 

e* 

X 

.-« 

ex 

x 

e~x 

ex 

x 

e-x 

SMITHSONIAN  TABLES 


266 


Natural  Logarithms. 


u 

lOOell 

«FO' 

u 

lOOeU 

«FO' 

u 

lOOell 

o>Fo' 

u 

lOQeU 

«F0' 

600 

6.39693 

167 

650 

6.47097 

154 

700 

6.55108 

143 

750 

6.62007 

133 

601 

6.39859 

166 

651 

6.47851 

154 

701 

6.55251 

H3 

75i 

6.62141 

133 

602 

6.40O26 

166 

652 

6.48004 

153 

702 

6.55393 

142 

752 

6.62274 

133 

603 

6.4OI92 

166 

653 

6.48158 

153 

703 

6.55536 

142 

753 

6.62407 

133 

604 

6.40357 

166 

654 

6.483H 

153 

704 

6.55678 

142 

754 

6.62539 

133 

605 
606 

6.40523 
6.40688 

165 
165 

655 
656 

6.48464 
6.48616 

153 
152 

705 

706 

6.55820 
6.55062 

142 

142 

755 
756 

6.62672 
6.62804 

132 
132 

607 

6.40853 

165 

657 

6.48768 

152 

707 

6.56103 

141 

757 

6.62936 

132 

608 

6.4IOI7 

164 

658 

6.48920 

152 

708 

6  .  56244 

141 

758 

6.63068 

132 

609 

6.4II82 

164 

659 

6.49072 

152 

709 

6.56386 

141 

759 

6.63200 

132 

610 

6.41346 

164 

660 

6.49224 

152 

710 

6.56526 

141 

760 

6.63332 

132 

611 

6.4I5IO 

164 

661 

6.49375 

151 

711 

6.56667 

141 

761 

6.63463 

131 

612 

6.41673 

163 

662 

6.49527 

151 

712 

6.56808 

140 

762 

6.63595 

131 

613 

6.41836 

163 

663 

6.49677 

151 

7i3 

6.56948 

140 

763 

6.63726 

131 

614 

6.41999 

163 

664 

6.40828 

151 

7H 

6.57088 

140 

764 

6.63857 

131 

615 

6.42162 

163 

665 

6.49979 

150 

715 

6.57228 

140 

765 

6.63988 

131 

616 

6.42325 

162 

666 

6.50129 

150 

716 

6.57368 

140 

766 

6.64118 

131 

617 

6.42487 

162 

667 

6.50279 

150 

717 

6.57508 

139 

767 

6.64249 

130 

618 

6.42649 

162 

668 

6.50429 

150 

7i8 

6.57647 

139 

768 

6.64379 

130 

619 

6.428II 

162 

669 

6.50578 

149 

719 

6.57786 

139 

769 

6.64509 

130 

620 

6.42972 

161 

670 

6.50728 

149 

720 

6.57925 

139 

770 

6.64639 

130 

621 

6.43133 

161 

671 

6.50877 

149 

721 

6.58064 

139 

771 

6.64769 

130 

622 

6.43294 

161 

672 

6.51026 

149 

722 

6.58203 

772 

6.64898 

130 

623 

6.43455 

161 

673 

6.5H75 

149 

723 

6.58341 

138 

773 

6.65028 

129 

624 

6.43615 

160 

674 

6.51323 

148 

724 

6.58479 

138 

774' 

6.65157 

129 

625 

6.43775 

160 

675 

6.5I47I 

148 

725 

6.58617 

138 

775 

6.65286 

129 

626 

6-43935 

160 

676 

6.51619 

148 

726 

6.58755 

138 

776 

6.65415 

129 

627 

6.44095 

159 

677 

6.51767 

148 

727 

6.58893 

138 

777 

6.65544 

129 

628 

6.44254 

159 

678 

6.5I9I5 

147 

728 

6.59030 

137 

778 

6.65673 

129 

629 

6.44413 

159 

679 

6.52062 

147 

729 

6.59167 

137 

779 

6.65801 

128 

630 

6.44572 

159 

680 

6.52209 

147 

730 

6.59304 

137 

780 

6.65929 

128 

631 

6.44731 

158 

681 

6.52356 

H7 

731 

6.59441 

137 

78i 

6.66058 

128 

632 

6.44889 

158 

682 

6.52503 

147 

732 

6.59578 

137 

782 

6.66185 

128 

633 

6.45047 

158 

683 

6.52649 

146 

733 

6.59715 

136 

783 

6.66313 

128 

634 

6.45205 

158 

684 

6.52796 

146 

734 

6.59851 

136 

784 

6.66441 

128 

635 

6.45362 

157 

685 

6.52942 

146 

735 

6.59987 

136 

785 

6.66568 

127 

636 

6.45520 

157 

686 

6.53088 

146 

736 

6.60123 

136 

786 

6.66696 

127 

637 

6.45677 

157 

687 

6.53233 

146 

737 

6.60259 

136 

787 

6.66823 

127 

638 

6.45834 

157 

688 

6.53379 

145 

738 

6.60394 

136 

788 

6.66950 

127 

639 

6.45990 

156 

689 

6.53524 

US 

739 

6.60530 

135 

789 

6.67077 

127 

i 

640 

6.46147 

156 

690 

6.53669 

145 

740 

6.60665 

135 

790 

6.67203 

127 

641 

6.46303 

156 

691 

6.53814 

H5 

74i 

6.60800 

135 

791 

6.67330 

126 

642 

6.46459 

156 

692 

6.53959 

H5 

742 

6.60935 

135 

792 

6.67456 

126 

643 

6.46614 

156 

693 

6.54103 

144 

743 

6.61070 

135 

793 

6.67582 

126 

644 

6.46770 

155 

694 

6.54247 

144 

744 

6.61204 

134 

794 

6.67708 

126 

645 

6.40925 

155 

695 

6.54391 

144 

745 

6.61338 

134 

795 

6.67834 

126 

646 

6.47O8O 

155 

696 

6.54535 

144 

746 

6.61473 

134 

796 

6.67960 

126 

647 

6.47235 

155 

697 

6.54679 

143 

747 

6.61607 

134 

797 

6.68085 

125 

648 

6.473'89 

154 

698 

6.54822 

143 

748 

6.61740 

134 

798 

6.68211 

125 

649 

6.47543 

154 

699 

6.54965 

143 

749 

6.61874 

134 

799 

6.68336 

125 

650 

6.47697 

154 

700 

6.55108 

143 

750 

6.62007 

133 

800 

6.68461 

125 

ex 

X 

e-x 

e* 

x 

e~x 

ex 

X 

e—  x 

ex 

x 

e—  x 

SMITHSONIAN  TABLES 


267 


Natural  Logarithms. 


u 

lOfleU 

«F«' 

u 

lOfleU 

«F0 

u 

lOQ.U 

«FO' 

u 

loo-u 

«FO' 

800 

6.68461 

125 

850 

6.74524 

118 

900 

6.80239 

in 

950 

6.85646 

105 

801 

6.68586 

125 

851 

6.74641 

118 

001 

6.80351 

in 

95i 

6.85751 

105 

802 

6.68711 

125 

852 

6.74759 

117 

002 

6.80461 

in 

952 

6.85857 

105 

803 

6.68835 

125 

853 

6.74876 

117 

903 

6.80572 

in 

953 

6.85961 

105 

804 

6.68960 

124 

854 

6.74993 

117 

904 

6.80683 

in 

954 

6.86066 

105 

805 

6.69084 

124 

855 

6.75110 

117 

905 

6.80793 

no 

955 

6.86I7I 

105 

806 

6.69208 

124 

856 

6.75227 

117 

906 

6.80904 

1  10 

956 

6.86276 

105 

807 

6.69332 

124 

857 

6.75344 

117 

907 

6.8IOI4 

1  10 

957 

6.86380 

104 

808 

6.69456 

124 

858 

6.7546o 

117 

908 

6.8II24 

no 

958 

6.86485 

104 

809 

6.69580 

124 

859 

6.75577 

116 

909 

,6.81235 

no 

959 

6.86589 

104 

810 

6.69703 

123 

860 

6.75693 

116 

910 

6.81344 

no 

960 

6.86693 

104 

811 

6.69827 

123 

86  1 

6.75809 

116 

911 

6.81454 

1  10 

961 

6.86797 

104 

812 

6.69950 

123 

862 

6.75926 

116 

912 

6.81564 

IIO 

962 

6.86901 

104 

813 

6.70073 

123 

8& 

6.76041 

116 

913 

6.81674 

1  10 

963 

6.87005 

104 

814 

6.70196 

123 

864 

6.76157 

116 

914 

6.81783 

109 

964 

6.87109 

104 

815 

6.70319 

123 

865 

6.76273 

116 

915 

6.8l892 

109 

965 

6.87213 

104 

816 

6.70441 

123 

866 

6.76388 

115 

916 

6.82002 

109 

966 

6.87316 

104 

817 

6.70564 

122 

867 

6.76504 

H5 

917 

6.82III 

109 

967 

6.87420 

103 

818 

6.70686 

122 

868 

6.76619 

115 

918 

6.8222O 

109 

968 

6.87523 

103 

819 

6.70808 

122 

869 

6.76734 

ii5 

919 

6.82329 

109 

969 

6.87626 

103 

820 

6.70930 

122 

870 

6.76849 

US 

920 

6.82437 

109 

970 

6.87730 

103 

821 

6.71052 

122 

871 

6.76964 

n5 

921 

6.82546 

109 

971 

6.87833 

103 

822 

6.71174 

122 

872 

6.77079 

H5 

922 

6.82655 

108 

972 

6.87936 

103 

823 

6.71296 

122 

873 

6.77194 

US 

923 

6.82763 

108 

973 

6.88038 

103 

824 

6.71417 

121 

874 

6.77308 

114 

924 

6.82871 

108 

974 

6.88I4I 

103 

825 

6.71538 

121 

875 

6.77422 

114 

925 

6.82979 

108 

975 

6.88244 

103 

826 

6.71659 

121 

876 

6.77537 

114 

926 

6.83087 

108 

976 

6.88346 

102 

827 

6.71780 

121 

877 

6.77651 

114 

927 

6.83195 

108 

977     6.88449 

IO2 

828 

6.71901 

121 

878 

6.77765 

114 

928 

6.83303 

108 

978     6.88551 

102 

829 

6.72022 

121 

879 

6.77878 

114 

929 

6.834H 

108 

979 

6.88653 

102 

830 

6.72143 

1  2O 

880 

6.77992 

114 

930 

6.83518 

108 

980 

6.88755 

IO2 

831 

6.72263 

1  2O 

881 

6.78106 

114 

931 

6.83626 

107 

98i 

6.88857 

102 

832 

6.72383 

I2O 

882 

6.78219 

113 

932 

6.83733 

107 

982 

6.88959 

IO2 

833 

6.72503 

I2O 

883 

6.78333 

113 

933 

6.83841 

107 

983 

6.89061 

102 

834 

6.72623 

I2O 

884 

6.78446 

113 

934 

6.83948 

107 

984 

6.89163 

IO2 

835 

6.72743 

I2O 

885 

6.78559 

113 

935 

6.84055 

107 

985 

6.89264 

102 

835 

6.72863 

1  2O 

886 

6.78672 

113 

936 

6.84162 

107 

986 

6.89366 

IOI 

837 

6.72982 

119 

887 

6.78784 

113 

937 

6.84268 

107 

987 

6.89467 

IOI 

838 

6.73102 

119 

888 

6.78897 

113 

938 

6.84375 

107 

988 

6.89568 

IOI 

839 

6.73221 

119 

889 

6.79010 

112 

939 

6.84482 

106 

989 

6.89669 

IOI 

840 

6.73340 

119 

890 

6.79122 

112 

940 

6.84588 

106 

990 

6.89770 

IOI 

841 

6.73459 

119 

891 

6.79234 

112 

941 

6.84094 

106 

991 

6.89871 

IOI 

842 

6.73578 

119 

892 

6.79347 

112 

942 

6.84801 

106 

992 

6.89972 

IOI 

843 

6.73697 

119 

893 

6-79459 

112 

943 

6.84907 

106 

993 

6.90073 

IOI 

844 

6.73815 

118 

894 

6.79571 

112 

944 

6.85013 

106 

994 

6.90174 

IOI 

845 

6.73934 

118 

895 

6.79682 

112 

945 

6.85II8 

106 

995 

6.90274 

IOI 

846 

6.74052 

118 

896 

6.79794 

112 

946 

6.85224 

106 

6.90375 

100 

847 

6.74170 

118 

897 

6.79906 

III 

947 

6.85330 

106 

907 

6.90475 

100 

848 

6.74288 

118 

898 

6.80017 

III 

948 

6.85435 

105 

998 

6.90575 

IOO 

849 

6.74406 

118 

to 

6.80128 

III 

949 

6.85541 

105 

999 

6.90675 

IOO 

850 

6.74524 

118 

900 

6.80239 

III 

950 

6.85646 

105 

1000 

6.90776 

IOO 

e* 

X 

•~x 

ex 

X 

e~x 

ex 

X 

e~x 

ex 

X 

e~x 

SMITHSONIAN  TABLES 


268 


Natural  Logarithms. 


u 

Logeu 

u 

Log,u 

u 

LOfleU 

u 

lOOeU 

u 

LOOeU 

IOOO 

6.90776 

1361 

7.21598 

1721 

7.45066 

2III 

7.65492 

2503 

7.82525 

1009 

6.91672 

1367 

7-22037 

1723 

7.45182 

2113 

7.65586 

2521 

7.83241 

1013 

6.92067 

1373 

7.22475 

1733 

7.45761 

.2129 

7.66341 

2531 

7.83637 

1019 

6.92658 

1381 

7.23056 

1741 

7.46221 

21311 

7.66435 

2539 

7.83953 

102  1 

6.92854 

1399 

7.24351 

1747 

7.46566 

2137 

7.66716 

2543 

7.84110 

1031 

6.93828 

1409 

7.25004 

1753 

7.46908 

2141 

7.66903 

2549 

7.84346 

1033 

6.94022 

1423 

7.26052 

1759 

7.47250 

2143 

7.66996 

2551 

7.84424 

1039 

6.9460*1 

1427 

7.26333 

1777 

7.48268 

2153 

7.67462 

2557 

7.84659 

IO49 

6-95559 

1429 

7.26473 

1783 

7.48605 

2161 

7.67833 

2579 

7.85516 

1051 

6.95750 

1433 

7.26753 

1787 

7.48829 

2179 

7.68662 

2591 

7.85980 

1061 

6.96697 

1439 

7.27170 

1789 

7.48941 

2203 

7.69758 

2593 

7.86057 

1063 

6.96885 

1447 

7.27725 

1801 

7.49610 

2207 

7.69939 

2609 

7.86672 

1069 

6.97448 

I45H 

7.28001 

1811 

7.50163 

2213 

7.702110 

2617 

7.86978 

1087 

6.99118 

1453 

7.28139 

1823 

7.50824 

2221 

7.70571 

2621 

7.8713-1 

1091 

6.99485 

1459 

7.28551 

1831 

7.51262 

2237 

7.71289 

2633 

7.87588 

1093 

6.99568 

1471 

7.29370 

1847 

7.52132 

2239 

7.71378 

2647 

7.88118 

1097 

7.00033 

1481 

7.30047 

1861 

7.5-2887 

2243 

7.71-557 

2657 

7.88495 

1103 

7.00579 

1483 

7.30182 

1867 

7.53209 

2251 

7.71913 

2659 

7.88571 

1109 

7.01121 

1487 

7.30452 

1871 

7.53423 

2267 

7.72621 

2663 

7.887.21 

1117 

7.01840 

1489 

7.30586 

1873 

7.53530 

2269 

7.72709 

2671 

7.89021 

1123 

7-02376 

1493 

7.30854 

1877 

7.53743 

2273 

7.72886 

2677 

7.89245 

1129 

7.02909 

1499 

7.31255 

1879 

7.53849 

228l 

7.73237 

2683 

7.89469 

1151 

7.04839 

I5H 

7.32053 

1889 

7.54380 

(2287 

7.73500 

2687 

7.89618 

H53 

7.05012 

1523 

7.32844 

1901 

7.551014 

2293 

7.73762 

2689 

7.89692 

1163 

7.05876 

1531 

7.33368 

1907 

7.55329 

2297 

7.73936 

2693 

7.89841 

1171 

7.06561 

1543 

7.34148 

1913 

7.55643 

2309 

7.74457 

2699 

7.90064 

1181 

7.0741-2 

1649 

7.34536 

I93i 

7.56579 

2311 

7.74544 

2707 

7.90360 

1187 

7.07918 

1553 

7.34794 

1933 

7.56683 

2333 

7.75491 

2711 

7.90507 

H93 

7.08423 

T559 

7.35180 

1949 

7.57507 

2339 

7.75748 

2713 

7.90581 

I2OI 

7.09091 

1567 

7.35692 

1951 

7.57610 

2341 

7.75833 

2719 

7.90802 

1213 

7.10085 

1571 

7-35947 

1973 

7.58731 

•2347 

7.76089 

2729 

7.91^169 

1217 

7.10414 

1579 

7.36455 

1979 

7.59035 

2351 

7.76260 

2731 

7.91242 

1223 

7.10906 

1583 

7.36708 

1987 

7.59438 

2357 

7.76514 

2741 

7.91608 

I22p 

7.11396 

1597 

7.37588 

1993 

7.59740 

2371 

7.77107 

2749 

7.91899 

1231 

7.II558 

1601 

7.37838 

1997 

7.59940 

2377 

7.77359 

2753 

7.92045 

1237 

7.12044 

1607 

7.38212 

1909 

7.60040 

2381 

7.77528 

2767 

7.92552 

1249 

7.13010 

1609 

7.38337 

2003 

7.60240 

2383 

7.77612 

(2777 

7.92913 

1259 

7.13807 

1613 

7.38585 

2OII 

7.60639 

2389 

7.77863 

2789 

7-93344 

1277 

7.15227 

1619 

7.38956 

2017 

7.60937 

*      ^*Jf 

2393 

7.78030 

2791 

7.93416 

1279 

7.15383 

1621 

7.39080 

2027 

7.61431 

2399 

7.78281 

2797 

7.93630 

1283 

7-15696 

1627 

7-39449 

2029 

7.61530 

2411 

7.78780 

2801 

7-93773 

1289 

7.16162 

1637 

7.40062 

2039 

7.62021 

2417 

7.79028 

2803 

7.93845 

1291 

7.16317 

1657 

7.41276 

2053 

7.62706 

2423 

7.79276 

2819 

7.94414 

1297 

7.16781 

1663 

7.41638 

2063 

7.63192 

2437 

7.79852 

2833 

7.94909 

1301 

7.17089 

1667 

7.41878 

2069 

7.63482 

2441 

7.80016 

2837 

7.95050 

1303 

7.17242 

1669 

7.41998 

2081 

7.64060 

2447 

7.80262 

2843 

7.95262 

1307 

7-17549 

1693 

7.43426 

2083 

7.64156 

2459 

7.80751 

2851 

7-95543 

1319 

7-  '18463 

1697 

7.43662 

2087 

7.64348 

.  > 

2467 

7.81076 

2857 

7-95753 

1321 

7.18614 

1699 

7.43780 

2089 

7.64444 

<2473 

7.81319 

2861 

7.95893 

1327 

7.19068 

1709 

7-44'366 

2099 

7.64922 

2477 

7.81480 

2879 

7.96520 

e* 

X 

ex 

x 

ex 

X 

ex 

X 

ex 

X 

SMITHSONIAN  TABLES 


269 


Natural  Logarithms. 


u 

LofleU 

u 

LOQ.U 

u 

LoOeU 

U 

Log,u 

u 

LOQeU 

2887 

7.96797 

3323 

8.10862 

3709 

8.21852 

4129 

8.32579 

4561 

8.42530 

2897 

7.97M3 

3329 

8.  i  1043 

3719 

8.22I2I 

4133 

8.32676 

4567 

8.42661 

2903 

7-97350 

3331 

8.  11-103 

3727 

8.22336 

4139 

8.32821 

4583 

8.430II 

2909 

7.97556 

3343 

8.11462 

3733 

8.22497 

41-53 

8.33159 

4591 

8.43185 

2917 

7.97831 

3347 

8.11582 

3739 

8.22657 

4157 

8.33255 

4597 

8.43310 

2927 

7.98173 

3359 

8.11940 

3761 

8.23244 

4159 

8.33303 

4603 

8.43446 

2959 

7.98582 

336i 

8.11099 

3767 

8.23403 

4177 

8.33735 

4621 

8.43837 

2953 

7-99058 

3371 

8.12296 

3769 

8.23456 

4201 

8.34308 

4637 

8.44182 

2957 

7.99193 

3373 

8.12356 

3779 

8.23721 

4211 

8.34546 

4639 

8.44225 

2963 

7.99396 

3389 

8.12829 

3793 

8.24091 

4217 

8.34688 

4043 

8.44312 

2969 

7.99598 

3391 

8.12888 

3797 

8.24197 

4219 

8.34735 

4649 

8.44441 

2971 

7.99665 

3407 

8.  13359 

3803 

8.24355 

4229 

8.34972 

4651 

8.44484 

2999 

8.00603 

3413 

8.13535 

3821 

8.24827 

4231 

8.35019 

4657 

6.44613 

3001 

8.00670 

3433 

8.14119 

3823 

8.24879 

4241 

8.35255 

4663 

8-4474T 

301  1 

8.01003 

3449 

8.14584 

3833 

8.25II4O 

4243 

8.35303 

4673 

8.44956 

3019 

8.01268 

3457 

8.14816 

3847 

8.25505 

4253 

8.35538 

4679 

8.45084 

3023 

8.01400 

346i 

8.14931 

3851 

8.25609 

4259 

8.35679 

4691 

8-45340 

3037 

8.01863 

3463 

8.14989 

3^53 

8.25661 

4261 

8.35726 

4703 

8.45596 

3041 

8.01994 

3467 

8.15104 

3863 

8.25920 

4271 

8.35960 

4721 

8.4597* 

3049 

8.02257 

3469 

8.15162 

3777 

8.26282 

4273 

8.36007 

4723 

8.46020 

3061 

8.O265O 

3491 

8.15794 

3881 

8.26385 

4283 

8.36241 

4729 

8.46147 

3067 

8.02846 

3499 

8.16023 

3889 

8.26591 

4289 

8.36381 

4733 

8.46231 

3079 

8.03236 

35ii 

8.16366 

3907 

8.27053 

4297 

8.36567 

4751 

8.466II 

3083 

8.03366 

3517 

8.  16536 

39ii 

8.27155 

4327 

8.37263 

4759 

8.46779 

3089 

8.03560 

3527 

8.168.20 

3917 

8.27308 

4337 

8.37494 

4783 

8.47282 

3109 

8.04206 

3529 

8.16877 

'3919 

8.27359 

4339 

8.37540 

4787 

8.47366 

3H9 

8.04527 

3533 

8.16990 

3923 

8.27461 

4349 

8-37770 

4789 

8.47408 

3121 

8.04591 

3539 

8.17160 

3929 

8.27614 

4357 

8.37954 

4793 

8.47491 

3137 

8.05IO2 

3541 

8.17216 

3931 

8.27665 

4363 

8.38092 

4799 

8.476l6 

3163 

8.05928 

3547 

8.17386 

3943 

8.27970 

4373 

8.38320 

4801 

8.47653 

3167 

8.06054 

3557 

8.117667 

3947 

8.280?I 

4391 

8.38731 

4813 

8.47908 

3169 

8.06II7 

3559 

8.  17723 

3967 

8.28577 

4397 

8.38868 

4817 

8.47991 

3181 

8.00495 

3571 

8.18060 

3989 

8.29130 

4409 

8.39140 

4831 

8.48281 

3187 

8.06684 

358i 

8.18340 

4001 

8.29430 

4421 

8.39412 

4861 

8.48900 

3191 

8.06809 

3583 

8.  18396 

4003 

8.29480 

4423 

8.39457 

4871 

8.49105 

3203 

8.07I&4 

3593 

8.18674 

4007 

8.29580 

4441 

8.39863 

4877 

8.40229 

3209 

8.07371 

3607 

8.19063 

4013 

8.29729 

4447 

8.39998 

4889 

8.49474 

3217 

8.O762O 

3613 

8.  19229 

4019 

8.29879 

4451 

8.40088 

4903 

8.49760 

3221 

8.07745 

3617 

8.  19340 

4021 

8.29929 

4457 

8.40223 

4909 

8.49883 

3229 

8.07993 

3023 

8.19506 

4027 

8.30078 

4463 

8.40358 

4919 

8.50086 

3251 

8.08672 

3631 

8.  19726 

4049 

8.30623 

448i 

8.40760 

4931 

8.50330 

3253 

8.08733 

3637 

8.19891 

4051 

8.30672 

4483 

8.40805 

4933 

8.50370 

3257 

8.08856 

3643 

8.20056 

4057 

8.30820 

4493 

8.41028 

4937 

8.50451 

3259 

8.08918 

3659 

8.20495 

4073 

8.3I0I4 

4507 

8.41339 

4943 

8.50573 

3271 

8.09285 

3671 

8.20822 

4079 

8.3I36I 

4513 

8.41472 

4951 

8.50734 

3^99 

8.  10137 

3673 

8.20876 

4091 

8.31654 

4517 

8.41560 

4957 

8.50856 

3301 

8.10198 

3677 

8.20985 

4093 

8.31703 

4519 

8.41605 

4967 

8.51057 

3307 

8.10380 

3691 

8.21365 

4099 

8.31850 

4523 

8.41693 

4969 

8.51097 

3313 

8.  10561 

3097 

8.21528 

4111 

8.32142 

4547 

8.42222 

4973 

8.51178 

3319 

8.10742 

3701 

8.21636 

4127 

8.3253'I 

4549 

8.42266 

4987 

6.51459 

e* 

X 

•x 

X 

e>< 

X 

ex 

X 

ex 

X 

SMITHSONIAN  TABLES 


270 


Natural  Logarithms. 


u 

LOQell 

u 

LoOeU 

u 

LOOeU 

u 

Log«u 

u 

LOfleU 

4993 

8.51579 

5437 

8.60098 

5849 

8.67403 

6287 

8.746241 

6733 

"8.81478 

4999 

8.51099 

5441 

8.60172 

5851 

8.67437 

6299 

8.74815 

6737 

8.81537 

5003 

8.51779 

5443 

8.60209 

5857 

8.67539 

6301 

8.74846 

6761 

8.31893 

5009 

8.  51899 

5449 

8.60319 

5861 

8.67608 

6311 

8.75005 

,  6763 

8.81922 

SOU 

8.51939 

5471 

8.60722 

5867 

8.67710 

6317 

8.75100 

6779 

8.82158 

'5021 

8.52138 

5477 

8.60831 

5869 

8.67744 

6323 

8.75195 

6781 

8.82188 

5023. 

8.52178 

5479 

8.60868 

5879 

8.67914 

6329 

8.75290 

6791 

8.82335 

5039 

8.52496 

5483 

8.60941 

588)1 

8.67948 

6337 

8.75416 

6793 

8.82365 

5051 

8.52734 

5501 

8.61269, 

5897 

8.68220 

6343 

8.755ri 

6803 

8.82512 

5059 

8.52892 

5503 

8.6I3O5 

5903 

8.68322 

6353 

8.75668 

6823 

8.82805 

5077 

8.53248 

5507 

8.61378 

5923 

8.68660 

6359 

8.75763 

6827 

8.82864 

5081 

8.53326 

5519 

8.61595 

5927 

8.68727 

6361 

8.75794 

6829 

8.82893 

5087 

8.53444 

5521 

8.6l63I 

5939 

8.68930 

6367 

8.75888 

6833 

8.82952 

5099 

8.53680 

5527 

8.61740 

'5953 

8.69165 

6373 

8.75983 

6841 

8.83069 

5101 

8.53719 

5531 

8.  61812 

5931 

8.69634 

6379 

8.76077 

6857 

8.83303 

5107 

8.53837 

5557 

8.62281 

5987 

8.69735 

6389 

8.76233 

6863 

8.83390 

5H3 

8.53954 

5563 

8.62389 

6007 

8.70068 

6397 

8.76358 

6869 

8.83477 

5H9 

8.54071 

5569 

8.62497 

6011 

8.70135 

6421 

8.76733 

6871 

8.83506 

5147 

8.54617 

5573 

8.62569 

6029 

8.70434 

6427 

8.76826 

6883 

8.83681 

5153 

8.54733 

558i 

8.62/712 

6037 

8.70566 

6449 

8.77168 

6889 

8.83768 

5167 

8.55005 

5591 

8.62891 

6043 

8.70666 

6451 

8.77199 

6907 

8.84029 

5171 

8.55082 

5623 

8.63462 

6047 

8.70732 

6469 

8.77478 

6911 

8.84087 

5179 

8.55237 

5639 

8.63746 

6053 

8.70831 

6473 

8.77539 

6917 

8.84174 

5189 

8.55430 

5641 

8.63782 

6067 

8.71062 

6481 

8.77663 

6947 

8.84607 

5197 

8.55584 

5647 

8.63888 

6073 

8.71161 

6491 

8.77817 

6949 

8.8463S 

5209 

8.55814 

5651 

8.63959 

6079 

8.71260 

6521 

8.78278 

6959 

8.84779 

5227 

8.56159 

5653 

8.63994 

6089 

8.71424 

6529 

8.78401 

6961 

8.84808 

5231 

8.56236 

5657 

8.64065 

6091 

8.71457 

6547 

8.78676 

6967 

8.84894 

S'23'3 

8.56274 

5659 

8.64100 

6101 

8.71621 

>- 

6551 

8.78737 

6971 

8.84951 

5237 

8.56350 

5669 

8.64277 

6113 

8.71817 

6553 

8.78768 

6977 

8.85037 

5261 
5273 

8.56808 
8.57035 

5683 
5689 

8.64523 
8.64629 

6121 
6131 

8.71948 

8.72111 

6563 
6569 

8.78920 
8.79012 

6983 

6991 

8.85123 
8.85238 

5279 

8.57149 

5693 

8.64699 

6133 

8.72144 

6571 

8.79042 

6997 

8.85324 

5281 

8.57187 

5701 

8.64840 

6i43 

8.72307 

6577 

8.79133 

7001 

8.85381 

5297 

8.57490 

57i  i 

8.65015 

6151 

8.72437 

6581 

8.79194 

7013 

8.85552 

5303 

8.57603 

5717 

8.65120 

6163 

8.72632 

6599 

8.79467 

7019 

8.85638 

5309 

8.57716 

5737 

8.65469 

6173 

8.72794 

6607 

8.79588 

7027 

8.85752 

5323 

8.57979 

5741 

8.65539 

6i97 

8.73182 

6619 

8.79770 

7039 

8.85922 

5333 

8.58167 

5743 

8.65574 

6199 

8.73214 

6637 

8.80042 

7043 

8.85979 

5347 

8.58429 

5749 

8.65678 

6203 

8.73279 

6653 

8.80282 

7057 

8.86178 

5351 

8.58504 

5779 

8.66199 

6211 

8.73408 

6659 

8.80372 

7069 

8.86347 

538i 

8.59063 

5783 

8.66268 

6217 

8.73504 

6661 

8.80402 

7079 

8.86489 

5387 

8.59174 

5791 

8.66406 

6221 

8.73569 

6673 

8.80582 

7103 

8.86827 

5393 

8.59286 

5801 

8.66579 

6229 

8.73697 

6679 

8.80672 

7109 

8.86912 

5399 

8-59397 

5807 

8.66682 

6247 

8.73986 

6689 

8.80822 

7121 

8.87080 

5407 

8.59545 

58i3 

8.66785 

6257 

8.74146 

6691 

8.80852 

7127 

8.87165 

5413 

8.59656 

5821 

8.66923 

6263 

8.74241 

6701 

8.81001 

7129 

8.87193 

5417 

8.59730 

5827 

8.67026 

6269 

8.74337 

6703 

8.81031 

7151 

8.87501 

5419 

8.50767 

5839 

8.67231 

6271 

8.74369 

6709 

8.81121 

7159 

8.87613 

5421 

8.59988 

5843 

8.67300 

6277 

8.74465 

6719 

8.81269 

7177 

8.87864 

e* 

X 

ex 

X 

e* 

X 

ex 

X 

6* 

X 

SMITHSONIAN  TABLES 


271 


Natural  Logarithms. 


u 

LofleU 

u 

LOdeU 

u 

LOOe" 

u     Looeu 

u 

Udell 

7187 

8.88003 

7621 

8.93866 

8093 

8.99875 

8573 

9.05637 

9001 

9.10509 

7193 

8.88086 

7639 

8.94102 

8101 

8.99974 

8581 

9.05731 

9007 

9.10576 

7207 

8.88281 

7643 

8.94155 

8111 

9.00008 

8597 

9.05917 

9011 

9.I062O 

7211 

8.88336 

7649 

8.94233 

8117 

9.OOI72 

8599 

9.05940 

0013 

9.  10642 

7213 

8.88364 

7669 

8.94494 

8123 

9.00245 

8609 

9.06056 

9029 

9.IO820 

7219 

8.88447 

7673 

8.94546 

8i47 

9.00541 

8623 

9.06219 

0041 

9.10953 

7229 

8.88586 

7681 

8.946511 

8161 

9.00712 

8627 

9.06265 

9043 

9.10975 

7237 

8.88696 

7687 

8.947^9 

8167 

9.00786 

8629   9.06288 

9049 

9.  IIO4I 

7243 

8.88779 

7691 

8.94781 

8171 

9.00835 

8641 

9.  06427 

9059 

9.IH5I 

7247 

8.88834 

7699 

8.94885 

8179 

9-00933 

8647 

9.06497 

9067 

9.11240 

7253 

8.88917 

7703 

8.94937 

8191 

9.01079 

8663 

9.06682 

9091 

9.11504 

7283 

8.89330 

7717 

8.95118 

8209 

9.01299 

8669 

9-06731 

9103 

9.11636 

7297 

8.89522 

7723 

8.95196 

8219 

9.OI42O 

8677 

9-06843 

9109 

9.11702 

7307 

8.89659 

7727 

8.95248 

8221 

9.01445 

8681 

9.06889 

9127 

9.11899 

7309 

8.89686 

7741 

8.95429 

8231 

9.01566 

8689 

9.06981 

9133 

9.11965 

7321 

8.89850 

7753 

8.95584 

8233 

9.01591 

8693 

9.07027 

9137 

9.12009 

7331 

8.89987 

7757 

8.95635 

8237 

9.0II639 

8699 

9.07096 

9151 

9.12162 

7333 

8.9OOI4 

7759 

8.95661 

8243 

9.0I7I2 

8707 

9.07188 

9157 

9.12227 

7349 

8.00232 

7789 

8.96047 

8263 

9.01954 

8713 

9.07257 

9161 

9.12271 

7351 

8.90259 

7793 

8.96098 

8269 

9.02O27 

8719 

9.07326 

9173 

9.12402 

7369 

8.90504 

78i7 

8.96406 

8273 

9.02075 

8731 

9.07464 

9181 

9.  12489 

7393 

8.90829 

7823 

8.96482 

8287 

Q.02244 

8737 

9.07532 

9187 

9.12554 

7411 

8.9IO72 

7829 

8.96559 

8291 

9.02293 

8741 

9.07578 

9199 

9.12685 

7417 

8.9H53 

7841 

8.96712 

8293 

9.02317 

8747 

9.07647 

9203 

9.12728 

7433 

8.91368 

7853 

8.96765 

8297 

9-02365 

8753 

9.07715 

9209 

9.12794 

7451 

8.9l6lO 

7867 

8.97043 

8311 

9.02634 

8761 

9.07807 

9221 

9.12924 

7457 

8.9II69I 

7873 

8.97119 

8317 

9.02606 

8779 

9.08012 

9227 

9.12989 

7459 

8.9I7I8 

7877 

8.97170 

8329 

9.02750 

8783 

9.08057 

9239 

9.13119 

7477 

8.91959 

7879 

8.97196 

8353 

9.03038 

8803 

9.08285 

9241 

9.1314'! 

748i 

8.92OI2 

7883 

8.97246 

8363 

9.03157 

8807 

9.08330 

9257 

9.13314 

7487 

8.92O92 

7901 

8.97474 

8369 

9.03'229 

8819 

9.08466 

9277 

9.13529 

7489 

8.92119 

7907 

8.97550 

8377 

9.03325 

8821 

9.08489 

9281 

9.13572 

7499 

8.92252 

7919 

8.97702 

8387 

9.03444 

8831 

9.08602 

9283 

9-  13594 

7507 

8.92359 

7927 

8.97803 

8389 

9.03468 

8837 

9.08670 

9293 

9.13702 

7517 

8.92492 

7933 

8.97879 

8419 

9.03825 

8839 

9.08693 

9311 

9.13895 

7523 

8.92572 

7937 

8.97929 

8423 

9.03872 

8849 

9.08806 

9319 

9.13981 

7529 

8.92652 

7949 

8.98080 

8429 

9-03943 

8861 

9.08941 

9323 

9.14024 

7537 

8.92758 

7951 

8.08105 

8431 

9.03967 

8863 

9.08064 

9337 

9.14174 

7541 

8.928II 

7963 

8.08256 

8443 

9.04109 

8867 

9.09009 

9341 

9.14217 

7547 

8.92891 

7993 

8.98632 

8447 

9.04157 

8887 

9.09234 

9343 

9-14238 

7549 

8.92917 

8009 

8.98832 

8461 

9.04322 

8893 

9.09302 

9349 

9-  14302 

7559 

8.93049 

8011 

8.98857 

8467 

9-04393 

8923 

9.09639 

9371 

9-  U538 

756i 

8.93076 

8017 

8.98932 

8501 

9.04794 

8929 

9.09706 

9377 

9.  14602 

7573 

8.93234 

8039 

8.99206 

8513 

9-04935 

8933 

9.09751 

9391 

9.I475I 

7577 

8.93287 

8053 

8.99380 

8521 

9.05029 

8941 

9.09840 

9397 

9.14815 

7583 

8.93366 

8059 

8.99454 

8527 

9.05099 

8951 

9.09952 

9403 

9.14878 

7589 

8.93446 

8069 

8.99578 

8537 

9.05216 

8963 

9.10086 

9413 

9.14985 

7591 

8.93472 

8081 

8.99727 

8539 

9.05240 

8969 

9-IOI53 

94-19 

9.15048 

7603 

8.93630 

8087 

8.99801 

8543 

9.05287 

8971 

9-JOT75 

9421 

9.15070 

7607 

8.93682 

8089 

8.99826 

8563 

9.055-2U 

8999 

9.10487 

9431 

9.15176 

e* 

X 

ex 

X 

ex 

* 

e* 

X 

ex 

X 

SMITHSONIAN  TABLES 


272 


Natural  Logarithms. 


u 

Logeu 

u 

LogeU 

U 

Log,u 

u 

Log«u 

u 

Loot-u 

9433 

9.I5I97 

9551 

9.16440 

9719 

9.18184 

9833 

9.  19350 

9967 

9.20703 

9437 

9-  15239 

9587 

9.l68l6 

97-21 

9.  18204 

9839 

9.19411 

9973 

9.20764 

9439 

9.15261 

9601 

9.16962 

9733 

9.18328 

9851 

9-19533 

10000 

9.21034 

9461 

9-  15493 

9613 

9.17087 

9739 

9-18389 

9857 

9.19594 

100000 

II.5I293 

9463 

9.I55I4 

9619 

9.I7I50 

9743 

9.18430 

9859 

9.19614 

9467 

9.15557 

9623 

9.I7I9I 

9749 

9-  18492 

9871 

9.19736 

9473 

9.15620 

9629 

9.17253 

9767 

9.  18676 

9883 

9.19857 

9479 

9.15683 

9631 

9.17274 

9769 

9.18697 

9887 

9.19898 

9491 

9.15810 

9643 

9-17399 

978i 

9.  18820 

9901 

9.20039 

9497 

9.15873 

9649 

9.I746I 

9787 

9.I888I 

9907 

9.20100 

9511 

9.16020 

9661 

9.17585 

9791 

9.  18922 

9923 

9.20261 

9521 

9.16126 

9677 

9.  I775I 

9803 

9.19044 

9929 

9.20322 

9533 

9.16251 

9679 

9.17771 

9811 

9.19126 

9931 

9-20342 

9539 

9.^6314 

9689 

9.  17875 

9817 

9.I9I87 

9941 

9.20442 

9547 

9.16398 

9697 

9.17957 

9829 

9.19309 

9949 

9.20523 

ex 

X 

ex 

X 

e* 

X 

ex 

X 

ex 

X 

Coefficients  for  Computing, 

F^F.in-lV.*  |  %+  5-  /J0±  i  (!L  -  i)yo]  . 

n 

n2 

Diff. 

*-(£-} 

Diff. 

n 

n2 

Diff. 

±("~-\\ 

Diff. 

6 

\2\2       ) 

6 

12  \2       / 

o.oo 

+0.0000 

—  o.oooo 

0.25 

+O.OIO4 

—0.0202 

.01 

.0000 

O 

.0008 

.26 

-OII3 

9 

.O2O9 

7 

.02 

.0001 

I 

.0017 

9 

8 

.27 

.OI22 

9 

.O2I7 

7 

.03 

.0002 

I 

.0025 

8 

.28 

.0131 

y 

9 

.O224 

8 

.04 

.0003 

I 

.0033 

9 

.29 

.0140 

10 

.0232 

7 

0.05 

+O.OOO4 

—0.0042 

0.30 

+0.0150 

—0.0239 

.06 

.0006 

2 

.0050 

.31 

.Ol6o 

10 

.0246 

.07 

.0008 

2 

.0058 

.32 

.0171 

1  1 

.0253 

7 

.08 

.OOII 

3 

.0066 

•  33 

.0182 

1  1 

.O2Ob 

.09 

.0014 

3 
3 

.0075 

8 

•34 

.0193 

ii 
ii 

.0267 

7 
7 

O.IO 

+0.0017 

—0.0083 

0.35 

+O.02O4 

—  O.O274 

.11 

.0020 

3 

.0091 

.36 

.O2l6 

12 

.0281 

7 

.12 

.0024 

4 

.0099 

•  37 

.0228 

12 

.0287 

•• 

-13 

.0028 

4 

.0107 

.38 

.0241 

13 

.0294 

I 

.14 

.0033 

5 

.0116 

8 

•39 

.0254 

13 

13 

.0300 

u 

7 

0.15 

+0.0038 

—  0.0124 

0.40 

+0.0267 

—  0.03O7 

.16 

.0043 

.0132 

.41 

.0280 

13 

.0313 

•17 

.0048 

5 

.0140 

.42 

.0294 

14 

.0319 

.18 

.0054 

.0148 

•43 

.0308 

14 

.0325 

.19 

.0060 

7 

.0155 

I 

•44 

.0323 

15 
IS 

.0331 

6 

O.2O 

+0.0067 

—0.0163 

0.45 

+0.0338 

-0.0337 

.21 

.0074 

7 

.0171 

.46 

•  .0353 

15 

.0343 

t 

.22 

.0081 

7 

.0179 

•  47 

.0368 

15 

.0348 

i 

•23 

.0088 

7 

.0187 

•  48 

.0384 

f* 

•  0354 

U 

c 

.24 

.0096 

8 

.0194 

8 

•49 

.0400 

17 

.0359 

1 

0.25 

+0.0104 

—  O.O2O2 

0.50 

+0.0417 

—0.0365 

SMITHSONIAN  TABLES 


273 


TABLE  VI 


THE  fiUDERMANNIAN 


275 


The  Gudermannian. 


u 

gdu 

U.FO' 

gd  u 

u>F0' 

u 

gdu 

»F0' 

gdu 

«F0' 

o   /   // 

tt 

0    /     // 

~ 

o.ooo 

O.OOO  OOOO 

oooo 

0  OO  00.  OO 

206.26 

O.O50 

0.049  9792 

9988 

2  51  48.95 

206.OI 

.001 

.001  oooo 

oooo 

o  03  26.26 

206.26 

.051 

.050  9779 

9987 

2  55  14-95 

2o6.0O 

.002 

.002  oooo 

oooo 

o  06  52.53 

206.26 

.052 

.051  9766 

9986 

2  58  40.94 

205.99 

.003 

.003  oooo 

oooo 

o  10  18.79 

206.26 

.053 

.052  9752 

9986 

3  02  06.92 

205.98 

.004 

.004  oooo 

oooo 

o  13  45-06 

206.26 

.054 

•053  9738 

9985 

3  05  32.89 

205.96 

0.005 

0.005  oooo 

oooo 

o  17  11.32 

206.26 

0.055 

0.054  9723 

9985 

3  08  58.85 

205.95 

.006 

.006  oooo 

oooo 

0  20  37.58 

206.26 

.056 

.055  9708 

9984 

3  12  24.80 

205.94 

.007 

.006  0999 

oooo 

o  24  03.84 

206.26 

•057 

.056  9692 

9984 

3  15  50-73 

205.93 

.008 

.007  9999 

oooo 

o  27  30.10 

206.26 

.058 

.057  9^75 

9983 

3  19  16.66 

205.02 

.009 

.008  9999 

oooo 

o  30  56.36 

206.26 

.059 

.058  9658 

9983 

3  22  42.57 

205.91 

O.OIO 

0.009  9998 

9999 

o  34  22.  61 

206.25 

0.060 

0.059  9640 

9982 

3  26  08.47 

205.89 

.on 

.010  9998 

9999 

o  37  48.87 

206.25 

.061 

.060  9622 

998i 

3  29  34-36 

205.88 

.012 

.oil  9997 

9999 

o  41  15.12 

206.25 

.062 

.061  9603 

9981 

3  33  00.23 

205.87 

.013 

.012  9996 

9999 

o  44  41.37 

206.25 

.063 

.062  9584 

9980 

3  36  26.10 

205.86 

.014 

.013  9995 

9999 

o  48  07.61 

206.24 

.064 

.063  9564 

9980 

3  39  51-94 

205.84 

0.015 

0.014  9994 

9999 

o  51  33-86 

206.24 

0.065 

0.064  9543 

9979 

3  43  17.78 

205.83 

.016 

•015  9993 

9999 

o  55  00.10 

206.24 

.066 

.065  9521 

9978 

3  46  43-60 

205.82 

.017 

.016  9992 

9999 

o  58  26.33 

206.23 

.067 

.066  9499 

0978 

3  50  09.41 

205.8o 

.018 

.017  9990 

9998 

I  01  52-57 

206.23 

.068 

.067  9477 

9977 

3  53  35-21 

205-79 

.019 

.018  9989 

9998 

i  05.18.80 

206.23 

.069 

.068  9453 

9976 

3  57  00.99 

205.77 

0.020 

0.019  9987 

9908 

i  08  45.02 

2O5.22 

0.070 

0.069  9429 

9976 

4  oo  26.76 

205.76 

.O2I 

.020  9985 

9998 

I  12  11.24 

206.22 

.071 

.070  9404 

9975 

4  03  52.51 

205.75 

.022 

.021  9982 

9998 

I  15  37.46 

2O5.2I 

.072 

.071  9379 

9974 

4  07  18.25 

205-73 

.023 

.022  0980 

9997 

I  19  03.67 

206.21 

•073 

.072  9352 

9973 

4  10  43.08 

205.72 

.024 

.023  9977 

9997 

I  22  29.88 

206.21 

•074 

.073  9326 

9973 

4  14  09.68 

205.70 

O.O25 

0.024  9974 

9997 

I  25  56.08 

2O6.2O 

0.075 

0.074  9298 

9972 

4  17  35.38 

205.69 

.026 

.025  9971 

9997 

I  29  22.28 

206.2O 

.076 

.075  9269 

9971 

4  21  01.06 

205.67 

.027 

.026  9967 

9996 

I  32  48.47 

2O6.I9 

.077 

.076  9240 

9970 

4  24  26.72 

205.65 

.028 

.027  0963 

9996 

I  36  14.66 

206.18 

.078 

.077  9210 

9970 

4  27  52.37 

205.64 

.029 

.028  9959 

9996 

I  39  40.84 

206.18 

.079 

.078  9180 

9969 

4  31  18.00 

205.62 

0.030 

0.029  9955 

9995 

I  43  07.02 

2O6.I7 

0.080 

0.079  9148 

9968 

4  34  43.61 

2O5.6l 

.031 

.030  9950 

9995 

I  46  33.19 

2O6.I7 

.081 

.080  9116 

9967 

4  38  09.21 

205.59 

.032 

.031  9945 

9995 

i  49  59-35 

2O6.l6 

.082 

.081  9083 

9966 

4  41  34.79 

205.57 

•033 

.032  0940 

9995 

i  53  25.50 

206.15 

.083 

.082  0049 

9966 

4  45  00.36 

205.56 

.034 

.033  9935 

9994 

I  56  51-65 

2O6.I5 

.084 

.083  9014 

9965 

4  48  25.90 

205.54 

0.035 

0.034  0929 

9994 

2  00  17.79 

206.14 

0.085 

0.084  8978 

9964 

4  51  51.44 

205.52 

.036 

.035  9922 

9994 

2  03  43-93 

206.13 

.086 

.085  8942 

9963 

4  55  16.95 

205.50 

•037 

.036  9916 

9993 

2  O7  10.  06 

206.12 

.087 

.086  8905 

9962 

4  58  42.44 

205.49 

.038 

.037  9909 

9993 

2  IO  36.18 

206.12 

.088 

.087  8866 

9061 

5  02  07.92 

205-47 

.039 

.038  9901 

9992 

2  14  O2.29 

206.  II 

.089 

.088  8827 

9961 

5  05  33.38 

•*>5  -45 

0.040 

0.039  9893 

9992 

2  17  28.39 

2O6.IO 

0.000 

0.089  8787 

9960 

5  08  58.82 

205.43 

.041 

.040  9885 

9992 

2  20  54.49 

206.09 

.091 

.090  8747 

9959 

5  12  24.25 

205.41 

.042 

.041  9877 

9991 

2  24  2O.58 

206.08 

.092 

.091  8705 

9958 

5  15  49.65 

205.39 

.043 

.042  9868 

9991 

2  27  46.65 

2O6.O7 

•093 

.092  8662 

9957 

5  19  15.03 

205.38 

.044 

.043  9858 

9990 

2  31  12.72 

206.07 

.094 

.093  8619 

9956 

5  22  40.40 

205.36 

0.045 

0.044  9848 

9990 

2  34  38.79 

2O6.O6 

0.095 

0.094  8574 

9955 

5  26  05.75 

205.34 

.046 

.045  9838 

9989 

2  38  04.84 

206.05 

.096 

.095  8529 

9954 

5  29  31.08 

205.32 

.047 

.046  9827 

9989 

2  41  30.88 

206.04 

.097 

.096  8482 

9953 

5  32  56.38 

205.30 

.048 

.047  9816 

9988 

2  44  56.91 

2O6.O3 

.098 

.097  8435 

9952 

5  36  21.67 

205.28 

.049 

.048  9804 

9988 

2  48  22.93 

206.02 

.099 

.098  8387 

0051 

5  39  46.94 

205.26 

0.050 

0.049  9792 

9988 

2  51  48.95 

206.0I 

O.IOO 

0.099  8337 

9950 

5  43  12.19 

205.24 

u 

2  tan-He")-  * 

«>  s  ch  u 

2  tan-He"  )-900 

wsech  u 

u 

2tan-'(e»)-? 

wsechu 

2tan-'(e«)-9(r) 

M  sech  u 

IMITHSONIAN    TABLES 


276 


The  Gudermannian. 


II 

gd  u 

«Fo' 

gdu 

«F0' 

u 

gd  u 

«F0' 

gdu 

<-F0' 

o   /   // 

o 

O    /     // 

H 

O.IOO 

0.099  8337 

9950 

5  43  12.19 

205.24 

0.150 

0.149  4406 

9889 

8  33  44-35 

203.97 

.101 

.100  8287 

9949 

5  46  37-42 

205.22 

.151 

.  150  4294 

9887 

8  37  08.30 

203.94 

.102 

.101  8236 

9948 

5  50  02.62 

205.20 

.152 

.151  4181 

9886 

8  40  32.22 

203.90 

.103 

.102  8184 

9947 

5  53  27.81 

205.18 

.153 

.152  4065 

9884 

8  43  56.11 

203.87 

.104 

.103  8130 

9946 

5  56  52.97 

205.15 

•  154 

•153  3949 

9883 

8  47  19-96 

203.84 

0.105 

0.104  8076 

9945 

6  oo  18.12 

205.13 

0.155 

0.154  3831 

9881 

8  50  43-79 

203.81 

.106 

.105  8021 

9944 

6  03  43.24 

205.11 

.156 

.155  37ii 

9880 

8  54  07.59 

203.78 

.107 

.106  7964 

9943 

6  07  08.34 

205.09 

.157 

•  156  3590 

9878 

8  57  31.35 

203.75 

.108 

.107  7907 

9942 

6  10  33.42 

205.07 

.158 

.157  3467 

9876 

9  oo  55.o8 

203.72 

.109 

.108  7848 

9941 

6  13  58.48 

205.05 

.159 

.158  3343 

9875 

9  04  18.78 

203.68 

O.IIO 

0.109  7788 

9940 

6  17  23.51 

205.02 

0.160 

0.159  3217 

9873 

9  07  42.45 

203.65 

.III 

.no  7728 

9939 

6  20  48.52 

205.00 

.161 

.160  3089 

9872 

9  ii  06.09 

203.62 

.112 

.in  7666 

9938 

6  24  13.51 

204.98 

.162 

.161  2960 

9870 

9  14  29.69 

203.59 

•113 

.112  7603 

9936 

6  27  38.48 

204.95 

.163 

.162  2830 

9869 

9  17  53-26 

203.55 

.114 

•113  7539 

9935 

6  31  03.42 

204.93 

.164 

.163  2697 

9867 

9  21  16.80 

203.52 

O.II5 

0.114  7474 

9934 

6  34  28.34 

204.91 

0.165 

0.164  2564 

9865 

9  24  40.31 

203.49 

.116 

.115  7407 

9933 

6  37  53.24 

204.88 

.166 

.165  2428 

9864 

9  28  03.78 

203.46 

.117 

.116  7340 

9932 

6  41  i8.ii 

204.86 

.167 

.166  2291 

9862 

9  31  27.22 

203.42 

.118 

.117  7271 

9931 

6  44  42.96 

204.84 

.168 

.167  2153 

9861 

9  34  50.62 

203.39 

.119 

.118  7201 

9930 

6  48  07.78 

204.81 

.169 

.168  2OI2 

9859 

9  38  13-99 

203-35 

O.I2O 

0.119  7130 

9928 

6  51  32.59 

204.79 

0.170 

O.l69  l87O 

9857 

9  41  37.33 

203.32 

.121 

.120  7058 

9927 

6  54  57.36 

204.76 

.171 

.170  1727 

9856 

9  45  00.63 

203.29 

.122 

.121  6985 

9926 

6  58  22.11 

204-74 

.172 

.171  1581 

9854 

9  48  23.00 

203.25 

•123 

.122  6910 

9925 

7  01  46.84 

204.71 

.173 

.172  1434 

9852 

9  51  47-14 

203.22 

.124 

.123  6834 

9924 

70S  11.54 

204.69 

.174 

.173  1286 

9851 

9  55  10.33 

203.18 

0.125 

0.124  6757 

9922 

7  08  36.22 

204.66 

0.175 

0.174  1136 

9849 

9.58  33.50 

203.15 

.126 

.125  6679 

9921 

7  12  00.87 

204.64 

.176 

.175  0083 

9847 

10  01  56.63 

203.11 

.127 

.126  66OO 

9920 

7  15  25.49 

204.61 

.177 

.  176  0830 

9845 

10  05  19.72 

203.08 

.128 

.127  6519 

9919 

7  18  50.09 

204.59 

.178 

.  177  0674 

9844 

10  08  42.78 

203.04 

.129 

.128  6437 

9917 

7  22  14.67 

204.56 

.179 

.  178  0517 

9842 

10  12  05.80 

203.00 

0.130 

0.129  6354 

9916 

7  25  39.22 

204-53 

0.180 

0.179  0358 

9840 

10  15  28.78 

202.97 

.131 

.I3O  6269 

9915 

7  29  03.74 

204.51 

.181 

.180  0197 

9838 

10  18  51.73 

202.93 

.132 

.131  6183 

9913 

7  32  28.23 

204.48 

.182 

.181  0035 

•9837 

IO  22  14.65 

202.00 

.133 

.132  6096 

9912 

7  35  52.70 

204.45 

.183 

.181  9871 

9835 

10  25  37.52 

202.86 

.134 

.133  6008 

9911 

7  39  I7.I4 

204.43 

.184 

.182  9705 

9833 

10  29  00.36 

202.82 

0.135 

0.134  59l8 

9910 

7  42  41.55 

204.40 

0.185 

0.183  9537 

9831 

10  32  23.17 

2O2  .  78 

.136 

•135  5827 

9908 

7  46  05.94 

204-37 

.186 

.  184  9367 

9829 

10  35  45-93 

202.75 

.137 

•136  5734 

9907 

7  49  30.29 

204.34 

.187 

.185  9196 

9828 

10  39  08.66 

202.71 

.138 

.137  5641 

9906 

7  52  54.62 

204.32 

.188 

.186  9022 

9826 

10  42  3L35 

202.67 

.139 

.138  5545 

9904 

7  56  18.93 

204.29 

.189 

.187  8847 

9824 

10  45  54.01 

2O2.63 

0.140 

0.139  5449 

9903 

7  59  43.20 

204.26 

0.190 

o.  188  8670 

9822 

10  49  16.62 

2O2.6O 

.141 

.140  5351 

9901 

8  03  07-45 

204.23 

.191 

.  189  8492 

5820 

10  52  39.20 

2O2.56 

.142 

.141  5252 

9900 

8  06  31.66 

204.20 

.192 

.190  8311 

9818 

10  56  01.74 

2O2.52 

.143 

.142  5151 

9899 

8  09  55.85 

204.17 

.193 

.191  8129 

9817 

10  59  24.24 

2O2.48 

.144 

.143  5049 

9897 

8  13  20.  01 

204.14 

.194 

.192  7944 

9815 

ii  02  46.71 

202.44 

0.145 

0.144  4946 

9896 

8  16  44.14 

204.12 

0.195 

0.193  7758 

0813 

ii  06  09.13 

2O2.4O 

.146 

.145  4841 

9894 

8  20  08.24 

204.09 

.196 

.194  7570 

9811 

ii  09  31-51 

202.37 

.147 

.  146  4734 

9893 

8  23  32.31 

204.06 

.197 

.195  738o 

9809 

II  12  53.86 

202.33 

.148 

.147  4626 

9891 

8  26  56.35 

204.03 

.198 

.196  7188 

9807 

ii  16  16.17 

202.29 

.149 

•148  4517 

9890 

8  30  20.36 

204.00 

.199 

.197  6994 

9805 

ii  19  38.43 

202.2-5 

0.150 

0.149  4406 

9889 

8  33  44-35 

203.97 

0.200 

0.198  6798 

9803 

ii  23  00.66 

2O2.2I 

u 

2tan-'(e»)-£ 

<»s:chu 

2tan-He«)-«00 

wsechu 

U 

2  tan-He")-^ 

wsechu 

atan-Keuy-SO0 

wsech  u 

SMITHSONIAN  TABLES 


277 


The  Gudermannian. 


u 

gd  u 

«F0' 

gdu 

U.FO" 

u 

gd  u 

<oFo' 

gdu 

•Fo' 

o   /   // 

II 

o   /    // 

// 

0.200 

o.  198  6798 

9803 

II  23  00.66 

202.21 

0.250 

0.247  4358 

9695 

H  10  37-30 

199^98 

.201 

.199  66oi 

9801 

II  26  22.85 

202.17 

.251 

.248  4052 

9693 

14  13  57.26 

199.93 

.202 

.200  6401 

9799 

II  29  44.99 

202.13 

.252 

.249  3744 

9691 

14  17  17.16 

199-88 

.203 

.2OI  6200 

9797 

u  33  07.10 

202.09 

•  253 

•250  3434 

9688 

14  20  37.02 

199.84 

.204 

.202  5996 

9795 

II  36  29.17 

202.05 

.254 

.251  3121 

9686 

14  23  56.83 

199.79 

0.205 

0.203  5790 

9794 

u  39  51.19 

202.01 

0.255 

0.252  2805 

9683 

14  27  16.59 

199-74 

.206 

.204  5583 

9792 

ii  43  13.18 

2OI.96 

.256 

.253  2488 

9681 

14  30  36.31 

199-69 

.207 

•205  5374 

9790 

II  46  35.12 

201.92 

•  257 

.254  2167 

9679 

14  33  55-97 

199.64 

.208 

.206  5162 

9788 

u  49  57-02 

201.88 

.258 

.255  1845 

9676 

14  37  15.58 

199-59 

.209 

.207  4949 

9786 

II  53  18.89 

201.84 

.259 

.256  1520 

9674 

14  40  35.14 

199-53 

0.210 

0.208  4733 

9783 

II  56  40.71 

201.80 

0.260 

0.257  H92 

9671 

14  43  54.65 

199.48 

.211 

.209  4515 

978i 

12  oo  02.48 

201.76 

.261 

.258  0862 

9669 

14  47  14.10 

199-43 

.212 

.210  4296 

9779 

12  03  24.22 

201.71 

.262 

.259  0530 

9666 

14  50  33.51 

199.38 

.213 

.211  4074 

9777 

12  06  45.91 

201.67 

.263 

.260  0195 

9664 

14  53  52.87 

199-33 

.214 

.212  3851 

9775 

12  IO  07.56 

201.63 

.264 

.260  9857 

9661 

14  57  12.  18 

199.29 

0.215 
.2l6 

0.213  3625 

.214  3397 

9773 
9771 

12  13  29.17 

12  16  50.74 

201.59 
201.54 

0.265 
.266 

0.261  9518 
.262  9175 

£% 

9656 

15  00  31.43 
15  03  50.63 

199-24 
199.19 

.217 

.215  3167 

9769 

12  20  12.26 

201.50 

.267 

.263  8830 

9654 

15  07  09.78 

199.13 

.218 

.216  2935 

9767 

12  23  33.74 

201.46 

.268 

.264  8483 

9651 

15  10  28.88 

199.08 

.219 

.217  2701 

9765 

12  26  55.18 

201.42 

.269 

.265  8133 

9649 

15  13  47-93 

199.03 

O.22O 

0.218  2465 

9763 

12  30  16.57 

201.37 

0.270 

0.266  7781 

9646 

15  17  06.92 

198.98 

.221 

.219  2227 

9761 

12  33  37-92 

201.33 

.271 

.267  7425 

9644 

15  20  25.86 

198.93 

.222 

.220  1986 

9759 

12  36  59-23 

201.28 

.272 

.268  7068 

9641 

15  23  44-75 

198.87 

.223 

.221  1744 

9756 

12  4O  2O.49 

201.24 

.273 

.269  6708 

9639 

15  27  03.59 

198.82 

.224 

.222  1499 

9754 

12  43  41-71 

2OI.2O 

.274 

.270  6345 

9636 

15  30  22.37 

198.77 

0.225 

0.223  1252 

9752 

12  47  02.88 

201.15 

0.275 

0.271  5980 

9633 

15  33  41.10 

108.71 

.226 

.224  1003 

9750 

12  5O  24.OI 

2OI.II 

.276 

.272  5612 

9631 

15  36  59-78 

198.66 

.227 

.225  0752 

9748 

12  53  45-10 

2OI.06 

.277 

.273  5242 

9628 

15  40  18.41 

198.61 

.228 

.226  0409 

9746 

12  57  06.14 

201.02 

.278 

.274  4868 

9626 

15  43  36.98 

198.55 

.229 

.227  0243 

9743 

13  oo  27.13 

200.97 

.279 

.275  4493 

9623 

15  46  55-49 

198.50 

0.230 
.231 

0.227  9986 
.228  9726 

9741 
9739 

13  03  48.08 
13  07  08.99 

200.93 
200.88 

0.280 
.281 

0.276  4114 
.277  3734 

9620 

9618 

15  50  13.95 
15  53  32.36 

198-45 
198.38 

.232 

.229  9464 

9737 

13  10  29.85 

200.84 

.282 

.278  3350 

96I-S 

15  56  50.72 

198.33 

•233 

.230  9199 

9735 

13  13  50.66 

200.79 

.283 

.279  2964 

9612 

16  oo  09.02 

198.27 

-234 

.231  8933 

9732 

13  17  11.42 

200.74 

.284 

.280  2575 

9610 

16  03  27.26 

198.22 

O.235 

0.232  8664 

9730 

13  20  32.15 

200.70 

0.285 

0.281  2184 

9607 

16  06  45-45 

198.16 

.236 

•233  8393 

9728 

13  23  52.82 

200.65 

.286 

.282  1789 

9604 

16  10  03.58 

198.11 

.237 

.234  8120 

9726 

13  27  13.45 

200.60 

.287 

.283  1393 

9602 

16  13  21.66 

198.05 

.238 

.235  7844 

9723 

13  30  34-03 

200.56 

.288 

•284  0993 

9599 

16  16  39.69 

198.00 

.239 

.236  7566 

9721 

13  33  54.56 

200.51 

.289 

.285  0591 

9596 

16  19  57.66 

197-94 

O.24O 

0.237  7286 

9719 

13  37  15-05 

200.46 

0.290 

0.286  0186 

9594 

16  23  15.57 

197.89 

.241 

.238  7004 

9716 

13  40  35-49 

200.42 

.291 

.286  9778 

9591 

16  26  33.43 

197.83 

.242 

.239  6719 

9714 

13  43  55-88 

200.37 

.292 

.287  9368 

9588 

16  29  51.23 

197.77 

•243 

.240  6432 

9712 

13  47  16.23 

200.32 

.293 

.288  8955 

9586 

16  33  08.97 

197.72 

.244 

.241  6143 

97io 

13  50  36.53 

200.27 

.294 

.289  8539 

9583 

16  36  26.66 

197.66 

0.245 
.246 

0.242  5851 
.243  5557 

9707 
9705 

13  53  56.77 
13  57  16.98 

200.23 
200.18 

0.295 
.296 

0.200  8l2I 
.291  7699 

958o 
9577 

16  39  44.30 
16  43  01.87 

197-60 
197.55 

.247 

.244  5261 

9703 

14  oo  37.13 

200.13 

.297 

.292  7275 

9575 

16  46  19.39 

197.49 

.248 

.245  4902 

9700 

14  03  57-23 

200.08 

.298 

.293  6849 

9572 

16  49  36.85 

197.43 

•  249 

.246  4661 

9698 

14  07  17-29 

200.03 

.299 

.294  6419 

9569 

16  52  54.26 

197.38 

0.250 

0.247  4358 

9695 

14  10  37.30 

199.98 

0.300 

0.295  5987 

9566 

16  56  11.60 

197.32 

u 

2  ton-He0)-! 

<•<  sech  u 

2ton-1(e«)-900 

wsech  u 

u 

2  ton-He")— 

wsechu 

2tan-'(e«)-900 

«  tech  u 

SMITHSONIAN  TABLES 


278 


The  Gudermannian. 


u 

gdu 

«tf 

gdu 

-w 

u 

gd  u 

«FO' 

gdu 

«* 

o       y        // 

0 

0          /           // 

m 

0.300 

0.295  5987 

9566 

16  56  11.60 

197.32 

0.350 

0.343  0655 

9417 

19  39  22.34 

194.25 

.301 

.296  5552 

9563 

16  59  28.89 

197.26 

•  351 

.344  0071 

9414 

19  42  36.55 

I94.I8 

.302 

.297  5114 

956i 

17  02  46.13 

197.20 

•  352 

.344  0483 

9411 

19  45  50.70 

194.11 

.303 

.298  4673 

9558 

17  06  03.30 

197.15 

.353 

•345  8893 

9408 

19  49  04.78 

194.05 

.304 

.299  4229 

9555 

17  09  20.42 

197.09 

•354 

.346  8299 

9405 

19  52  18.80 

193.98 

0.305 

0.300  3783 

9552 

17    12   37.48 

197.03 

0.355 

0.347  7702 

9401 

19  55  32.75 

193.92 

.306 

.301  3334 

9549 

17    15   54.48 

196.97 

.356 

.348  7101 

9398 

19  58  46.63 

193.85 

.307 

.302  2882 

9547 

17    19   11.42 

196.91 

.357 

.349  6498 

9395 

20  02  00.45 

193.78 

.308 

.303  2427 

9544 

17   22   28.30 

196.85 

•  3-58 

•350  5891 

9392 

20  05  14.20 

193.72 

.309 

.304  1969 

9541 

17  25  45.12 

196.79 

•359 

.351  528i 

9388 

20  08  27.88 

193.65 

0.310 

0.305  1509 

9538 

17  29  01.89 

196.74 

0.360 

0.352  4668 

9385 

20    II   4L50 

193.58 

.311 

.306  1045 

9535 

17  32  18.60 

196.68 

.361 

•353  4052 

9382 

20    14   55-05 

193.52 

.312 

.307  0579 

9532 

17  35  35-24 

196.62 

.362 

•354  3432 

9378 

20  18  08.54 

193.45 

.313 

.308  ono 

9529 

17  38  51.83 

196.56 

.363 

•355  2809 

9375 

2O  21    21.95 

193.38 

.314 

.308  9638 

9526 

17  42  08.36 

196.50 

.364 

.356  2183 

9372 

20  24  35.30 

193.32 

0.315 

0.309  9163 

9524 

17  45  24.83 

196.44 

0.365 

0.357  1554 

9369 

20  27  48.59 

193.25 

.316 

.310  8685 

9521 

17  48  41.23 

196.38 

.366 

.358  0921 

9366 

20  31   01.80 

I93.I8 

.317 

.311  8204 

95i8 

17  51  57.58 

196.32 

.367 

•359  0285 

9362 

20  34  14.95 

193.11 

.318 

.312  7721 

9515 

17  55  13-87 

196.26 

.368 

.359  9646 

9359 

20  37  28.03 

193.05 

.319 

.313  7234 

9512 

17  58  30.10 

196.20 

.369 

.360  9003 

9356 

2O  4O  4I.O4 

192.98 

0.320 

0.314  6744 

9509 

18  01  46.26 

196.14 

0.370 

0.361  8358 

9352 

20  43  53.08 

192.91 

.321 

.315  6252 

9506 

18  05  02.37 

196.08 

•371 

.362  7708 

9349 

20  47  06.86 

192.84 

.322 

.316  5757 

9503 

18  08  18.42 

196.01 

•  372 

•363  7056 

9346 

20  50    19.66 

192.77 

.323 

.317  5258 

9500 

18  u  34.40 

195.95 

•  373 

.364  6400 

9343 

20  53  32.40 

192  .  7O 

.324 

.318  4757 

9497 

18  14  50.32 

195.89 

•  374 

.365  5741 

9339 

20  56  45-07 

192.63 

0.325 

0.319  4252 

9494 

18  18  06.  19 

195.83 

0.375 

0.366  5078 

9336 

20  59  57.67 

192.57 

.326 

.320  3745 

9491 

18  21  21.99 

195.77 

.376 

.367  4413 

9332 

21   O3    IO.20 

192.50 

.327 

.321  3235 

9488 

18  24  37.72 

195.71 

•  377 

.368  3743 

9329 

21   O6  22.66 

192.43 

.328 

.322  2721 

0485 

18  27  53.40 

195.65 

.378 

.369  3071 

9326 

21  09  35.05 

192.36 

.329 

.323  2205 

9482 

18  31  09.02 

195.58 

.379 

•370  2395 

9322 

21    12  47.38 

192.29 

0.330 

0.324  1686 

9479 

18  34  24.57 

195.52 

0.380 

0.371  1716 

9319 

21  15  59.63 

192.22 

.331 

.325  1163 

9476 

18  37  40.06 

195.46 

.381 

.372  1033 

9316 

21    19    11.82 

192.15 

.332 

.326  0638 

9473 

18  40  55-49 

195.40 

.382 

•373  0347 

9312 

21   22   23.93 

192.08 

.333 

.327  ono 

9470 

18  44  10.85 

195.33 

.383 

•373  9658 

9309 

21   25   35.97 

I92.OI 

.334 

.327  9578 

9467 

18  47  26.16 

195.27 

.384 

•374  8965 

9305 

21   28  47-95 

191.94 

0.335 

0.328  9044 

9464 

18  50  41.40 

195.21 

0.385 

0.375  8268 

9302 

21    31    59.85 

191.87 

.336 

.329  8506 

946i 

18  53  56.57 

195.15 

.386 

•376  7569 

9299 

21  35  n.68 

I9I.8O 

•  337 

•330  7965 

9458 

18  57  11.69 

195.08 

.387 

.3776866 

9295 

21    38  23.45 

I9L73 

•  338 

.331  7422 

9455 

19  oo  26.74 

195.02 

.388 

.378  6159 

9292 

21   41   35.14 

191.66 

•339 

.332  6875 

9452 

19  03  41.72 

194.95 

.389 

•379  5449 

9288 

21  44  46.76 

I9L59 

0.340 

0.333  6325 

9449 

1-9  06  56.65 

194.89 

0.390 

0.380  4736 

9285 

21  47  58.31 

I9L5I 

•  341 

•334  5772 

9445 

19  10  11.50 

194.83 

•  391 

.381  4019 

9281 

21  51  09.79 

191.44 

•  342 

•335  52i6 

9442 

19  13  26.30 

194.76 

•  392 

.382  3299 

9278 

21  54  21.  20 

I9L37 

•  343 

.336  4657 

9439 

19  16  41.03 

194.70 

•  393 

.383  2575 

9275 

21  57  32.53 

I9L30 

•  344 

•337  4095 

9436 

19  19  55.70 

194.63 

.394 

.384  1848 

9271 

22  OO  43.80 

I9L23 

0.345 
.346 

0.338  3529 
.339  2961 

9433 
9430 

19  23  10.30 
19  26  24.84 

194.57 
194.51 

0.395 
.396 

0.385  i  i  17 
.386  0383 

9268 
9264 

22  03   54.99 
22  O7  O6.  I  I 

I9I.I6 
191.09 

•  347 

.340  2389 

9427 

19  29  39.31 

194.44 

•  397 

.386  9645 

9261 

22    IO   I7.l6 

I9I.OI 

-348 

.341  1814 

9424 

19  32  53-72 

194.38 

.398 

.387  8904 

9257 

22    13   28.14 

190.94 

•  349 

.342  1236 

9420 

19  36  08.06 

194.31 

•399 

.388  8159 

9254 

22   l6  39.04 

190.87 

0.350 

0.343  0655 

9417 

19  39  22.34 

194.25 

0.400 

0.389  74ii 

9250 

22   19  49.88 

190.80 

u 

2  tan-He*)-^ 

w  sech  u 

">"-'<°°«°° 

<»sechu 

u 

2t™-I 

<»sechu 

*,»-*** 

<»  sech  u 

SMITHSONIAN  TABLES 


279 


The  Gudermannian. 


u 

gd  u 

»F0' 

gdu 

«F0' 

u 

gd  u 

<oF0' 

gd  u 

•Fo' 

o   /   // 

// 

0    /     // 

// 

0.400 

0.389  74U 

9250 

22  19  49.88 

I9O.80 

0.450 

0.435-  5388 

9066 

24  57  16.34 

187.01 

.401 

.390  6660 

9247 

22  23  OO.64 

190.72 

•  451 

.436  4453 

9063 

25  oo  23.31 

186.93 

.402 

•391  5904 

9243 

22  26  11.32 

190.65 

•  452 

•437  3514 

9059 

25  03  30.20 

186.85 

.403 

.392  5146 

9240 

22  29  21.94 

190.58 

•  453 

.438  2571 

9055 

25  06  37.01 

186.77 

.404 

•  393  4383 

9236 

22  32  32.48 

190.51 

•  454 

.439  1624 

9051 

25  09  43.74 

186.69 

0.405 

0.394  36l8 

9232 

22  35  42.95 

190.43 

0.455 

0.440  0673 

9047 

25*  12  50.39 

186.61 

.406 

.395  2848 

9229 

22  38  53-35 

190.36 

.456 

.440  9718 

9043 

25  15  56.96 

186.53 

.407 

.396  2075 

9225 

22  42  03.67 

190.29 

•  457 

.441  8759 

9040 

25  19  03.46 

186.45 

.408 

.397  1299 

9222 

22  45  13.92 

190.21 

.458 

•442  7797 

9036 

25  22  09.87 

186.37 

.409 

.398  0519 

9218 

22  48  24.09 

190.14 

•459 

•443  6831 

9032 

25  25  16.20 

186.29 

0.410 

0.398  9735 

9215 

22  51  34.19 

190.06 

0.460 

0.444  586i 

9028 

25  28  22.46 

186.21 

.411 

.399  8948 

9211 

22  54  44-22 

189.99 

.461 

.445  4886 

9024 

25  31  28.63 

186.13 

.412 

.400  8157 

9207 

22  57  54-lS 

189.92 

.462 

.446  3909 

9020 

25  34  34.72 

186.05 

.413 

.401  7363 

9204 

23  01  04.06 

189.84 

.463 

.447  2927 

9016 

25  37  40.74 

185.97 

.414 

.402  6565 

9200 

23  04  13.86 

189.77 

.464 

.448  1941 

9012 

25  40  46.67 

185.89 

0.415 

0.403  5763 

9197 

23  07  23.59 

189.69 

0.465 

0.449  0951 

9008 

25  43  52.52 

185.81 

.416 

.404  4958 

9193 

23  10  33-25 

189.62 

.466 

.449  9958 

9004 

25  46  58.29 

185-73 

.417 

.405  4M9 

9189 

23  13  42.83 

189.54 

.467 

.450  8060 

9001 

25  50  03.98 

185.65 

.418 

.406  3337 

9186 

23  16  52-.  34 

189.47 

.468 

.451  7959 

8997 

25  53  09.59 

185-57 

.419 

.407  2521 

9182 

23  20  01.77 

189.39 

.469 

.452  0954 

8993 

25  56  15.12 

185.49 

0.420 

0.408  1701 

9178 

23  23  11.13 

189.32 

0.470 

0.453  5944 

8989 

25  59  20.57 

185.41 

.421 

.409  0878 

9175 

23  26  20.41 

189.24 

.471 

•454  4931 

8985 

26  02  25.93 

185.33 

.422 

.410  0051 

9171 

23  29  29.62 

I89.I7 

.472 

.455  39M 

8581 

26  05  31.22 

185.24 

.423 

.410  9220 

9168 

23  32  38.75 

189.09 

•  473 

.456  2893 

8977 

26  08  36.42 

185.16 

.424 

.411  8386 

9164 

23  35  47.8i 

189.02 

.474 

.457  1868 

8973 

26  ii  41-54 

185.08 

0.425 

0.412  7548 

9160 

23  38  56.79 

188.04 

0.475 

0.458  0839 

8969 

26  14  46.58 

185.00 

.426 

.413  6706 

9157 

23  42  05.69 

188.87 

.476 

.4589806 

8965 

26  17  51-54 

184.92 

.427 

.414  5861 

9153 

23  45  14.52 

188.79 

•477 

.459  8/69 

8961 

26  20  56.42 

184.84 

.428 

.415  5012 

9149 

23  48  23.27 

188.71 

.478 

.460  7728 

8957 

26  24  OI.2I 

184.75 

.429 

.416  4159 

^9145 

23  51  31-95 

188.64 

•  479 

.461  6683 

8953 

26  27  05.93 

184.67 

0.430 

0.417  3303 

9142 

23  54  40.55 

188.56 

0.480 

0.462  5634 

8949 

26  3O  IO.56 

184.59 

.431 

.418  2443 

9138 

23  57  49-07 

188.49 

.481 

.463  4581 

8945 

26  33  15.10 

184.51 

.432 

.419  1579 

9U4 

24  oo  57-52,  188.41 

.482 

.464  3524 

8941 

26  36  19.57 

184.42 

•433 

.420  0711 

9131 

24  04  05.89  188.33 

.483 

.465  2464 

8937 

26  39  23.95 

184.34 

•434 

.420  9840 

9127 

24  07  14.18 

188.26 

.484 

.466  1399 

8933 

26  42  28.25 

184.26 

0.435 

0.421  8965 

9123 

24  10  22.40 

188.18 

0.485 

0.467  0330 

8929 

26  45  32.47 

184.18 

.436 

.422  8086 

9119 

24  13  30.54  188.10 

.485 

.467  9257 

8925 

26  48  36.60 

184.09 

•  437 

.423  7204 

9116 

24  16  38.60 

188.02 

'  .487 

.468  8180 

8921 

26  51  40.65 

184.01 

.438 

.424  6318 

9112 

24  19  46.59 

187.95 

.488 

.469  7099 

8917 

26  54  44-62 

183.93 

•439 

.425  5428 

9108 

24  22  54.50 

187.87 

.489 

.470  6014 

8913 

26  57  48.50 

183.84 

0.440 

0.426  4534 

9104 

24  26  02.33 

187.79 

0.400 

0.471  4925 

8909 

27  oo  52.31 

183.76 

.441 

.427  3636 

9101  24  29  10.08 

187.71 

•  49' 

•472  3832 

8905 

27  03  56.02 

183.68 

.442 

.428  2735 

9097  24  32  17.75 

187.64 

.492 

•473  2735 

8901 

27  06  59.66 

183.59 

•443 

.429  1830 

9093  24  35  25.35 

187.56 

•  493 

•474  1633 

8897 

27  10  03.21 

183.51 

.444 

.430  0921 

9089 

24  38  32.87 

187.48 

.494 

.475  0528 

SX<J3 

27  13  06.68 

183.42 

0.445 

0.431  0009 

9085 

24  41  40.31 

187.40 

0.495 

0.475  9419 

8889 

27  16  10.06 

183.34 

.446 

.431  9092 

9082  24  44  47.67 

187.32 

.496 

.476  8305 

8885 

27  19  13.36 

183.26 

•  447 

.432  8172 

9078  24  47  54.96 

187.24 

•  497 

•477  7i88 

8880 

27  22  16.57 

183.17 

.433  7248 

9074  24  51  02.16 

187.17 

.498 

.478  6066 

8876 

27  25  19.70 

183.09 

•449 

.434  6320 

9070 

24  54  09.29 

187.09 

•499 

.479  4941 

8872 

27  28  22.75 

183.00 

0.450 

0.435  5388 

9066 

24  57  16.34 

187.01 

0.500 

0.480  3811 

8868 

27  31  25.71 

182.92 

u 

2Um-'<e«)-* 

usechu 

2  Un-'(eu)-90- 

"techu 

u 

2tan-'(e«)-J 

<*>sechu 

2tan-'(c«)-900 

<•>  sech  u 

SMITHSONIAN  TABLES 


280 


The  Gudermannian. 


u 

gdu 

«Fo' 

gdu 

«F0' 

u 

gd  u 

a.Fo' 

gdu 

«F0' 

o   /   // 

// 

o   /   // 

// 

0.500 

0.480  3811 

8868 

27  31  25.71 

182.92 

0.550 

0.524  1996 

8657 

30  02  03.92 

178.57 

.501 

.481  2677 

8864 

27  34  28.59 

182.83 

•551 

.525  0651 

8653 

30  05  02.45 

178.48 

.502 

.482  1539 

8860 

27  37  31.38 

182.75 

•  552 

.525  9302 

8649 

30  08  00.88 

178.39 

.503 

.483  0397 

8856 

27  40  34.09 

182.67 

•  553 

.526  7948 

8644 

30  10  59.23 

178.30 

.504 

•483  9251 

8852 

27  43  36.71 

182.58 

•  554 

.527  6590 

8640 

30  13  57.48 

178.21 

0.505 

0.484  8100 

8848 

27  46  39.25 

182.50 

0.555 

0.528  5228 

8636 

30  16  55.65 

178.12 

.506 

.485  6946 

8844 

27  49  41.70 

182.41 

•  556 

.529  386i 

8631 

30  19  53.72 

178.03 

.507 

.486  5787 

8839 

27  52  44.07 

182.33 

.557 

.530  2490 

8627 

30  22  51.71 

177.94 

.508 

.487  4625 

8835 

27  55  46.35 

182.24 

.558 

•  531  HIS 

8622 

30  25  49.60 

177.85 

.509 

.488  3458 

8831 

27  58  48.55 

182.15 

•  559 

•531  9735 

8618 

30  28  47.41 

177.76 

0.510 

0.489  2287 

8827 

28  oi  50.66 

182.07 

0.560 

0.532  8351 

8614 

30  31  45-12 

177.67 

.511 

.490  I  I  12 

8823 

28  04  52.69 

181.98 

.561 

.533  6962 

8609 

30  34  42.75 

177.58 

.512 

.490  9933 

8819 

28  07  54.63 

181.90 

.562 

•534  5569 

8605 

30  37  40.28 

177.49 

.513 

.491  8749 

8814 

28  10  56.48 

181.81 

•  563 

•535  4172 

8601 

30  40  37.73 

177.40 

.514 

.492  7562 

8810 

28  13  58.25 

181.73 

.564 

.536  2771 

8596 

30  43  35.08 

177.31 

0.515 

0.493  6370 

8806 

28  16  59-94 

181.64 

0.565 

0.537  1365 

8592 

30  46  32.35 

177.22 

.516 

.494  5174 

8802 

28  20  01.53 

i8i.55 

.566 

.537  9954 

8587 

30  49  29.52 

177.13 

.517 

•495  3974 

8798 

28  23  03.04 

181.47 

.567 

.538  8539 

8583 

30  52  26.60 

177.04 

.518 

.496  2769 

8794 

28  26  04.47 

181.38 

.568 

.539  7120 

8579 

30  55  23.59 

176.95 

.519 

.497  1561 

8789 

28  29  05.81 

181.29 

.569 

.540  5696 

8574 

30  58  20.49 

176.85 

0.520 

0.498  0348 

8785 

28  32  07.06 

181.21 

0.570 

0.541  4268 

8570 

31  oi  17.30 

176.76 

.521 

.498  9131 

8781 

28  35  08.22 

181.12 

•  571 

.542  2836 

8565 

31  04  14.02 

176.67 

.522 

.499  7910 

8777 

28  38  09.30 

181.04 

•  572 

•543  1399 

8561 

31  07  10.65 

176.58 

.523 

.500  6685 

8773 

28  41  10.29 

180.95 

•  573 

.543  9958 

8556 

31  10  07.18 

176.49 

.524 

•501  5456 

8768 

28  44  11.20 

180.86 

•  574 

.544  8512 

8552 

31  13  03.63 

176.40 

0.525 

0.502  4222 

8764 

28  47  12.  oi 

180.77 

0.575 

0.545  7062 

8548 

31  15  59.98 

176.31 

.526 

.503  2984 

8760 

28  50  12.75 

180.69 

.576 

.546  5607 

8543 

31  18  56.24 

176.22 

.527 

.504  1742 

8756 

28  53  13.39 

180.60 

•  577 

.547  4148 

8539 

31  21  52.41 

176.12 

.528 

.505  0495 

8752 

28  56  13-95 

180.51 

.578 

.548  2685 

8534 

31  24  48.49 

176.03 

.529 

•505  9245 

8747 

28  59  14.41 

180.43 

•  579 

.549  1217 

8530 

31  27  44-47 

175.94 

0.530 

0.506  7990 

8743 

29  02  14.80 

180.34 

0.580 

0.549  9744 

8525 

31  30  40.37 

175.85 

.531 

.507  6731 

8739 

29  05  15.09 

180.25 

.581 

.550  8267 

8521 

31  33  36.17 

175.76 

.532 

.508  5468 

8735 

29  08  15.30 

180.16 

.582 

.551  6786 

8516 

31  36  31.88 

175-66 

•  533 

.509  4200 

8730 

29  ii  15.42 

180.07 

.583 

•552  5300 

8512 

31  39  27.50 

175.57 

-534 

.510  2928 

8726 

29  14  15.45 

179.99 

.584 

•553  3810 

8508 

31  42  23.03 

175.48 

0.535 

0.511  1652 

8722 

29  17  15.39 

179.90 

0.585 

0.554  2315 

8503 

3'i  45  18.46 

175.39 

.536 

.512  0372 

8717 

29  20  15.24 

179.81 

.586 

-555  0816 

8499 

31  48  13.80 

175.30 

•  537 

.512  9087 

8713 

29  23  15.01 

179.72 

.587 

•555  9313 

8494 

31  51  09.05 

175.20 

.538 

.513  7798 

8709 

29  26  14.69 

179.63 

.588 

.556  7804 

8490 

31  54  04.21 

I75.II 

•539 

.514  6505 

8705 

29  29  14.28 

179.55 

.589 

•557  6292 

8485 

31  56  59.27 

175.02 

0.540 

0.515  5207 

8700 

29  32  13-78 

179.46 

0.590 

0.558  4775 

8481 

31  59  54.25 

174.93 

•  541 

.516  3905 

8696 

29  35  13-20 

179.37 

•  591 

•559  3253 

8476 

32  02  49.  13 

174.83 

•  542 

.517  2599 

8692 

29  38  12.52 

179.28 

.592 

.560  1727 

8472 

32  05  43.91 

174.74 

.543 

.518  1289 

8687 

29  41  11.76 

179.19 

•  593 

.561  0196 

8467 

32  08  38.61 

174.65 

•  544 

•5i8  9974 

8683 

29  44  10.91 

179.  10 

.594 

.561  8661 

8463 

32  ii  33.21 

174-55 

o>-545 

0.519  8655 

8679 

29  47  09.96 

179.01 

0.595 

0.562.7122 

8458 

32  14  27.71 

174.46 

.546 

.520  7332 

8675 

29  50  08.93 

178.93 

.596 

063  5577 

8454 

32  17  22.13 

174.37 

.547 

.521  6004 

8670 

29  53  07.81 

178.84 

•  597 

.564  4029 

8449 

32  20  16.45 

174.27 

.548 

.522  4673 

8666 

29  56  06.  61 

178.75 

.598 

.565  2476 

8445 

32  23  10.68 

174-18 

•  549 

.523  3336 

8662 

29  59  05.31 

178.66 

•  599 

.566  0918 

8440 

32  26  04.81 

174.09 

0.550 

0.524  1996 

8657 

30  02  03.92 

178.57 

0.6oo 

0.566  9356 

8436 

32  28  58.85 

173.99 

u 

2tan-Ke«)~ 

<«>  sech  u 

2tan-1(e«)-90° 

w  sech  u 

u 

2  tan-He")-^ 

wsechu 

Ztan-Keuh-SO0 

u>  sech  u 

MITHSONIAN   TABLES 


28l 


The  Gudermannian. 


u 

gd  u 

«F0' 

gd  u 

«F0' 

u 

gdu 

O.FO' 

gdu 

«Fo' 

0          /            // 

M 

0.600 

0.566  9356 

8436 

32  28  58.85 

173.99 

0.650 

0.6o8  5398 

8205 

34  52  00.34 

169.24 

.601 

.567  7789 

8431 

32  31  52.80 

173.90 

.651 

.609  3600 

8200 

34  54  49.52 

169.14 

.002 

.568  6218 

8426 

32  34  46.66 

I73.8I 

.652 

.610  1708 

8195 

34  57  38.62 

169.04 

.003 

.569  4642 

8422 

32  37  40.42 

173.71 

.653 

.610  9991 

8191 

35  oo  27.61 

168.95 

.004 

•570  3061 

8417 

32  40  34.09 

173.62 

.654 

.6ll  8179 

8186 

35  03  16.51 

168.85 

0.605 

0.571   1476 

8413 

32  43  27.66 

173.53 

0.655 

0.612  6363 

8181 

35  06  05.31 

168.75 

.606 

.571  9887 

8408 

32  46  21.14 

173-43 

.656 

.613  4542 

8i77 

35  08  54-01 

168.66 

.607 

.572  8293 

8404 

32  49  14.52 

173.34 

.657 

.614  2716 

8172 

35  u  42.62 

168.56 

.608 

•573  6694 

8399 

32  52  07.82 

173.24 

.658 

.615  0886 

8167 

35  14  3LI3 

168.46 

.609 

•574  5091 

8395 

32  55  01.01 

173.15 

.659 

.615  9051 

8163 

35  17  19-54 

168.36 

0.610 

0.575  3484 

8390 

32  57  54.12 

173.06 

0.660 

0.616  7211 

8158 

35  20  07.86 

168.27 

.611 

.576  1871 

8385 

33  oo  47.13 

172.96 

.661 

.617  5366 

8i53 

35  22  56.08 

168.17 

.612 

•577  0255 

8381 

33  03  40.04 

172.87 

.662 

.618  3517 

8148 

35  25  44.20 

168.07 

.613 

.577  8633 

8376 

33  06  32.86 

172.77 

.663 

.619  1663 

8144 

35  28  32.22 

167.97 

.614 

.578  7007 

8372 

33  09  25.59 

172.68 

.664 

.619  9804 

8i39 

35  31  20.14 

167.88 

0.615 

0.579  5377 

8367 

33  12  18.22 

172.59 

0.665 

0.620  7041 

8134 

35  34  07.97 

167.78 

.616 

.580  3741 

8363 

33  15  10.76 

172.49 

.666 

.621  6073 

8129 

35  36  55.70 

167.68 

.617 

.581    2IO2 

8358 

33  18  03.20 

172.40 

.667 

.622  4200 

8125 

35  39  43-34 

167.58 

.618 

.582  0457 

8353 

33  20  55.55 

172.30 

.668 

.623  2322 

8120 

35  42  30.87 

167.49 

.619 

.582  8809 

8349 

33  23  47.81 

172.21 

.669 

.624  0440 

8115 

35  45  18.31 

167.39 

0.620 

0.583  7155 

8344 

33  26  39.97 

172.11 

0.670 

0.624  8553 

8110 

35  48  05.65 

167.29 

.621 

.584  5497 

8340 

33  29  32.03 

172.02 

.671 

.625  6661 

8106 

35  50  52.89 

167.19 

.622 

085  3834 

8335 

33  32  24.00 

171.92 

.672 

.626  4764 

8101 

35  53  40.03 

167.09 

.623 

.586  2167 

8330 

33  35  J5-87 

171.83 

.673 

.627  2863 

8096 

35  56  27.08 

167.00 

.624 

087  0495 

8326 

33  38  07.65 

I7L73 

.674 

.628  0956 

8091 

35  59  14.03 

166.90 

0.625 

0.587  8819 

8321 

33  40  59-34 

171.64 

0.675 

0.628  9046 

8087 

36  02  00.88 

166.83 

.626 

.588  7137 

8317 

33  43  50.93 

I7L54 

.676 

.629  7130 

8082 

36  04  47.63 

166.70 

.627 

089  5452 

8312 

33  46  42.42 

I7L45 

.677 

.630  5209 

8077 

36  07  34.28 

166.60 

.628 

.500  3761 

8307 

33  49  33-82 

I7L35 

.678 

.631  3284 

8072 

36  10  20.84 

166.51 

.629 

.591  2066 

8303 

33  52  25.12 

171.26 

.679 

•632  1354 

8068 

36  13  07.29 

166.41 

0.630 

0.592  0367 

8298 

33  55  16.33 

171.16 

0.680 

0.632  9420 

8063 

36  15  53.65 

166.31 

.631 

.592  8662 

8293 

33  58  07.44 

171.06 

.681 

.633  748o 

8058 

36  18  39.91 

166.21 

.632 

•593  6954 

8289 

34  oo  58.46 

170.97 

.682 

.634  5536 

8053 

36  21   26.07 

166.11 

.633 

.594  5240 

8284 

34  03  49.38 

170.87 

.683 

.635  3587 

8049 

36  24   12.14 

166.01 

•634 

•595  3522 

8280 

34  06  40.20 

170.78 

.684 

.636  1633 

8044 

36  26  58.10 

165.92 

0.635 

0.596  1799 

8275 

34  09  30.93 

170.68 

0.685 

0.636  9675 

8039 

36  29  43-97 

165.82 

.636 

•597  0072 

8270 

34  12  21.56 

170.59 

.686 

•637  77ii 

8034 

36  32  29.74 

165.72 

.637 

•597  8339 

8266 

34  15  12.10 

170.49 

.687 

•638  5743 

8029 

36  35  I5.4I 

165.62 

.638 

.5986603 

8261 

34  18  02.54 

170.39 

.688 

•639  3770 

8025 

36  38  00.98 

165.52 

•639 

.599  486i 

8256 

34  20  52.89 

170.30 

.689 

.640  1792 

8020 

36  40  46.45 

165.42 

0.640 

0.600  3115 

8252 

34  23  43.14 

I/0.2O 

0.600 

0.640  9810 

8015 

36  43  31.82 

165.32 

.641 

.601   1364 

8247 

34  26  33.29 

I/O.  II 

.691 

.641  7823 

8010 

36  46  17-09 

165.22 

.642 

.601  9609 

8242 

34  29  23.35 

170.01 

.692 

.642  5830 

8006 

36  49  02.27 

165.13 

.643 

.602  7849 

8238 

34  32  13.31 

169.91 

.693 

.643  3834 

8001 

36  51  47.34 

165.03 

.644 

.603  6084 

8233 

34  35  03.17 

169.82 

.694 

.644  1832 

7996 

36  54  3-'-  32 

164.93 

0.645 

0.604  4315 

8228 

34  37  52.04 

169.72 

0.695 

0.644  9825 

799i 

36  57  17-20 

164.83 

.646 

.605  2541 

8224 

34  40  42.61 

169.62 

.696 

.645  7814 

7986 

37  oo  01.98 

164.73 

.647 

.606  0762 

8219 

34  43  32.19 

169.53 

.697 

.646  5798 

798i 

37  02  46.66 

164.63 

.648 

.606  8979 

8214 

34  46  21.67 

169.43 

.698 

•647  3777 

7977 

37  05  31.  -'4 

164.53 

.649 

.607  7190 

8210 

34  49  H.05 

169.33 

.699 

.648  1751 

7972 

37  08  15-7-' 

164.43 

0.650 

0.608  5398 

8205 

34  52  00.34 

169.24 

0.700 

0.648  9721 

7967 

37  u  00.10 

164.33 

u 

2ton-'(e»)~ 

<•»  sech  u 

Ztan-Keuh-SO0 

M  sech  u 

u 

2  ton-He")-  g 

«-sechu 

2tan-'(e»)-9ff> 

«•'  sech  u 

SMITHSONIAN  TABLES 


282 


The  Gudermannian. 


I 

gd  u 

«F0' 

gdu 

<«>Fu' 

u 

gdu 

"Fo' 

gd  u 

«F0' 

0    /    // 

/7 

o   y   // 

// 

0.700 

0.648  9721 

7967 

37  ii  00.10 

164.33 

0.750 

0.688  2014 

7724 

39  25  51.72 

159.32 

.701 

.649  7685 

7962 

37  13  44.38 

164.23 

•751 

.688  9735 

7719 

39  28  30.98 

159.22 

.702 

.650  5645 

7957 

37  16  28.57 

164.13 

•  752 

.689  7451 

7714 

39  31  10.15 

159.11 

.703 

.651  3600 

7953 

37  19  12.65 

164.03 

.753 

.690  5163 

7709 

39  33  49-21 

159.01 

.704 

.652  1550 

7948 

37  21  56.63 

163.93 

•  754 

.691  2870 

7704 

39  36  28.18 

158.91 

0.705 

0.652  9496 

7943 

37  24  40.52 

163.84 

0.755 

0.692  0572 

7699 

39  39  07.04 

158.81 

.706 

.653  7436 

7938 

37  27  24.31 

163.74 

.756 

.692  8269 

7694 

39  41  45.80 

158.71 

.707 

.654  5372 

7933 

37  30  07-99 

163.64 

•  757 

•693  596i 

7690 

39  44  24.46 

158.61 

.708 

.655  3303 

7928 

37  32  51.58 

163.54 

.758 

.694  3648 

7685 

39  47  03.01 

158.51 

.709 

.656  1229 

7924 

37  35  35.o6 

163.44 

•  759 

.695  1330 

7680 

39  49  41.47 

158.40 

0.710 

0.656  9150 

7919 

37  38  18.45 

163.34 

0.760 

0.695  9007 

7675 

39  52  19-82 

158.30 

.711 

.657  7067 

79U 

37  41  01.74 

163.24 

.761 

.6966679 

7670 

39  54  58.07 

158.20 

.712 

.658  4978 

7909 

37  43  44.92 

163  .  14 

.762 

.697  4347 

7665 

39  57  36.23 

158.10 

.713 

.659  2885 

7904 

37  46  28.01 

163.04 

.763 

.698  2009 

7660 

40  oo  14.28 

158.00 

.714 

.660  0787 

7899 

37  49  11.00 

162.94 

.764 

.6989667 

7655 

40  02  52.22 

157.90 

0.715 

0.660  8684 

7895 

37  51  53.89 

162.84 

0.765 

0.699  7319 

7650 

40  05  30.07 

157.80 

.716 

.661  6576 

7890 

37  54  36.68 

162.74 

.766 

.700  4967 

7645 

40  08  07.81 

157.69 

.717 

.662  4463 

7885 

37  57  19.36 

162.64 

.767 

.701  2610 

7640 

40  10  45.46 

157.59 

.718 

.663  2346 

7880 

38  oo  01.95 

162.54 

.768 

.702  0248 

7635 

40  13  23.00 

157.49 

.719 

.664  0223 

7875 

38  02  44.44 

162.44 

.769 

.702  7880 

7630 

40  16  00.44 

157.39 

0.720 

0.664  8096 

7870 

38  05  26.83 

162.34 

0.770 

0.703  5508 

7625 

40  18  37.78 

157.29 

.721 

.665  5964 

7865 

38  08  09.11 

162.24 

.771 

.704  3131 

7620  40  21  15.01 

157.19 

.722 

.666  3827 

7861 

38  10  51.30 

162.14 

•  772 

•70S  0750 

76l6 

40  23  52.15 

157.08 

.723 

.667  1685 

7856 

38  13  33-39 

162.04 

•  773 

.705  8363 

76ll 

40  26  29.18 

156.08 

.724 

•667  9539 

7851 

38  16  15.37 

I6I.94 

•  774 

.706  5971 

7606 

40  29  06.  i  i 

156.88 

0.725 

0.668  7387 

7846 

38  18  57.26 

161.84 

0.775 

0.707  3574 

76OI 

40  31  42.94 

156.78 

.726 

.669  5231 

7841 

38  21  39.05 

161.74 

.776 

.708  1173 

7596 

40  34  19.67 

156.68 

.727 

.670  3069 

7836 

38  24  20.73 

161.64 

.777 

.708  8766 

7591 

40  36  56.29 

156.57 

.728 

.671  0903 

7831 

38  27  02.32 

I6I.54 

.778 

.709  6354 

7586 

40  39  32.82 

156.47 

.729 

.671  8732 

7827 

38  29  43.80 

I6I.43 

.779 

.710  3938 

7581 

40  42  09.24 

156.37 

0.730 

0.672  6556 

7822 

38  32  25.19 

161.33 

0.780 

0.711  1516 

7576 

40  44  45.56 

156.27 

.731 

.673  4376 

78i7 

38  35  06.47 

l6l.23 

.781 

.711  9090 

7571 

40  47  21.77 

156.17 

.732 

.674  2190 

7812 

38  37  47.65 

l6l.I3 

.782 

.712  6659 

7566 

40  49  57.89 

156.06 

•  733 

.675  oooo 

7807 

38  40  28.74 

161.03 

.783 

.713  4223 

756i 

40  52  33-90 

155-96 

•  734 

.675  7804 

7802 

38  43  09.72 

160.93 

.784 

.714  1781 

7556 

40  55  09.81 

155.86 

0.735 

0.676  5604 

7797 

38  45  50.60 

160.83 

0.785 

0.714  9335 

7551 

40  57  45.62 

155.76 

.736 

.677  3399 

7792 

38  48  31.38 

160.73 

.786 

.715  6884 

7546 

41  oo  21.33 

155-66 

.737 

.678  1189 

7788 

38  51  12.06 

160.63 

.787 

.716  4428 

7541 

41  02  56.94 

155-55 

.738 

.678  8974 

7783 

38  53  52.64 

160.53 

.788 

.717  1967 

7537 

41  05  32.44 

155.45 

•  739 

.679  6754 

7778 

38  56  33-12 

100.43 

.789 

.717  9501 

7532 

41  08  07.84 

155.35 

0.740 

0.680  4530 

7773 

38  59  13.50 

160.33 

0.790 

0.718  7030 

7527 

41  10  43.14 

155.25 

.741 

.681  2300 

7768 

39  oi  53.77 

160.23 

•  791 

.719  4554 

7522 

4i  13  18.33 

155.15 

.742 

.682  0065 

7763 

39  04  33-95 

160.13 

•  792 

.720  2073 

7517 

41  15  53-43 

155.04 

•  743 

.682  7826 

7758 

39  07  14-02 

l6o.O2 

•  793 

.720  9588 

7512 

41  18  28.42 

154.94 

•  744 

.683  5582 

7753 

39  09  54.00 

159.92 

.794 

.721  7097 

7507 

41  21  03.31 

154.84 

0.745 

0.684  3333 

7748 

39  12  33.87 

159.82 

0.795 

0.722  4601 

7502 

41  23  38.10 

154.74 

.746 

.685  1079 

7744 

39  15  13.64 

159.72 

.796 

.723  2101 

7497 

41  26  12.78 

154.63 

.747 

.685  8820 

7739 

39  17  53.31 

159.62 

.797 

.723  9595 

7492 

41  28  47.36 

154.53 

.748 

.686  6556 

7734 

39  20  32.88 

159.52 

.798 

.724  7084 

7487 

41  31  21.84 

154.43 

•  749 

.687  4287 

7729 

39  23  12.35 

159.42 

•  799 

.725  4569 

7482 

41  33  56.22 

154.33 

0.750 

0.688  2014 

7724 

39  25  51.72 

159.32 

0.800 

0.726  2048 

7477 

41  36  30.50 

154-22 

u 

2tan-Ke«)-| 

cosechu 

Zten-W-go0 

wsechu 

u 

2tan-'(eu)~ 

wsechu 

Ztan-Keuh-SO0 

w  sech  u 

SMITHSONIAN  TABLES 


283 


The  Gudermannian. 


u 

gdu 

-FO' 

gd  u 

.* 

u 

gdu 

«FO' 

gdu 

»F0' 

0          /            // 

m 

o       /        // 

M 

0.800 

0.726  2048 

7477 

41  36  30.50 

154-22 

0.850 

0.762  9677 

7228 

43  42  53.38 

149.09 

.801 

.726  9523 

7472 

41  39  04.67 

154.12 

.851 

.763  6902 

7223 

43  45  22.41 

148.98 

.802 

.727  6992 

7467 

41  41  38.74 

154.02 

.852 

.764  4122 

7218 

43  47  51-34 

148.88 

.803 

.728  4457 

7462 

41  44  12.71 

153.92 

.853 

.765  1338 

7213 

43  50  20.17 

148.78 

.804 

.729  1916 

7457 

41  46  46.57 

153.81 

.854 

.765  8548 

7208 

43  52  48.89 

148.67 

0.805 

0.729  9371 

7452 

41  49  20.34 

153.71 

0.855 

0.766  5754 

7203 

43  55  17.52 

148.57 

.806 

.730  6821 

7447 

41  51  54-00 

I53.6I 

.856 

•767  2954 

7198 

43  57  46.04 

148.47 

.807 

.731  4266 

7442 

41  54  27.56 

153.51 

.857 

.768  0149 

7193 

44  oo  14.45 

148.36 

.808 

•732  1705 

7437 

41  57  01.01 

153.40 

.858 

.768  7340 

7188 

44  02  42.76 

148.26 

.809 

.732  9140 

7432 

41  59  34.36 

153.30 

.859 

.769  4525 

7183 

44  05  10.97 

148.16 

0.810 

0.733  6570 

7427 

42  02  07.62 

153.20 

0.860 

0.770  1706 

7178 

44  07  39.o8 

148.06 

.811 

.734  3995 

7422 

42  04  40.76 

I53-IO 

.861 

.770  8881 

7173 

44  10  07.08 

147.95 

.812 

.735  UU 

7417 

42  07  13.81 

152.99 

.862 

.771  6051        7168 

44  12  34.98 

147.85 

.813 

.735  8829 

7412 

42  09  46.75 

152.89 

.863 

.772  3217       7163 

44  15  02.78 

147-75 

.814 

.736  6239 

7407 

42    12    19.59 

152.79 

.864 

.773  0377 

7158 

44  17  30.48 

147-64 

0.815 

0.737  3644 

7402 

42  14  52.33 

152.69 

0.865 

0.773  7533 

7153 

44  19  58.07 

147-54 

.816 

.738  1044 

7397 

42  17  24.96 

152.58 

.866 

.774  4683 

7148 

44  22  25.56 

147-44 

.817 

.738  8439 

7392 

42  19  57.50 

152.48 

.867 

•775  1829 

7143 

44  24  52.94 

147-33 

.818 

.739  5829 

7387 

42  22   29-93 

152.38 

.868 

•775  8969 

7138 

44  27  20.22 

147.23 

.819 

.740  3214 

7383 

42   25  O2.25 

152.28 

.869 

.776  6104 

7133 

44  29  47.40 

147.13 

0.820 

0.741  0594 

7378 

42   27  34.48 

152..  17 

0.870 

0.777  3235 

7128 

44  32  14-48 

147-02 

.821 

.741  7969 

7373 

42   30  O6.6O 

152.07 

.871 

.778  0360 

7123 

44  34  41.45 

146.92 

.822 

.742  5339 

7368 

42   32   38.62 

151.97 

.872 

.778  7481 

7118 

44  37  08.32 

146.82 

.823 

.743  2704 

7363 

42  35  10.53 

151.86 

.873 

•779  4596 

7113 

44  39  35.09 

146.71 

.824 

.744  0064 

7358 

42  37  42.34 

151.76 

.874 

.780  1707 

7108 

44  42  01.75 

146.61 

0.825 

0.744  7420 

7353 

42  40  14.05 

151.66 

0.875 

0.780  8812 

7103 

44  44  28.31 

146.51 

.826 

•745  4770 

7348 

42  42  45.66 

I5L56 

.876 

.781  5912 

7098 

44  46  54-77 

146.41 

.827 

.746  2115 

7343 

42  45  17.17 

I5L45 

.877 

.782  3008 

7093 

44  49  21.12 

146.30 

.828 

.746  9455 

7338 

42  47  48.57 

I5L35 

.878 

.783  0008 

7088 

44  51  47.37 

146.20 

.829 

.747  6790 

7333 

42  50  19.87 

I5L25 

.879 

.783  7184 

7083 

44  54  13.52 

146.  10 

0.830 

0.748  4120 

7328 

42  52  51.06 

I5LI4 

0.880 

0.784  4264 

7078 

44  56  39.56 

145.99 

.831 

.749  1446 

7323 

42  55  22.16 

151.04 

.881 

.785  1340 

7073 

44  59  05.50 

145.89 

.832 

•749  8766 

73i8 

42  57  53-15 

150.94 

.882 

.785  8410 

7068 

45  oi  31.34 

145.79 

.833 

.750  6081 

7313 

43  oo  24.04 

150.84 

.883 

.786  5476 

7063 

45  03  57.o8 

145.68 

.834 

.751  3391 

7308 

43  02  54.82 

150.73 

.884 

.787  2536 

7058 

45  06  22.71 

145.58 

0.835 

0.752  0697 

7303 

43  05  25.50 

150.63 

0.885 

0.787  9591 

7053 

45  08  48.24 

145.48 

.836 

•752  7997 

7298 

43  07  56.08 

150.53 

.886 

.788  6642 

7048 

45  u   13-66 

145.37 

.837 

.753  5292 

7293 

43  10  26.56 

150.42 

.887 

.789  3687 

7043 

45  13  38.59 

145.27 

.838 

•754  2582 

7288 

43  12  56.93 

150.32 

.888 

.790  0728 

7038 

45  16  04.21 

145.17 

1  .839 

.7549868 

7283 

43  15  27.20 

150.22 

.889 

.790  7763 

7033 

45  18  29.32 

145.06 

0.840 

0.755  7148 

7278 

43  17  57.37 

150.12 

0.890 

0.791  4794 

7028 

45  20  54-34 

144.96 

.841 

.756  4423 

43  20  27.43 

150.01 

.891 

.792  1819 

7023 

45  23  19.25 

144.86 

.842 

•757  1694 

7268 

43  22  57.39 

149.91 

.892 

.792  8839 

7018 

45  25  44.05 

144.76 

.843 

.757  8959 

7263 

43  25  27.25 

149.81 

.893 

.793  5855 

7013 

45  28  08.76 

144.65 

.844 

.758  6219 

7258 

43  27  57.01 

149.70 

.894 

.794  2865 

7008 

45  30  33.36 

144.55 

0.845 
.846 

0.759  3475 
.760  0725 

7248 

43  30  26.66 
43  32  56.21 

149.60 
149.50 

0.895 
.896 

0.794  9871 
.795  6871 

7003 
6998 

45  32  57.85 
45  35  22.25 

144.45 

144.34 

.847 
.848 

.760  7970 
.761  5211 

7238 

43  35  25.65 
43  37  55.00 

149.39 
149.29 

.796  3867 
.797  0857 

6993 
6988 

45  37  46.54 
45  40  10.73 

144.24 
144.14 

.849 

.762  2446 

7233 

43  40  24.24 

149.19 

.899 

•797  7843 

6983 

45  42  34.81 

144.03 

0.850 

0.762  9677 

7228 

43  42  53.38 

149.09 

0.900 

0.798  4823 

6978 

45  44  58.80 

143.93 

- 

2  tan-He")  -j 

wsechu 

2tan-'(e«)-902 

<•>  sech  u 

u 

2*"-'<">-i 

wsechu 

2  tan-He"  )-90° 

<»  sech  u 

SMITHSONIAN  TABLES 


284 


The  Gude  rmannian. 


• 

gd  u 

»F0' 

gdu 

«oF0' 

u 

gdu 

->FO' 

gdu 

«Fo' 

0.900 

0.798  4823 

6978 

o   /   // 

45  44  58.8o 

143-93 

* 

0.950 

0.832  7479 

6728 

47  42  46.58 

I  38*78 

.901 

•799  1798 

0973 

45  47  22.67 

143.83 

.951 

.833  4205 

6723 

47  45  05.31 

138.  68 

.902 

•799  8769 

6968 

45  49  46.45 

143.72 

.952 

.834  0926 

6719 

47  47  23.94 

138.58 

.903 

.800  5734 

6963 

45  52  10.12 

143.62 

.953 

.834  7642 

6714 

47  49  42.47 

138.48 

.904 

.801  2695 

6958 

45  54  33.69 

143.52 

.954 

.835  4353 

6709 

47  52  00.89 

138.37 

0.905 

0.801  9650 

6953 

45  56  57.16 

143.42 

0.955 

0.836  1059 

6704 

47  54  19.22 

138.27 

.906 

.802  6601 

6948 

45  59  20.52 

143.31 

.956 

.836  7700 

6699 

47  56  37.44 

138.17 

.907 

•803  3546 

6943 

46  01  43.78 

143.21 

•957 

.837  4456 

6694 

47  58  55-55 

138.07 

.908 

.804  0487 

6938 

46  04  06.94 

143  .  I  I 

.958 

.838  1147 

6689 

48  01  13.57 

137.96 

.909 

.804  7422 

6933 

46  06  30.00 

143-00 

•959 

.838  7833 

6684 

48  03  31.48 

137.86 

0.910 

0.805  4353 

6928 

46  08  52.95 

142.90 

0.960 

0.839  4514 

6679 

48  05  49.29 

137.76 

.911 

.806  1278 

6923 

46  ii  15.79 

142.80 

.961 

.840  1191 

6674 

48  08  07.00 

137.66 

.912 

.806  8198 

6918 

46  13  38.54 

142.69 

.962 

.840  7862 

6669 

48  10  24.60 

U7.55 

.913 

.807  5H4 

6913 

46  16  01.18 

142.59 

.963 

.841  4528 

6664 

48  12  42.IO 

137.45 

.914 

.808  2024 

6908 

46  18  23.72 

142.49 

.964 

.842  1190 

6659 

48  14  59-50 

137.35 

0.915 

0.808  8930 

6903 

46  20  46.16 

142.38 

0.965 

0.842  7846 

6654 

48  17  16.80 

137.25 

.916 

•809  5830 

6898 

46  23  08.49 

142.28 

.966 

.843  4497 

6649 

48  19  33-99 

137.14 

.917 

.810  2726 

6893 

46  25  30.72 

142.18 

.967 

.844  1144 

6644 

48  21  51.09 

137.04 

.918 

.810  9616 

6888 

46  27  52.85 

142.08 

.968 

.844  7785 

6639 

48  24  08.08 

136.04 

.919 

.811  6502 

6883 

46  30  14.87 

141.97 

.969 

.845  4422 

6634 

48  26  24.96 

136.84 

0.920 

0.812  3383 

6878 

46  32  36.79 

141.87 

0.970 

0.846  1053 

6629 

48  28  41.75 

136.73 

.921 

.813  0258 

6873 

46  34  58.6i 

141.77 

.971 

.846  7680 

6624 

48  30  58.43 

136.63 

.922 

.813  7129 

6868 

46  37  20.33 

141.66 

.972 

.847  4301 

6619 

48  33  I5.oi 

136.53 

.923 

.814  3994 

6863 

46  39  41.94 

141.56 

•973 

.848  0918 

6614 

48  35  3L49 

136.43 

.924 

.815  0855 

6858 

46  42  03.45 

141.46 

•974 

.848  7530 

6609 

48  37  47.87 

136.32 

0.925 

0.815  7710 

•6853 

46  44  24.85 

I4L35 

0.975 

0.849  4136 

6604 

48  40  04.14 

136.22 

.926 

.816  4561 

6848 

46  46  46.16 

141.25 

.976 

.850  0738 

6599 

48  42  20.31 

136.12 

.927 

.817  1406 

6843 

46  49  07.36 

I4LI5 

•  977 

.850  7335 

6594 

48  44  36.38 

136.02 

.928 

.817  8247 

6838 

46  51  28.45 

141-05 

.978 

.851  3927 

6589 

48  46  52.34 

135.92 

.929 

.818  5083 

6833 

46  53  49-45 

140.94 

•979 

.852  0514 

6584 

48  49  08.21 

I35.8I 

0.930 

0.819  1913 

6828 

46  56  10.34 

140.84 

0.980 

0.852  7096 

6579 

48  51  23.97 

135.71 

.931 

.819  8739 

6823 

46  58  31.13 

140.74 

.981 

.853  3673 

6574 

48  53  39.63 

I35.6I 

.932 

.820  5560 

6818 

47  oo  51.81 

140.63 

.982 

.854  0245 

6570 

48  55  55.19 

135.51 

•933 

.821  2375 

6813 

47  03  12.40 

140.53 

.983 

.854  6812 

6565 

48  58  10.64 

135.40 

•934 

.821  9186 

6808 

47  05  32.88 

140.43 

.984 

.855  3374 

6560 

49  oo  26.00 

135.30 

0.935 

0.822  5092 

6803 

47  07  53.25 

140.33 

0.985 

0.855  9931 

6555 

49  02  41.25 

135.20 

.936 

.823  2792 

6798 

47  10  13.53 

140.22 

.986 

.856  6483 

6550 

49  04  56.40 

135.10 

•  937 

.823  9588 

6793 

47  12  33.70 

140.  12 

.987 

.857  3030 

£545 

49  07  11.44 

135-00 

.938 

.824  6379 

6788 

47  14  53.77 

I4O.O2 

.988 

.857  9573 

6540 

49  09  26.39 

134.89 

•  939 

.825  3164 

6783 

47  17  13-74 

139.91 

.989 

.858  6110 

6535 

49  II  41.23 

134.79 

0.040 

0.825  9945 

6778 

47  19  33.6o 

I39.8I 

0.990 

0.859  2642 

6530 

49  13  55-97 

134.69 

.941 

.826  6721 

6773 

47  21  53.36 

139.71 

.991 

.859  9170 

6525 

49  16  10.  61 

134.59 

.942 

.827  3492 

6768 

47  24  13-02 

I39.6I 

.992 

.860  5692 

6520 

49  1825.15 

134.49 

•943 

.828  0257 

6763 

47  26  32.57 

139.50 

.993 

.86l  22IO 

6515 

49  20  39.58 

134.38 

.944 

.828  7018 

6758 

47  28  52.02 

139.40 

.994 

.851  8723 

6510 

49  22  53.92 

134-28 

0.945 

0.829  3774 

6753 

47  31  n.37 

139.30 

0.995 

0.862  5230 

6505 

49  25  08.  15 

I34.I8 

.946 

.830  0525 

6748 

47  33  30.62 

139.20 

.996 

.863  1733 

6500 

49  27  22.28 

135.08 

•947 

.830  7271 

6743 

47  35  49.76 

139.09 

•  997 

.863  8231 

6495 

49  29  36.30 

133.98 

.948 

.831  4012 

6738 

47  38  08.80 

138.99 

.998 

.864  4724 

6490 

49  31  50.23 

133.87 

.949 

.832  0748 

6733 

47  40  27.74 

138.89 

.999 

.865  I  i  12 

6485 

49  34  04.05 

133.77 

0.950 

0.832  7479 

6728 

47  42  46.58 

138.78 

I.OOO 

0.865  7695 

6481 

49  36  17.77 

133.67 

u 

2  tan-He*)™ 

<«>  sech  u 

2lan-»(e«)-900 

<»  sech  u 

u 

2tan-Ke«)-£ 

<»  sech  u 

Ztan-Ke^-SO0 

co  sech  u 

SMITHSONIAN  TABLES 


285 


The  Gudermannian. 


u 

gdu 

«FO' 

gdu 

«F0' 

u 

gdu 

<oF0' 

gdu 

«F0' 

1.  000 

0.865  7695 

6481 

49<V  17-77 

133*67 

1.050 

0.897  5576 

6235 

ox// 

51  25  34.55 

i28?6i 

.001 

.866  4173 

6476 

49  38  31-39 

133.57 

.051 

.808  1809 

6230 

51  27  43.11 

128.51 

.002 

.867  0646 

6471 

49  40  44.91 

133.47 

.052 

.8988037 

6225 

51  29  51.57 

128.41 

.003 

.867  7H4       6466 

49  42  58.33 

133.37 

•  053 

.899  4260 

6221 

51  31  59.92 

128.31 

.004 

.858  35/8 

6461 

49  45  11.64 

133.26 

•  054 

.900  0478 

6216 

51  34  08.  18 

128.21 

1.005 

0.869  0036 

6456 

49  47  24.86 

I33.I6 

1.055 

0.900  6691 

6211 

51  36  16.34 

128.11 

.006 

.879  6489 

6451 

49  49  37.97 

133.06 

.056 

.901  2900 

6206 

51  38  24.40 

128.01 

.007 

.870  2938 

6446 

49  5i  50.98 

132.06 

.057 

.901  9103 

62OI 

51  40  32.36 

127.91 

.008 

.870  9381 

6441 

49  54  03.89 

132.86 

.058 

.802  5302 

6196 

51  42  40.21 

127.81 

.009 

.871  5820 

6436 

49  56  16.69 

132.76 

.059 

.903  1496 

6191 

51  44  47-97 

127.71 

I.OIO 

0.872  2254 

6431 

49  58  29.40 

132.65 

i.  060 

0.903  7685 

6187 

51  46  55.63 

127.61 

.Oil 

.872  8682 

6426 

50  oo  42.00 

132.55 

.061 

.904  3869 

6l82 

51  49  03.18 

127.51 

.012 

.873  5io6 

6421 

50  02  54.50 

132.45 

.052 

.905  0048 

6177 

51  51  10.64 

127.41 

.013 

.874  1525 

6416 

50  05  06.90 

132.35 

.063 

.905  6222 

6172 

51  53  18.00 

127.31 

.014 

•874  7939 

6412 

50  07  19.20 

I32.25 

.064 

.906  2392 

6167 

51  55  25.25 

127.21 

1.015 

0.875  4348 

6407 

50  09  31.40 

132.15 

1.065 

0.906  8557 

6162 

51  57  32.41 

127.11 

.016 

.876  0752  i      6402 

50  ii  43.49 

132.04 

.066 

•907  47i6 

6157 

51  59  39.46 

127.01 

.017 

.876  7152  1     6397 

50  13  55-49 

I3L94 

.o57 

.908  0871 

6153 

52  oi  46.42 

126.91 

.018 

.877  3546 

6392 

50  16  07.38 

131.84 

.o58 

.908  7022 

6148 

52  03  53-27 

126.81 

.019 

.877  9936 

6387 

50  18  19.17 

131.74 

.069 

.909  3167 

6143 

52  06  00.03 

126.71 

I.O2O 

0.878  6320 

6382 

50  20  30.86 

131.64 

1.070 

0.909  9307 

6138 

52  08  06.68 

126.61 

.021 

.879  2700 

6377 

50   22   42.45 

I3L54 

.071 

.910  5443 

6133 

52  10  13.24 

126.51 

.022 

.879  9074 

6372 

•50  24  53-94 

131.44 

.072 

.911  1574 

6128 

52    12    19.70 

126.41 

.023 

.880  5444 

6367 

50  27  05.32 

I3L34 

.073 

.911  7699 

6123 

52    14  26.05 

126.31 

.024 

.881  1809 

6362 

50  29  16.61 

I3L23 

.074 

.912  3821 

6118 

52  16  32.31 

126.21 

1.025 

0.881  8169 

6357 

50  31  27.79 

I3LI3 

1.075 

0.912  9937 

6114 

52  18  38.46 

126.11 

.026 

.882  4524 

6353 

50  33  38.87 

I3L03 

.076 

.913  6048 

6109 

52  20  44-52 

126.01 

.027 

.883  0874 

6348 

50  35  49.85 

130.93 

.077 

.914  2155 

6104 

52  22   50.48 

125.91 

.028 

.883  7219 

6343 

50  38  00.73 

130.83 

.078 

.914  8256 

6009 

52  24  56.33 

125.81 

.029 

.8843560 

6338 

50  40  11.51 

130.73 

.079 

.915  4353 

6094 

52   27  02.09 

125.71' 

1.030 

0.884  9895 

6333 

50  42  22  .  19 

130.63 

1.080 

0.916  0445 

6090 

52  29  07.75 

125.61 

.031 

.885  6226 

6328 

50  44  32.76 

130.53 

.081 

.916  6532 

6085 

52  31  13.30 

125-51 

.032 

.886  2551 

6323 

50  46  43-24 

130.42 

.082 

.917  2615 

6080 

52  33  18.76 

125.41 

.033 

.886  8872 

6318 

50  48  53.6i 

130.32 

.083 

.917  8692 

6075 

52  35  24.12 

125.31 

.034 

.887  5188 

6313 

50  51  03.89 

130.22 

.084 

.918  4765 

6070 

52  37  29.38 

125.21 

1.035 

0.888  1499 

6308 

50  53  14.06 

I3O.I2 

1.085 

0.919  0833 

6065 

52  39  34-54 

125.11 

.036 

.888  7805 

6304 

50  55  24.13 

I3O.02 

.086 

.919  6896 

6061 

52  41  39-60 

125.01 

.037 

.889  4106 

6299 

50  57  34-10 

129.92 

.087 

.920  2954 

6056 

52  43  44.56 

124.91 

.038 

.890  0402 

50  59  43-97 

129.82 

.088 

.920  9008 

6051 

52  45  49-42 

124.81 

•039 

.8906693 

6289 

51  oi  53-74 

129.72 

.089 

.921  5056 

6046 

52  47  54-18 

124.71 

1.040 

0.891  2980 

6284 

51  04  03.41 

129.62 

1.090 

0.922  iioo 

6041 

52  49  58.85 

124.61 

.041 

.891  9262      6279 

51  06  12.98 

129.52 

.091 

.922  7139 

6037 

52  52  03.41 

124.51 

.042 

.892  5538      6274 

51  08  22.44 

129.42 

.092 

.923  3173 

6032 

52  54  07.87 

124.41 

•043 

.893  1810 

6269 

51  10  31.81 

129.32 

.093 

.923  9203 

6027 

52  56  12.24 

I  _\;  . 

.044 

.893  8077 

6264 

51    12  41.07 

129.21 

.094 

.924  5227 

6022 

52  58  16.50 

124.22 

1.045 

0.804  4339 

6260 

51    14  50.24 

I29.II 

1.095 

0.925  1247 

6017 

53  00  20.67 

124.12 

.046 

.895  0596 

6255 

51  16  59.30 

129.01 

.006 

.925  7262 

6013 

53  02  24.74 

124.02 

.047 

.895  6848 

6250 

51  19  08.26 

128.91 

.097 

.926  3272 

6008 

53  04  28.70 

123.92 

.048 

.8963096 

6245 

51   21    17.12 

I28.8I 

.098 

.926  9278 

6003 

53  06  32.57 

123.82 

.049 

.896  9338 

6240 

51  23  25.88 

128.71 

.099 

.927  5278 

5998 

53  08  36.34 

U3*M 

1.050 

0.897  5576 

6235 

5i  25  34-55 

I28.6I 

1.  100 

0.928  1274 

5993 

53  10  40.01 

123.62 

u 

2tan-'(e»)~ 

<»  sech  u 

2tan-1(e«)-900 

usech  u 

u 

2tan-1(e«)~ 

wsechu 

2  tan-He")  -90° 

<•»  sech  u 

SMITHSONIAN  TABLES 


286 


The  Gudermannian. 


u 

gdu 

o>Fo' 

gdu 

«F</  ' 

u 

gdu 

«Fo' 

gdu 

«F0< 

0    /    // 

// 

o   /   // 

// 

I.  TOO 

0.928  1274 

5993 

53  10  40.01 

123.62 

I.I50 

0.957  498o 

5756 

54  51  38.15 

118.72 

.IOI 

.928  7265 

5989 

53  12  43.59 

123.52 

•  151 

.958  0734 

5751 

54  53  36.82 

118.62 

.IO2 

.929  3251 

5984 

53  14  47.06 

123.42 

.152 

.958  6482 

5746 

54  55  35-39 

118.53 

.103 

.929  9232 

5979 

53  16  50.43 

123.32 

.153 

.559  2226 

5742 

54  57  33.87 

118.43 

.104 

.930  5209 

5974 

53  18  53-71 

123.23 

•  154 

•959  7965 

5737 

54  59  32.25 

118.33 

1.  105 

0.931  1181 

59^9 

53  20  56.89 

123.13 

1.  155 

0.960  3700 

5732 

55  oi  30.53 

II8.23 

.106 

.931  7148 

5965 

53  22  59.96 

123.03 

.156 

.960  9430 

5727 

55  03  28.72 

118.14 

.107 

.932  3110 

5960 

53  25  02.94 

122.93 

.157 

•961  5155 

5723 

55  05  26.81 

118.04 

.108 

.932  9067 

5955 

53  27  05.82 

122.83 

.158 

.962  0875 

57i8 

55  07  24.80 

117.94 

.109 

.933  5020 

5950 

53  29  08.60 

122.73 

.159 

.962  6591 

5713 

55  09  22.69 

H7.85 

I.  IIO 

0.934  0968 

5945 

53  31  11.29 

122.63 

1.160 

0.963  2302 

5709 

55  ii  20.49 

117-75 

.in 

.934  6911 

5941 

53  33  13.87 

122.54 

.161 

.963  8008 

5704 

55  13  18.19 

117.65 

.112 

.935  2849 

5936 

53  35  16.36 

122.44 

.162 

.064  37io 

5699 

55  15  I5.8o 

117.56 

.113 

.935  8782 

5931 

53  37  18.75 

122.34 

.163 

.964  9407 

5695 

55  17  13.31 

117.46 

.114 

.936  4711 

5926 

53  39  21.03 

122.24 

.164 

.965  5099 

5690 

55  19  10.72 

117.36 

1.  115 

0.937  0635 

5922 

53  41  23.22 

122.14 

1.165 

0.066  0787 

5685 

55  21  08.04 

117.27 

.116 

•937  6554 

5917 

53  43  25.32 

I22.O4 

.166 

.966  6470 

5681 

55  23  05.26 

117.17 

.117 

.938  2469 

5912 

53  45  27.31 

122.94 

.167 

.967  2148 

5676 

55  25  02.38 

117.07 

.118 

.938'  8378 

5907 

53  47  29.21 

121.85 

.168 

.967  7822 

5671 

55  26  59.41 

116.58 

.119 

.939  4283 

5902 

53  49  31.00 

121.75 

.169 

.968  3491 

5667 

55  28  56.34 

116.88 

1.  120 

0.940  0183 

5898 

53  51  32.70 

121.65 

1.170 

0.068  9155 

5662 

55  30  53.17 

116.79 

.121 

.940  6079 

5893 

53  53  34.30 

121.55 

.171 

.969  4815 

5657 

55  32  49-91 

116.69 

.122 

.941  1069 

5888 

53  55  35.8o 

121.45 

.172 

.970  0470 

5653 

55  34  46.55 

116.59 

.123 

.941  7855 

5883 

53  57  37.21 

121.35 

•  173 

.970  6120 

5648 

55  36  43-10 

116.50 

.124 

•942  3736 

5879 

53  59  38.51 

121.26 

.174 

.971  1766 

5643 

55  38  39-54 

116.40 

1.  125 

0.942  9613 

5874 

54  oi  39-72 

121.16 

1.  175 

0.971  7407 

5639 

55  40  35-90 

116.31 

.126 

.943  5484 

5869 

54  03  40.83 

121.06 

.1,76 

•972  3043 

5634 

55  42  32.16 

116.21 

.127 

.944  1351 

5864 

54  05  41.84 

120.96 

.177 

.972  8675 

5629 

55  44  28.32 

n6.ii 

.128 

.944  7213 

5860 

54  07  42.76 

120.86 

.178 

•973  4301 

5625 

55  46  24.38 

116.02 

.129 

•945  3070 

5855 

54  09  43.57 

120.77 

.179 

.973  9924 

5620 

55  48  20.35 

115-92 

1.130 

0.945  8923 

5850 

54  u  44.29 

120.67 

1.180 

0.974  5542 

5615 

55  50  16.22 

115.83 

.131 

.946  4771 

5845 

54  13  44.91 

120.57 

.181 

.975  1155 

5611 

55  52  12.00 

H5.73 

.132 

.947  0614 

5841 

54  15  45.43 

120.47 

.182 

.975  6763 

5606 

55  54  07.68 

115-63 

.133 

.947  6452 

5836 

54  17  45-86 

120.38 

.183 

.976  2367 

5601 

55  56  03.27 

115-54 

.134 

.948  2286 

5831 

54  19  46.18 

120.28 

.184 

.976  7966 

5597 

55  57  58.76 

115.44 

1.  135 

0.948  8115 

5826 

54  21  46.41 

120.18 

1.185 

0.977  356o 

5592 

55  59  54.15 

115-35 

.136 

.949  3939 

5822 

54  23  46.54 

120.08 

.186 

•977  9150 

5588 

56  oi  49-45 

115.25 

.137 

.949  9758 

5817 

54  25  46.58 

119.98 

..187 

.978  4735 

5583 

56  03  44-66 

115.16 

.138 

•950  5573 

5812 

54  27  46.51 

119.89 

.188 

.979  0316 

5578 

56  05  39.76 

115.06 

.139 

•951  1383 

5807 

54  29  46.35 

H9.79 

.189 

.979  5892 

5574 

56  07  34.78 

114.96 

1.140 

0.951  7188 

5803 

54  31  46.09 

119.69 

1.190 

0.080  1463 

5569 

56  09  29.69 

114.87 

.141 

.952  2588. 

5798 

54  33  45-74 

119.59 

.191 

.980  7030 

5564 

56  ii  24.51 

114.77 

.142 

.952  8784 

5793 

54  35  45.28 

119.50 

.192 

.981  2592 

556o 

56  13  19.24 

114.68 

.143 

.953  4575 

5789 

54  37  44-73 

119.40 

.193 

.981  8149 

5555 

56  15  13-87 

114.58 

.144 

•954  0361 

57&4 

54  39  44.08 

119-30 

.194 

.982  3702 

5551 

56  17  08.41 

114.49 

1.  145 

0.954  6143 

5779 

54  4i  43-34 

119.21 

1.  195 

0.982  9251 

5546 

56  19  02.85 

114-39 

.146 

.955  1920 

5775 

54  43  42.49 

119.11 

.196 

.983  4794 

5541 

56  20  57.19 

114.30 

.147 

.955  7692 

5770 

54  45  41.55 

119.01 

.197 

.984  0333 

5537 

56  22  51.44 

114.20 

.148 

.956  3460 

5765 

54  47  40.51 

118.91 

.198 

.984  5868 

5532 

56  24  45.00 

114.11 

.149 

.956  9222 

5760 

54  49  39.38 

118.82 

.199 

.985  1397 

5527 

56  26  39.66 

114.01 

1.150 

0.957  498o 

5756 

54  51  38.15 

118.72 

1.  200 

0.985  6922 

5523 

56  28  33.62 

113-92 

u 

2tan-'(e*)-^ 

<»  sech  u 

2tan~1(e«)-900 

<*>  sech  u 

u 

atan-W-— 

<•>  sech  u 

2tan-1(e*)-900 

eu  sech  u 

SMITHSONIAN  TABLES 


287 


The  Gude  rmannian. 


u 

gdu 

»F0' 

gdu 

«F«> 

u 

gdu 

„* 

gdu 

^ 

I.2OO 

0.985  6922 

5523 

56  28  33.62 

113*92 

1.250 

I.  012  7356 

5295 

0          /           // 

58  oi  31.72 

109/23 

.2OI 

.986  2443 

5518 

56  30  27.49 

113.82 

.251 

.OI3   2649 

5291 

58  03  20.89 

109.13 

.202 

.986  7959 

5514 

56  32  21.26 

H3.73 

.252 

.013   7938 

5286 

58  05  09.08 

109.04 

.203 

.987  3470 

5509 

56  34  14.94 

113.63 

.253 

.014  3222 

5282 

58  06  58.98 

108.95 

.204 

.987  8977 

5504 

56  36  08.53 

113-54 

•  254 

.014  85O2 

5277 

58  08  47-88 

108.86 

1.205 

0.988  4479 

5500 

56  38  02.02 

113.44 

1.255 

i.  015  3777 

5273 

58  10  36.69 

108.76 

.206 

.988  9977 

5495 

56  39  55.42 

113-35 

.256 

.015  9048 

5269 

58  12  25.40 

108.67 

.207 

.989  5470 

5491 

56  41  48.72 

H3.25 

•257 

.016  4314 

5264 

58  14  14.03 

io8'.s8 

.208 

.090  0958 

5486 

56  43  41  .92 

II3.I6 

.258 

.016  9576 

5260 

58  16  02.56 

108.49 

.209 

.990  6442 

5482 

56  45  35.03 

II3.06 

•  259 

.017  4833 

5255 

58  17  51.00 

108.39 

I.2IO 

0.991  1921 

5477 

56  47  28.05 

112.97 

1.260 

1.018  0086 

5251 

58  19  39-35 

108.30 

.211 

.991  7396 

5472 

56  49  20.97 

112.88 

.261 

.018  5335 

5246     58   21    27.6l 

108.21 

.212 

.992  2866 

5468 

56  51  13.80 

112.78 

.262 

.019  0578 

5242 

58  23  15.77 

108.12 

.213 

•992  8331 

5463 

56  53  06.54 

112.69 

.263 

.019  5818 

5237 

58  25  03.  84 

108.03 

.214 

•993  3792 

5459 

56  54  59-  17 

112.59 

.264 

.020  1053 

5233 

58  26  51.82 

107.93 

1.  215 

0.993  9249 

5454 

56  56  51.72 

112.50 

1.265 

1.020  6283 

5228 

58  28  39-71 

107.84 

.2l6 

.994  4700 

5449 

56  58  44.17 

112.40 

.266 

.021    1510 

5224 

58  30  27.50 

107.75 

.217 

.995  0148 

5445 

57  oo  36.53 

112.31 

.267 

.021   6731 

5219 

58  32  15.21 

107.66 

.218 

•995  5590 

5440 

57  02  28.79 

112.22 

.268 

.022    1948 

5215 

58  34  02.82 

107-57 

.219 

.996  1028 

5436 

57  04  20.96 

112.  12 

.269 

.022  7l6l 

5210 

58  35  50.34 

107.47 

1.220 

0.996  6462 

5431 

57  06  13.03 

112.03 

1.270 

1.023   2369 

5206 

58  37  37.77 

107.38 

.221 

.997  1891 

5427 

57  08  05.01 

111.93 

.271 

.023  7573 

52O2 

58  39  25.10 

107.29 

.222 

.997  7315 

5422 

57  09  56.90 

111.84 

.272 

.024  2772 

5197 

58  41  12.35 

107.20 

.223 

.998  2735 

54i8 

57  ii  48.69 

111.74 

.273 

.024  7967 

5193 

58  42  59-50 

107  .  i  i 

.224 

.998  8150 

54U 

57  13  40.39 

111.65 

.274 

.025  3158 

5188 

58  44  46.56 

107.02 

1.225 

0.999  356i 

5408 

57  15  31.99 

111.56 

1.275 

1.025  8344 

5184 

58  46  33-53 

106.92 

.226 

.999  8967 

5404 

57  17  23.50 

111.46 

.276 

.026  3526 

5179 

58  48  20.41 

106.83 

.227 

i.  ooo  4369 

5399 

57  19  14.92 

IH.37 

.277 

.026  8703 

5175 

58  50  07.20 

106.74 

.228 

.000  9766 

5395 

57  21  06.24 

111.28 

.278 

.027  3876 

5171 

58  51  53-90 

106.65 

.229 

.001  5158 

5390 

57  22  57.47 

III.I8 

.279 

.027  9044 

5166 

58  53  40-50 

106.56 

1.230 

I.OO2  0546 

5386 

57  24  48.60 

111.09 

1.280 

1.028  4208 

5162 

58  55  27.02 

106.47 

.231 

.002  5930 

538i 

57  26  39.64 

110.99 

.281 

.028  9367 

5157 

58  57  13.44 

106.38 

.232 

.003  1309 

5377 

57  28  30.59 

110.90 

.282 

.029  4523 

5153 

58  58  59-77 

106.29 

.233 

.003  6683 

5372 

57  30  21.45 

110.81 

.283 

.029  0673 

5H8 

59  oo  46.01 

106.19 

.234 

.004  2053 

5368 

57  32  12.21 

110.71 

.284 

.030  4819 

5144 

59  02  32.16 

106.10 

1.235 

1.004  7418 

5363 

57  34  02.88 

110.62 

1.285 

1.030  9961 

5UO 

59  04  18.22 

106.01 

.236 

.005  2779 

5359 

57  35  53-45 

no.53 

.286 

.031  5099 

5135 

59  06  04.19 

105.92 

.237 

.005  8135 

5354 

57  37  43.93 

110.43 

.287 

.032  0232 

5131 

59  07  50.o6 

105.83 

.238 

.006  3487 

5349 

57  39  34.32 

110.34 

.288 

.032  5360 

5126 

59  09  35.85 

ios-74 

.239 

.006  8834 

5345 

57  41  24.61 

110.25 

.289 

.033  0485 

5122 

59  u  21.54 

105.65 

1.240 

1.007  4177 

5340 

57  43  14.82 

110.15 

1.290 

1.033  5605 

5Il8 

59  13  07.15 

105.56 

.241 

.007  9515 

5336 

57  45  04.92 

no.  06 

.291 

.034  0720 

5H3 

59  14  52.66 

105.47 

.242 

.0084840 

5331 

57  46  54-94 

109.97 

.292 

.034  5831 

5109 

59  16  38.08 

105.38 

.243 

.009  0178 

5327 

57  48  44.86 

109.88 

.293 

.035  0938 

5104 

59  18  23.41 

105.29 

.244 

.009  5503 

5322 

57  50  34.69 

109.78 

.294 

.035  6040 

5100 

59  20  08.66 

105.20 

1.245 

i.oio  0823 

53i8 

57  52  24.43 

109.69 

1.295 

1.036  1138 

5096 

59  21  53.8i 

105  .  i  i 

.246 

.010  6139 

5313 

57  54  14.07 

109.60 

.296 

.036  6231 

5091 

59  23  38.87 

105.02 

.247 

.on  1450 

5309 

57  56  03.62 

109.50 

.297 

.037  1320 

5087 

59  25  23.84 

104.93 

.248 

.on  6756 

5304 

57  57  53.o8 

109.41 

.298 

.037  6405 

5083 

59  27  08.72 

104.83 

.249 

.012  2058 

5300 

57  59  42.44 

109.32 

.299 

.038  1485 

5078 

59  28  53-51 

104-74 

1.250 

I.  012  7356 

5295 

58  oi  31.72 

109.23 

1.300 

1.038  6561 

5074 

59  30  38.21 

104.65 

u 

*"-<">-l 

<•»  sech  u 

2tan-1(eu)-900 

wsechu 

u 

2  tan-He")-- 

<•»  sech  u 

2tan-Ue")-90c 

<»sechu 

SMITHSONIAN  TABLES 


288 


The  Gudermannian. 


u 

Odu 

»Fo' 

gdu 

<oF0' 

u 

ad  u 

«F0' 

gdu 

"Fo' 

0    /    // 

// 

o   /   // 

// 

1.300 

1.038  6561 

5074 

59  30  38.21 

104.65 

1.350 

1.063  4837 

4858 

60  55  59.27 

IOO.2I 

.301 

.039  1633 

5069 

59  32  22.82 

104.56 

.351 

.063  9694 

4854 

60  57  39-43 

100.12 

.302 

.039  6700 

5065 

59  34  07-34 

104.47 

•  352 

.064  4546 

4850 

60  59  19.51 

100.03 

.303 

.040  1763 

5061 

59  35  51.77 

104.38 

•  353 

.064  9393 

4846 

61  oo  59.50 

99.95 

.304 

.040  6822 

5056 

59  37  36.10 

104.29 

•354 

.065  4237 

4841 

61  02  39.41 

99.86 

1.305 

1.041  1876 

5052 

59  39  20.35 

104.29 

1.355 

1.065  9076 

4837 

61  04  19.22 

99.77 

.306 

.041  6926 

5048 

59  41  04.51 

104.11 

•  356 

.066  3911 

4833 

61  05  58.95 

99.69 

.307 

.042  1971 

5043 

59  42  48.58 

104.02 

•  357 

.066  8742 

4829 

61  07  38.59 

99.60 

.308 

.042  7012 

5039 

59  44  32.56 

103.93 

•  358 

.067  3568 

4824 

61  09  18.15 

99.51 

.309 

.043  2049 

5035 

59  46  16.45 

103.84 

•  359 

.067  8390 

4820 

61  10  57.61 

99.42 

i.3'0 

1.043  7o8i 

5030 

59  48  00.25 

103.76 

1.360 

i.  068  3209 

4816 

61  12  36.99 

99-34 

.311 

.044  2109 

5026 

59  49  43.96 

103.67 

.361 

.068  8022 

4812 

61  14  16.29 

99.25 

.312 

.044  7133 

5O2I 

59  51  27.58 

103.58 

.362 

.069  2832 

4808 

61  15  55-49 

99-16 

.313 

.045  2152 

5017 

59  53  11.  ii 

103.49 

.363 

.069  7637 

4803 

61  17  34.61 

99.08 

.314 

.045  7i67 

5013 

59  54  54.55 

103.40 

.304 

.070  2439 

4799 

61  19  13.64 

98.99 

I.3I5 

1.046  2178 

5008 

59  56  37.91 

103.31 

1.365 

1.070  7236 

4795 

61  20  52.59 

98.90 

.316 

.046  7184 

5004 

59  58  21.17 

103.22 

.366 

.071  2028 

4791 

61  22  31.45 

98.82 

.317 

.047  2186 

5000 

60  oo  04.34 

103.13 

.367 

.071  6817 

4786 

6l  24  IO.22 

98.73 

.318 

.047  7184 

4995 

60  01  47.43 

103.04 

.368 

.072  1601 

4782 

61  25  48.90 

98.64 

.319 

.048  2177 

4991 

60  03  30.42 

102.95 

.369 

.072  6382 

4778 

61  27  27.50 

98.56 

1.320 

1.048  7166 

4987 

60  05  13.33 

102.86 

1.370 

1.073  1158 

4774 

61  29  06.  01 

98.47 

.321 

.049  2151 

4983 

60  06  56.14 

102.77 

•  371 

.073  5929 

4770 

61  30  44-44 

98.38 

.322 

.049  7131 

4978 

60  08  38.87 

102.68 

.372 

.074  0697 

4766 

61  32  22.78 

98.30 

.323 

.050  2107 

4974 

60  10  21.51 

102.59 

•  373 

.074  546o 

476l 

61  34  01.03 

98.21 

•  324 

.050  7079 

4970 

60  12  04.06 

102.50 

•  374 

.075  O220 

4757 

61  35  39-20 

98.12 

1.325 

1.051  2046 

4965 

60  13  46.52 

102.42 

1.375 

1.075  4975 

4753 

61  37  17.26 

98.04 

.326 

.051  7009 

496i 

60  15  28.89 

102.33 

.376 

.075  9725 

4749 

61  38  55.27 

97-95 

.327 

.052  1968 

4957 

60  17  11.17 

102.24 

.377 

.076  4472 

4745 

61  40  33.18 

97.86 

.328 

.052  6923 

4952 

60  18  53-37 

102.15 

.378 

.076  9215 

4740 

61  42  ii.oo 

97.78 

.329 

.053  1873 

4948 

60  20  35-47 

102.06 

•  379 

.077  3953 

4736 

61  43  48.73 

97.69 

1-330 

1.053  6819 

4944 

6O  22  17.49 

101.97 

1.380 

1.077  8687 

4732 

61  45  26.38 

97.6i 

•  331 

.054  1760 

4939 

60  23  59.41 

101.88 

.381 

.078  3417 

4728 

61  47  03.94 

97.52 

•  332 

.0546698 

4935 

60  25  4L25 

101.79 

.382 

.078  8143 

4724 

61  48  41.42 

97.43 

•333 

.055  1631 

4931 

60  27  23.0O 

101.71 

.383 

.079  2865 

4720 

61  50  18.81 

97.35 

•  334 

•055  6559 

4927 

60  29  04.67 

101.62 

.384 

.079  7582 

4715 

61  51  56.12 

97.26 

1.335 

1.056  1484 

4922 

00  30  46.24 

101.53 

1.385 

1.080  2295 

4711 

61  53  33.34 

97.18 

.336 

.056  6404 

4918 

60  32  27.72 

101.44 

.386 

.080  7005 

4707 

61  55  10.47 

97.09 

.337 

.057  1320 

4914 

60  34  09.  12 

101.35 

.387 

.081  1710 

4703 

61  56  47.52 

97.01 

.338 

.057  6231 

4909 

60  35  50.43 

101.26 

.388 

.081  6411 

4699 

61  58  24.48 

96.92 

.339 

.058  1139 

4905 

60  37  31.65 

101.18 

.389 

.082  1107 

4695 

62  oo  01.36 

96.83 

1.340 

1.058  6042 

4001 

60  39  12.78 

101.09 

1.390 

1.082  5800 

4691 

62  01  38.15 

96.75 

•  341 

.059  0940 

4897 

60  40  53.83 

101.00 

•391 

.083  0488 

4686 

62  03  14.86 

96.66 

.342 

.059  5835 

4892 

60  42  34.78 

100.91 

.392 

•083  5173 

4682 

62  04  51.48 

96.58 

.343 

.060  0725 

4888 

60  44  15.65 

100.82 

».393 

.083  9853 

4678 

62  06  28.01 

96.49 

•  344 

.060  5611 

4884 

60  45  56.43 

100.74 

•  394 

.084  4529 

4674 

62  08  04.46 

96.41 

1.345 

1.061  0493 

4880 

60  47  37.12 

100.65 

1.395 

1.084  9201 

4670 

62  09  40.83 

96.32 

.346 

.061  5370 

4875 

60  49  17.73 

100.56 

•  396 

.085  3868 

4666 

62  II  17.11 

96.24 

.347 

.062  0243 

4871 

60  50  58.24 

100.47 

•  397 

.085  8532 

4662 

62  12  53.30 

96.15 

.348 

.062  5112 

4867 

60  52  38.67 

100.38 

.398 

.086  3192 

4657 

62  14  29.41 

96.017 

.349 

.062  9977 

4863 

60  54  19.01 

100.30 

•  399 

.086  7847 

4653 

62  16  05.44 

95.98 

1-350 

1.063  4837 

4858 

60  55  59.27 

100.21 

1.400 

1.087  2498 

4649 

62  17  41-37 

95.90 

u 

2  tan-He")-  jj 

wsechu 

2tan-1(e«)-900 

w  sech  u 

u 

2tan-Ke«)-£ 

wsechu 

2tan-1(e«)-900 

<»  sech  u 

SMITHSONIAN  TABLES 


289 


The  Gudermannian. 


u 

gdu 

»Fo' 

gdu 

«Fo' 

u 

gd  u 

«FO' 

gd  u 

<-F0' 

1.400 

1.087  2498 

4649 

o   /   // 

62  17  41.37 

95-90 

1.450 

1.109  9869 

4447 

63°3S'  Si'W 

91.72 

.401 

.087  7145 

4645 

62  19  17.23 

95.81 

.451 

.110  4314 

4443 

63  37  22.92 

91.64 

.402 

.088  1788 

4641 

62  20  53.00 

95-73 

•  452 

.1108755 

4439 

63  38  54-52 

91.56 

.403 

.088  6427 

4637 

62  22  28.68 

95.64 

•453 

.iii  3192 

4435 

63  40  26.03 

91.47 

.404 

.089  1062 

4633 

62  24  04.28 

95.56 

•454 

.in  7624 

4431 

63  41  57.46 

91-39 

1.405 

1.089  5093 

4629 

62  25  39.80 

95-47 

1.455 

I.  I  12  2O53 

4427 

63  43  28.82 

91.31 

.406 

.090  0320 

4625 

62  27  15.23 

95-39 

.456 

.112  6478 

4423 

63  45  00.08 

91.23 

.407 

.090  4942 

4620 

62  28  50.58 

95.30 

•457 

.113  0899 

4419 

63  46  31.27 

91.15 

.406 

.090  9561 

4616 

62  3O  25.84 

95-22 

.458 

.113  5316 

4415 

63  48  02.38 

91.07 

.409 

.091  4175 

4612 

62  32  01.02 

95.14 

•459 

.113  9729 

4411 

63  49  33-40 

90.98 

1.410 

1.091  8/85 

4608 

62  33  36.11 

95.05 

1.460 

I.  I  14  4138 

4407 

63  51  04.35 

90.90 

.411 

.092  3391 

4604 

62  35  II.  12 

94.97 

.461 

.114  8543 

4403 

63  52  35-21 

90.82 

.412 

.092  7993 

4600 

62  36  46.04 

94.88 

.462 

.115  2944 

4399 

63  54  05.99 

90.74 

.413 

.093  2591 

4596 

62  38  20.88 

94-80 

.463 

.115  7341 

4395 

63  55  36.68 

90.66 

.414 

•093  7l85 

4592 

62  39  55.64 

94.71 

.464 

.116  1734 

4391 

63  57  07.30 

90.58 

1.415 

1.094  1775 

4588 

62  41  30.31 

94-63 

1.465 

1.116  6124 

4387 

63  58  37.83 

90.49 

.416 

.094  6361 

4584 

62  43  04.90 

94-55 

.466 

.117  0509 

4383 

64  oo  08.29 

90.41 

.417 

.095  0942 

4580 

62  44  39.40 

94.46 

.467 

.117  4890 

4379 

64  oi  38.66 

90.33 

.418 

•095  5520 

4576 

62  46  13.82 

94-38 

.468 

.117  9268 

4375 

64  03  08.95 

90.25 

.419 

.096  0094 

4571 

62  47  48.16 

94.29 

.469 

.118  3641 

4372 

64  04  39.16 

90.17 

1.420 

1.096  4663 

4567 

62  49  22.41 

94.21 

1.470 

1.118  Son 

4368 

64  06  09.29 

90.09 

.421 

.096  9228 

4563 

62  50  56.58 

94.13 

.471 

.119  2377 

4364 

64  07  39-34 

90.01 

.422 

.097  3790 

4559 

62  52  30.66 

94.04 

.472 

.119  6738 

4360 

64  09  09.31 

89.93 

.423 

.097  8347 

4555 

62  54  04.66 

93.96 

•473 

.120  1096 

4356 

64  10  39.19 

89.85 

.424 

.098  2900 

4551 

62  55  38.58 

93.88 

.474 

.120  5450 

4352 

64  12  O9.OO 

89.76 

1.425 

1.098  7449 

4547 

62  57  12.41 

93-79 

1.475 

I.  120  0800 

4348 

64  13  38.72 

89.68 

.426 

.099  1994 

4543 

62  58  46.16 

93-71 

\476 

.121  4146 

4344 

64  15  08.37 

89-60 

.427 

.099  6536 

4539 

63  oo  19.83 

93-62 

•477 

.121  8488 

4340 

64  16  37-93 

89-52 

.428 

.100  1073 

4535 

63  01  53-41 

93-54 

.4178 

.122  2826 

4336 

64  18  07.41 

89.44 

.429 

.100  5606 

4531 

63  03  26.91 

93.46 

•  479 

.122  7l6l 

4332 

64  19  36.81 

89.36 

1.430 

i.ioi  0134 

4527 

63  05  00.33 

93-37 

1.480 

I.  123  1491 

4328 

64  21  O6.I3 

89.28 

.431 

.101  4659 

4523 

63  06  33.66 

93.29 

.481 

.123  5818 

4325 

64  22  35-37 

89.20 

.432 

.101  9180 

4519 

63  08  06.91 

93.21 

.482 

.124  OI4O 

4321 

64  24  04.53 

89.12 

•433 

.102  3697 

4515 

63  09  40.08 

93-13 

.483 

.124  4459 

4317 

64  25  33.61 

89-04 

•434 

.102  8210 

4511 

63  ii  13.16 

93-04 

.484 

.1248774 

4313 

64  27  02.  61 

88.96 

1-435 

1.103  2719 

4507 

63  12  46.16 

92.96 

1.485 

1.125  3085 

4309 

64  28  31.53 

88.88 

.436 

.103  7223 

4503 

63  14  19.08 

92.88 

.486 

.125  7392 

4305 

64  30  00.37 

88.80 

•437 

.104  1724 

4499 

63  15  5i.9i 

92.79 

.487 

.126  1695 

4301 

64  31  29.13 

88.72 

.438 

.104  6221 

4495 

63  17  24.66 

92.71 

.488 

.126  5994 

4297 

64  32  57.81 

88.64 

•  439 

.105  0714 

4491 

63  18  57-33 

92.63 

.489 

.127  0289 

4293 

64  34  26.41 

88.56 

1.440 

i.  105  5202 

4487 

63  20  29.92 

92.54 

1.490 

I.  127  458i 

4290 

64  35  54-93 

88.48 

.441 

.105  9687 

4483 

63  22  O2.42 

92.46 

•491 

.127  8869 

4286 

64  37  23.37 

88.40 

•442 

.106  4168 

4479 

63  23  34.84 

92.38 

.492 

.128  3152 

4282 

64  38  51.72 

88.32 

•  443 

.106  8644 

4475 

63  25  07.18 

92.30 

•493 

.128  7432 

4278 

64  40  20.00 

8S.-24 

•444 

.107  3H7 

4471 

63  26  39-44 

92.21 

.494 

.129  1708 

4274 

64  41  48.20 

88.16 

1-445 

i.  107  7586 

4467 

63  28  ii.  61 

92.13 

1.495 

1.129  598o 

4270 

<>4  43  16.32 

88.08 

.446 

.  108  2050 

4463 

63  29  43-70 

92.05 

.496 

.  130  0249 

4266 

64  44  44.36 

88.00 

•447 

.108  6511 

4459 

63  31  15.71 

91.97 

•497 

.130  4513 

4263 

64  46  12.32 

87.92 

.448 

.109  0968 

4455 

63  32  47.63 

91.88 

.498 

.1308774 

4259 

64  47  40.20 

87.84 

•449 

.109  5421 

4451 

63  34  19.48 

91.80 

.499 

.131  3031 

4255 

04  49  08.01 

87.76 

1.450 

1.109  9869 

4447 

63  35  51.24 

91.72 

1.500 

1.131  7283 

4251 

64  50  35-73 

87.68 

u 

2  tan-He")-  J 

<«  sech  u 

2tan->(e°)-900 

wsech  u 

u 

2tan-'(e«)-^ 

wsechu 

2tan-Ke«)-90° 

«•»  sech  u 

SMITHSONIAN  TABLES 


290 


The  Gudermannian. 


u 

gd  u 

<-Fo' 

gd  u 

«F0' 

u 

gdu 

«F0' 

gd  u 

«F0' 

1.500 

I.I3I  7283 

4251 

64  50  35-73 

87^68 

1.550 

1.152  5078 

4062 

0    /     // 

66  02  01.81 

83*78 

.501 

.132  1532 

4247 

64  52  03.37 

87.60 

.551 

•  152  9139 

4058 

66  03  25.55 

83.71 

.502 

.132  5778 

4243 

64  53  30.93 

87.52 

.552 

.153  3195 

4055 

66  04  49.22 

83.63 

.503 

.133  0019 

4239 

64  54  58.42 

87.44 

•553 

.153  7248 

4051 

66  06  12.  81 

83.55 

.504 

.133  4257 

4236 

64  56  25.82 

87.37 

.554 

.154  1297 

4047 

66  07  36.33 

83.48 

1.505 

I.  133  8490 

4232 

64  57  53.15 

87.29 

1.555 

1.  154  5342 

4043 

66  08  59.77 

83.40 

.506 

.134  2720 

4228 

64  59  20.40 

87.21 

.556 

.154  9384 

4040 

66  10  23.14 

83.33 

.507 

.  134  6946 

4224 

65  oo  47.56 

87.13 

•  557 

.155  342i 

4036 

66  ii  46.42 

83-25 

.508 

.135  n68 

422O 

65  02  14.65 

87.05 

.558 

.155  7456 

4032 

66  13  09.63 

83.17 

.509 

•135  5387 

4216 

65  03  41.66 

86.97 

.'559 

.156  1486 

4029 

66  14  32.77 

83.10 

1.510 

1.135  9601 

4213 

65  05  08.59 

86.89 

1.560 

1.156  5513 

4025 

66  15  55-83 

83.02 

.511 

.136  3812 

4209 

65  06  35.44 

86.81 

.561 

.  156  9536 

4021 

66  17  18.81 

82.95 

.512 

.  136  8019 

4205 

65  O8  02.22 

86.73 

.562 

•157  3556 

4018 

66  18  41.72 

82.87 

.513 

.137  2222 

42OI 

65  09  28.91 

86.66 

.563 

.157  7571 

4014 

66  20  04  .  55 

82.79 

.514 

.137  6421 

4197 

65  10  55-53 

86.58 

.564 

.158  1583 

4010 

66  21  27.31 

82.72 

1.515 

I.I38  O6l7 

4194 

65  12  22.07 

86.50 

1.565 

1.158  5592 

4007 

66  22  49-99 

82.64 

.516 

.  138  4808 

4100 

65  13  48.52 

86.42 

.566 

.  158  9597 

4003 

66  24  12.59 

82.57 

.517 

.1388006 

4186 

65  15  14.91 

86.34 

.567 

•  159  3598 

3999 

66  25  35.12 

82.49 

.518 

.139  3180 

4182 

65  16  41.21 

86.26 

.568 

•159  7595 

3996 

66  26  57.57 

82.42 

.519 

.  139  7300 

4178 

65  18  07.43 

86.18 

.569 

.160  1589 

3992 

66  28  19.95 

82.34 

1.520 

1.140  1537 

4175 

65  1933.58 

86.11 

1.570 

1.160  5579 

3988 

66  29  42.25 

82.26 

.521 

.140  5709 

4171 

65  20  59-64 

86.03 

•  571 

.  160  9566 

3985 

66  31  04.48 

82.19 

.522 

.140  9878 

4167 

65  22  25.63 

85.95 

.572 

.161  3548 

398i 

66  32  26.63 

82.11 

.523 

.141  4043 

4163 

65  23  51.54 

85.87 

•  573 

.161  7527 

3977 

66  33  48.71 

82.04 

.524 

.141  8205 

4159 

65  25  17.38 

85.79 

•  574 

.162  1503 

3974 

66  35  10.71 

8l.o6 

1.525 

1.142  2362 

4156 

65  26  43.13 

85.72 

1-575 

1.162  5475 

3970 

66  36  32.63 

81.89 

.526 

.142  6516 

4152 

65  28  08.  81 

85-64 

.576 

.  162  9443 

3966 

66  37  54.48 

81.81 

.527 

.143  0666 

4148 

65  29  34.41 

85.56 

•  577 

.163  3408 

3963 

66  39  16.26 

8i.74 

.528 

.143  4812 

4144 

65  30  59-93 

85.48 

•  578 

.163  7369 

3959 

66  40  37.96 

81.66 

.529 

.143  8954 

4141 

65  32  25.37 

85.40 

•  579 

.164  1326 

3955 

66  41  59.58 

8i.59 

1.530 

1.144  3093 

4137 

65  33  50.74 

85.33 

1.580 

1.164  5279 

3952 

66  43  21.13 

81.51 

.531 

.  144  7228 

4133 

65  35  16.02 

85.25 

.581 

.  164  9230 

3948 

66  44  42.61 

81.44 

.532 

•145  1359 

4129 

65  36  41-23 

85.17 

.582 

.165  3176 

3945 

66  46  04.01 

81.36 

•  533 

.145  5486 

4125 

65  38  06.37 

85.09 

.583 

.165  7119 

3941 

66  47  25.33 

81.29 

.534 

.145  9610 

4122 

65  39  31.42 

85.02 

.584 

.166  1058 

3937 

66  48  46.58 

Si.  21 

1.535 

1.146  3730 

4Il8 

65  40  56.40 

84.94 

1.585 

i  .  166  4993 

3934 

66  50  07.76 

8I.I4 

•  536 

.  146  7846 

4II4 

65  42  21.30 

84.86 

.586 

.  166  8925 

3930 

66  51  28.86 

8!.o6 

.537 

.147  1958 

4110 

65  43  46.12 

84.78 

.587 

.  167  2854 

3926 

66  52  49.89 

80.99 

.538 

.147  6067 

4107 

65  45  10.87 

84.71 

.588 

.  167  6778 

3923 

66  54  10.84 

80.92 

•  539 

.  148  0172 

4103 

65  46  35-54 

84.63 

.589 

.168  0699 

3919 

66  55  31.72 

80.84 

1.540 

1.1484273 

4099 

65  48  00.13 

84.55 

1-590 

1.168  4617 

39i6 

66  56  52.52 

80.77 

•  541 

.  148  8370 

4095 

65  49  24.64 

84.48 

.591 

.168  8531 

3912 

66  58  13.25 

80.69 

•  542 

.  149  2464 

4092 

65  50  49.08 

84.40 

•  592 

.169  2441 

3908 

66  59  33-91 

80.62 

.543 

.  149  6554 

4088 

65  52  13.44 

84.32 

.593' 

.169  6348 

3905 

67  oo  54.49 

80.54 

•  544 

.150  0640 

4084 

65  53  37-72 

84.25 

•  594 

.170  0251 

3901 

67  02  15.00 

80.47 

1.545 
.546 

1.150  4722 
.150  8801 

408l 

4077 

65  '55  01.93 
65  56  26.06 

84.17 
84.09 

I<S?J 
.596 

1.170  4150 
.  170  8046 

3898 
3894 

67  03  35.43: 
67  04  55.79 

80.40 
80.32 

•  547 

.151  2876 

4073 

65  57  SO.ii 

84.01 

•  597 

.171  1938 

3891 

67  06  16.07 

80.25 

.548 

.151  6947 

4069 

65  59  14.08 

83.94 

.598 

.171  5827 

3887 

67  07  36.28 

80.17 

•  549 

.152  1015 

4066 

66  oo  37.98 

83.86 

•  599 

.171  9712' 

3883 

67  08  56.42 

80.10 

1-550 

1.152  5078 

4062 

66  02  01.81 

83.78 

I.obo 

1.1723594 

3880 

67  10  16.48 

80.03 

u 

atan-Heu)-! 

wsechu 

2lan-Ke°)-900 

wsechu 

u 

2tan-J(e")-£ 

wsechu 

2tan-1(eu)-900 

(»  sech  u 

SMITHSONIAN  TABLES 


2QI 


The  Gudermannian. 


u 

gdu 

«F0' 

gdu 

U.FO" 

u 

gdu 

„* 

gd  u 

^ 

1.  600 

1.172  3594 

3880 

o   /   // 

67  10  16.48 

So'os 

1.650 

I.I9I  3170 

3704 

68°  1  5'  26^76 

76.41 

.601 

.172  7472 

3876 

67  II  36.47 

79-95 

.651 

.191  6872 

3701 

68  16  43.13 

76.34 

.602 

.173  1346 

3873 

67  12  56.39 

79-88 

.652 

.192  0571 

3097 

68  17  59-44 

76.27 

.603 

.173  5217 

3869 

67  14  16.23 

79.81 

.653 

.192  4267 

3694 

68  19  15.67 

76.20 

.604 

.173  90&4 

3865 

67  15  36.0O 

79-73 

.654 

.192  7960 

3691 

68  20  31.83 

76.12 

1.605 

I.  174  2048 

3862 

67  16  55-69 

79.66 

1.655 

I.I93  1648 

3687 

68  21  47.92 

76.05 

.606 

.174  6808 

3858 

67  18  15.31 

79-58 

.656 

•193  5334 

3684 

68  23  03.93 

75.98 

.607 

.175  0665 

3855 

67  19  34.86 

79-51 

.657 

.193  9016 

3680 

68  24  19.88 

75.91 

.608 

.175  4518 

3851 

67  20  54-34 

79-44 

.658 

.194  2695 

3677 

68  25  35.76 

75.84 

.609 

.175  8367 

3848 

67  22  13.74 

79.36 

.659 

.  194  6370 

3674 

6826  51.57 

75-77 

1.610 

1.176  2213 

3844 

67  23  33.07 

79.29 

1.660 

I.I95  0042 

3670 

68  28  07.30 

75-70 

.611 

.  176  6056 

3841 

67  24  52.32 

79.22 

.661 

.195  3710 

3667 

68  29  22.97 

75.63 

.612 

.  176  9895 

3837 

67  26  II.5O 

79-15 

.662 

•195  7375 

3663 

68  30  38.56 

75.56 

.613 

.  177  3730 

3834 

67  27  3O.6l 

79-07 

.663 

.196  1037 

3660 

68  31  54-09 

75.49 

.614 

.177  7562 

3830 

67  28  49.65 

79.00 

.664 

.  196  4695 

3656 

68  33  09.54 

75-43 

1.615 

1.178  1390 

3826 

67  30  08.  61 

78.93 

1.665 

1.196  8349 

3653 

68  34  24.93 

75.36 

.616 

.178  5215 

3823 

67  31  27.50 

78.85 

.666 

.197  2OOI 

3650 

68  35  40.24 

75.29 

.617 

.  178  9036 

3819 

67  32  46.32 

78.78 

.667 

.197  5649 

3646 

68  36  55-49 

75-22 

.618 

.  179  2853 

38l6 

67  34  05.06 

78.71 

.668 

.  197  9293 

3643 

68  38  10.66 

75.15 

.619 

.1796667 

3812 

67  35  23.73 

78.63 

.669 

.  198  2935 

3639 

68  39  25.77 

75.08 

1.620 

i  .  180  0478 

3809 

67  36  42.33 

78.56 

1.670 

I  .  198  6572 

3636 

68  40  40.80 

75-01 

.621 

.180  4285 

3805 

67  38  00.86 

78-49 

.671 

.  199  0207 

3633 

68  41  55-77 

74-94 

.622 

.180  8089 

3802 

67  39  19-31 

78.42 

.672 

.1993838 

3629 

68  43  10.66 

74-87 

.623 

.181  1889 

3798 

67  40  37.69 

78.34 

.673 

.199  7465 

3626 

68  44  25.49 

74.8o 

.624 

.181  5685 

3795 

67  41  56.00 

78.27 

.674 

.200  1090 

3623 

68  45  40.24 

74-72 

1.625 

1.181  9478 

3791 

67  43  H.24 

78.20 

1.675 

I.  200  4711 

3619 

68  46  54-93 

74.65 

.626 

.182  3268 

3788 

67  44  32.40 

78.13 

.676 

.200  8328 

3616 

68  48  09.55 

74-58 

.627 

.  182  7054 

3784 

67  45  50.49 

78.06 

.677 

.2OI  1942 

3612 

68  49  24.09 

74-51 

.628 

.183  0836 

378i 

67  47  08.51 

77.98 

.678 

.201  5553 

3609 

68  50  38.57 

74-44 

.629 

.183  4615 

3777 

67  48  26.46 

77-91 

.679 

.201  9160 

3606 

68  51  52.98 

74-37 

1.630 

1.183  8300 

3774 

67  49  44-33 

77.84 

1.680 

i.  202  2764 

3602 

68  53  07.32 

74.30 

.631 

.184  2162 

3770 

67  51  02.13 

77-77 

.681 

.202  6365 

3599 

68  54  21.58 

74-23 

.632 

.184  593i 

3767 

67  52  19.86 

77.69 

.682 

.202  0962 

3596 

68  55  35-78 

74-17 

.633 

.184  9696 

3763 

67  53  37.52 

77.62 

.683 

.203  3556 

3592 

68  56  49.92 

74.10 

.634 

.185  3457 

376o 

67  54  55.ii 

77-55 

.684 

.203  7147 

3589 

68  58  03.98 

74-03 

1.635 

1.185  7215 

3756 

67  56  12.62 

77.48 

1.685 

1.204  0734 

3586 

68  59  17.97 

73.o6 

.636 

.186  0970 

3753 

67  57  30.07 

77-41 

.686 

.204  4318 

3582 

69  oo  31.89 

73-89 

.637 

.186  4721 

3749 

67  58  47-44 

77.34 

.687 

.204  7899 

3579 

69  oi  45-75 

73.82 

.638 

.1868469 

3746 

68  oo  04.74 

77-26 

.688 

.205  1476 

3576 

69  02  59.53 

73-75 

.639 

.187  2213 

3742 

68  01  21.97 

77.19 

.689 

.205  5050 

3572 

69  04  13.25 

73-68 

1.640 

1.187  5953 

3739 

68  02  39.12 

77.12 

1.690 

1.205  8620 

3569 

69  05  26.90 

73.6i 

.641 

.  187  9691 

3735 

68  03  56.21 

77-05 

.691 

.206  2187 

3566 

69  06  40.48 

73-54 

.642 

.  188  3424 

3732 

68  05  13-22 

76.98 

.692 

.206  5751 

3562 

69  07  53.99 

73.48 

.643 

.188  7155 

3729 

68  06  30.16 

76.91 

.693 

.206  9312 

3559 

69  09  07.43 

73-41 

.644 

.189  0881 

3725 

68  07  47-03 

76.83 

.694 

.207  2869 

3556 

69  10  20.80 

73-34 

1.645 

I  .  189  4605 

3722 

68  09  03.83 

76.76 

1.695 

1.207  6423 

3552 

69  ii  34.11 

73-27 

.646 

.1898325 

37i8 

68  10  20.56 

76.69 

.696 

.207  9974 

3549 

69  12  47-34 

73-20 

-647 

.190  2041 

3715 

68  ii  37.22 

76.62 

•697 

.208  3521 

3546 

69  14  OO.5I 

73-13 

.648 

.190  5754 

68  12  53.80 

76.55 

.698 

.208  7065 

3542 

69  15  I3.6l 

73-07 

.649 

.  190  9463 

3708 

68  14  10.32 

76.48 

.699 

.209  0605 

3539 

69  16  26.64 

73-00 

1.650 

I.I9I  3170 

3704 

68  15  26.76 

76.41 

1.700 

1.209  4143 

3536 

69  17  39.6o 

72.93 

u 

jf 

wsechu 

2tan-'(e«)-900 

<•»  tech  u 

u 

"•"-'<">-i 

usechu 

"•"-""^ 

-sechu 

SMITHSONIAN  TABLES 


292 


The  Gudermannian. 


u 

QdU 

«F0' 

gd  u 

o.Fo' 

u 

gdu 

«FO' 

gd  u 

<oF0' 

0    /     // 

„ 

0    /     // 

// 

1.700 

1.209  4H3 

3536 

69  17  39.60 

72.93 

1.750 

1.226  6847 

3374 

70  17  01.89 

69.59 

.701 

.209  7677 

3532 

69  18  52.50 

72.86 

•  751 

.227  0219 

3370 

70  18  11.44 

69.52 

.702 

.210  1208 

3529 

69  20  05.32 

72.79 

.752 

.227  3588 

3367 

70  19  20.93 

69.45 

.703 

.210  4735 

3526 

69  21  18.08 

72.72 

•  753 

.227  0954 

3364 

70  20  30.35 

69.39 

.704 

.210  8259 

3522 

09  22  30.77 

72.66 

•  754 

.228  03l6 

2361 

70  21  39.71 

69.32 

1.705 

I.  211  1780 

3519 

69  23  43-39 

72.59 

1.755 

1.228  3676 

3358 

70  22  49.00 

69.26 

.706 

.211  5297 

35l6 

69  24  55-95 

72.52 

.756 

.228  7032 

3355 

70  23  58.23 

69.19 

.707 

.211  88l2 

3513 

69  26  08.43 

72-45 

•  757 

.229  0385 

3351 

70  25  07-39 

69.13 

.708 

.212  2323 

3509 

69  27  20.85 

72.38 

.758 

.229  3735 

3348 

70  26  16.48 

69.06 

.709 

.212  5830 

5506 

69  28  33.20 

72.32 

•  759 

.229  7082 

3345 

70  27  25.51 

69.00 

1.710 

I.  2  12  9335 

3503 

69  29  45.49 

72.25 

1.760 

1.230  0425 

3342 

70  28  34-48 

68.93 

.711 

.213  2836 

3499 

69  30  57.70 

72.18 

.761 

.230  3765 

3339 

70  29  43.38 

68.87 

.712 

.213  6334 

3496 

69  32  09.85 

72.11 

.762 

.230  7103 

3336 

70  30  52.22 

68.80 

.713 

.213  0828 

3493 

69  33  21.93 

72.05 

.763 

.231  0437 

3333 

70  32  00.09 

68.74 

.714 

.214  3319 

3490 

69  34  33-94 

71.98 

.764 

.231  3768 

3329 

70  33  09.69 

68.6> 

1.715 

1.214  6807 

3486 

69  35  45.89 

71.91 

1.765 

1.231  7006 

3326 

70  34  18.33 

68.61 

.716 

.215  0292 

3483 

69  36  57.76 

71.84 

.766 

.232  0420 

3323 

70  35  26.91 

68.54 

.717 
.718 

.215  3774 
.215  7252 

348o 
3477 

69  38  09.57 
69  39  21.32 

71.78 
71.71 

.767 
.768 

.232  3742 
.232  7060 

3320 
3317 

70  36  35.42 
70  37  43-87 

68.48 
68.42 

.719 

.216  0727 

3473 

69  40  32.99 

71.64 

.769 

.233  0376 

33M 

70  38  52.25 

68.35 

1.720 

I.  216  4198 

3470 

69  41  44.60 

71.58 

1.770 

1.233  3688 

3311 

70  40  00.57 

68.29 

.721 

.216  7667 

3467 

69  42  56.  14 

7i.5i 

•  771 

.233  6997 

3307 

70  41  08.83 

68.22 

.722 

.217  1132 

3464 

69  44  07.62 

71.44 

.772 

.234  0303 

3304 

70  42  17.02 

68.16 

.723 

.217  4594 

3400 

69  45  19.02 

71.37 

•  773 

.234  3606 

3301 

70  43  25.14 

68.09 

.724 

.217  8053 

3457 

69  46  30.37 

7i.3i 

•774 

.234  6905 

3298 

70  44  33.20 

68.03 

1.725 

i.  218  1508 

3454 

69  47  41.64 

71.23 

1.775 

1.235  O2O2 

3295 

7045  41.20 

67-96 

.726 

.218  4060 

3451 

69  48  52.85 

71.16 

.776 

•235  3495 

3292 

70  46  49.13 

67.90 

.727 

.218  8409 

3447 

69  50  03.99 

71.10 

•  777 

.235  6786 

3289 

70  47  57-00 

67.84 

.728 

.219  1855 

3444 

69  51  15.06 

71.03 

.778 

.236  0073 

3286 

70  49  04.80 

67.77 

.729 

.219  5297 

3441 

69  52  26.06 

70.96 

•  779 

.236  3357 

3283 

70  50  12.54 

67.71 

1.730 

I.2I98737 

3438 

69  53  37-90 

70.00 

1.780 

1.236  6638 

3279 

70  51  20.22 

67.64 

.731 

.220  2173 

3434 

69  54  47.88 

70.83 

.781 

.236  9916 

3276 

70  52  27.83 

67.58 

.732 

.220  5605 

3431 

69  55  58.68 

70.76 

.782 

.237  3i9i 

3273 

70  53  35.38 

67.52 

.733 

.220  0035 

3428 

69  57  09.42 

70.70 

.783 

.237  6463 

3270 

70  54  42.87 

67.45 

•  734 

.221  2461 

3425 

69  58  20.  10 

70.63 

.784 

.237  9731 

3267 

70  55  50.29 

67.39 

1.735 

I.  221  5885 

3422 

69  59  30.71 

70.56 

1.785 

1.238  2097 

3264 

70  56  57.65 

67.33 

.736 

.221  9304 

3418 

70  oo  41.25 

70.50 

.786 

.238  6259 

3261 

70  58  04.94 

67.26 

•  737 

.222  2721 

3415 

70  01  51.72 

70.43 

.787 

.238  9519 

3258 

70  59  12.17 

67.20 

.738 

.222  6135 

3412 

70  03  02.13 

70.37 

.788 

.239  2775 

3255 

71  oo  19.34 

67.13 

•  739 

.222  9545 

3409 

70  04  12.47 

70.30 

.789 

.239  6028 

3252 

71  01  26.44 

67.07 

1.740 

1.223  2952 

3405 

70  05  22.75 

70.23 

1.790 

1.2399279 

3249 

71  02  33.48 

67.01 

.741 

.223  6356 

3402 

70  06  32.96 

70.18 

.791 

.240  2526 

3246 

71  03  40.46 

66.94 

•  742 

.223  9757 

3399 

70  07  43.10 

70.11 

.792 

.240  5770 

3243' 

71  04  47-37 

66.88 

•743 

.224  3154 

3396 

70  08  53-18 

70.05 

•  793 

.240  9011 

3239 

71  05  54-22 

66.82 

•  744 

.224  6548 

3393 

70  10  03.19 

69.98 

.794 

.241  2249 

3236 

71  07  01.01 

66.76 

1.745 

1.224  9940 

3390 

70  ii  13.14 

69.91 

1.795 

1.241  5483 

3233 

71  08  07.73 

66.69 

.746 

.225  3328 

3386 

70  12  23.02 

69.85 

.796 

.241  8715 

3230 

71  09  14.39 

66.63 

•  747 

.225  6712 

3383 

70  13  32.84 

69.78 

•  797 

.242  1044 

3227 

71  10  20.99 

66.57 

.748 

.226  0094 

338o 

70  14  42.59 

69.72 

.798 

.242  5170 

3224 

71  II  27.52 

66.50 

•  749 

.226  3472 

3377 

70  15  52.27 

69.65 

•  799 

.242  8392 

3221 

71  12-  33-99 

66.44 

1.750 

1.226  6847 

3374 

70  17  01.89 

69.59 

1.800 

1.243  1612 

3218 

71  13  40.40 

66.38 

u 

2  tan-He")— 

«>sechu 

atan-Keih-SO0 

w  sech  u 

u 

2tan-Ke«)-!5 

wsechu 

Ztan-Keuh-eO0 

co  sech  u 

SMITHSONIAN  TABLES 


293 


The  Gudermannian. 


u 

gd  u 

O>FO' 

gd  u 

O.FO' 

U 

gdu 

«F0' 

odu 

«F</ 

1.  800 

1.243'  1612 

3218 

o   /   // 

71  13  40.40 

66?38 

1.850 

1.258  8759 

3069 

72  07  41.78 

» 

63.30 

.801 

.243  4828 

3215 

71  14  46.75 

66.31 

.851 

.219  1826 

3066 

72  08  45.05 

63.24 

.802 

.243  8042 

3212 

71  15  53.03 

66.25 

.852 

.259  4890 

3063 

72  09  48.26 

63:18 

.803 

.244  1252 

3209 

71  16  59.25 

66.19 

.853 

.259  7952 

3060 

72  10  51.41 

63.12 

.804 

.244  4460 

3206 

71  18  05.41 

66.13 

.854 

.260  ion 

3057 

72  II  54.50 

63.06 

1.805 

1.244  7664 

3203 

71  19  11.50 

66.06 

1.855 

1.260  4066 

3054 

72  12  57.53 

63.00 

.806 

.245  0865 

3200 

71  20  17.53 

66.00 

.856 

.260  7119 

3051 

72  14  OO.5O 

62.94 

.807 

.245  4064 

3i97 

71  21  23.50 

65.94 

.857 

.261  0169 

3048 

72  15  03.41 

62.88 

.808 

.245  7259 

3i94 

71  22  29.41 

65.88 

.858 

.261  3216 

3046 

72  16  06.26 

62.82 

.809 

.246  0451 

3191 

71  23  35.26 

65.81 

.859 

.261  6260 

3043 

72  17  09.05 

62.76 

1.810 

1.246  3640 

3188 

71  24  41.04 

65.75 

1.860 

1.261  9302 

3040 

72  18  11.78 

62.70 

.811 

.246  6827 

3185 

71  25  46.76 

65.69 

.861 

.262  2340 

3037 

72  19  14.45 

62.64 

.812 

.247  ooio 

3182 

71  26  52.42 

65.63 

.862 

.262  5375 

3034 

72  20  17.06 

62.58 

.813 

.247  3100 

3i79 

71  27  58.01 

65.56 

.863 

.262  8408 

3031 

72  21  I9.6l 

62.52 

.814 

.247  6367 

3176 

71  29  03.54 

65.50 

.864 

.263  1438 

3028 

72  22  22.  IO 

62.46 

1.815 

1.247  9541 

3i73 

71  .30  09.02 

65.44 

1.865 

1.263  4464 

3025 

72  23  24.54 

62.40 

.816 

.248  2712 

3170 

71  31  14.42 

65.38 

.866 

.263  7488 

3022 

72  24  26.91 

62.34 

.817 

.248  5880 

3167 

71  32  19.77 

65.32 

.867 

.264  0509 

3020 

72  25  29.22 

62.28 

.818 

.248  9046 

3164 

71  33  25.06 

65.25 

.868 

.264  3527 

3017 

72  26  31.47 

62.22 

.819 

.249  2208 

3161 

71  34  30.28 

65.19 

.869 

.264  6543 

3014 

72  27  33-67 

62.16 

1.820 

1.249  5367 

3158 

7i  35  35-44 

65.13 

1.870 

1.264  9555 

3011 

72  28  35.80 

62.11 

.821 

.249  8523 

3i55 

71  36  40.54 

65.07 

.871 

.265  2565 

3008 

72  29  37-88 

62.05 

.822 

.250  1676 

3152 

71  37  45.58 

65.01 

.872 

.265  5571 

3005 

72  30  39.90 

61.99 

.823 

.250  4826 

3i49 

71  38  50.56 

64.95 

.873 

.265  8575 

3002 

72  31  41-85 

61.93 

.824 

.250  7973 

3146 

71  39  55-47 

64.88 

.874 

.266  1576 

2999 

72  32  43-75 

61.87 

1.825 

1.251  1118 

3U3 

71  41  00.32 

64.82 

1.875 

1.266  4574 

2997 

72  33  45-59 

61.81 

.826 

.251  4259 

3140 

71  42  05.11 

64.76 

.876 

.266  7569 

2994 

72  34  47.37 

6i.75 

.827 

.251  7397 

3i37 

71  43  09.84 

64.70 

.877 

.267  0562 

72  35  49-09 

61.69 

.828 

.252  0532 

3i34 

71  44  14.51 

64.64 

.878 

.267  3551 

2988 

72  36  50.75 

61.63 

.829 

.252  3664 

3131 

71  45  19.12 

64.58 

.879 

.267  6538 

2985 

72  37  52.36 

6i.57 

1.830 

1.252  6794 

3128 

71  46  23.67 

64.52 

1.880 

1.267  9521 

2982 

72  38  53-90 

61.52 

.831 

.252  9920 

3125 

71  47  28.15 

64.45 

.881 

.268  2502 

2980 

72  39  55-39 

61.46 

.832 

.253  3043 

3122 

71  48  32.57 

64.39 

.882 

.268  5480 

2977 

72  40  56.82 

61.40 

.833 

.253  6164 

3119 

71  49  36.94 

64.33 

.883 

.268  8456 

2974 

72  41  58.19 

61.34 

.834 

.253  9281 

3116 

71  5041.24 

64.27 

.884 

.269  1428 

2971 

72  42  59.50 

61.28 

1.835 

1.254  2396 

3113 

71  51  45.48 

64.21 

1.885 

1.269  4308 

2068 

72  44  00.75 

61.22 

.836 

.254  5507 

3110 

71  52  49.66 

64.15 

.886 

.269  7364 

2965 

72  45  01.94 

61.16 

.837 

.254  8616 

3107 

71  53  53-77 

64.09 

.887 

.270  0328 

2962 

72  46  03.08 

6i.n 

.838 

.255  1721 

3104 

71  54  57.83 

64.03 

.888 

.270  3289 

2960 

7247  04.15 

61.05 

.839 

.255  4824 

3101 

71  56  01.83 

63.97 

.889 

.270  6248 

2957 

72  48  05.17 

60.99 

1.840 

1.255  7923 

3098 

71  57  05.76 

63.91 

1.890 

1.270  9203 

2954 

72  49  06.13 

60.93 

.841 

.256  IO2O 

3095 

71  58  09.64 

63-84 

.891 

.271  2156 

2951 

72  50  07.03 

60.87 

.842 

.256  4114 

3092 

71  59  13-45 

63.78 

.892 

.271  5106 

2948 

72  51  07.88 

60.81 

.843 

.256  7205 

3089 

72  oo  17.21 

63.72 

.893 

.271  8053 

2946 

72  52  08.66 

60.76 

.844 

.257  0293 

3086 

72  01  20.90 

63.66 

.894 

.272  0997 

2943 

72  53  09.39 

60.70 

1.845 

1.257  3378 

3084 

72  02  24.53 

63.60 

1.895 

1.272  3938 

2940 

7*2  54  10.06 

60.64 

.846 

.257  6460 

3081 

72  03  28.10 

63.54 

.896 

.272  6877 

2937 

72  55  10.67 

60.58 

.847 

.257  9539 

3078 

72  04  31.61 

63.48 

.897 

.272  9812 

2934 

72  56  11.23 

60.52 

.848 

.258  2615 

3075 

72  05  35.06 

63.42 

.898 

.273  2745 

2932 

72  57  11.72 

60.47 

.849 

.258  5688 

3072 

72  06  38.45 

63-36 

.899 

.273  5675 

2929 

72  58  12.  16 

60.41 

1.850 

1.2588759 

3069 

72  07  41.78 

63.30 

1.900 

1.273  8603 

2926 

72  59  12.54 

60.35 

u 

2tan-1(e»)-~ 

<•>  sech  u 

2tan-1(e«)-900 

wsechu 

u 

2tan-'(e»)-2 

o>  sech  u 

2tan-J(e«)-90° 

»  sech  u 

SMITHSONIAN  TABLES 


294 


The  Gudermannian. 


u 

gdu 

»Fo' 

gd  u 

«F0' 

u 

gd  u 

™ 

gdu 

" 

0    /    // 

m 

o   /   // 

m 

1.900 

1.273  8603 

2926 

72  59  12.54 

60.35 

1-950 

1.288  1451 

2789 

73  48  19.01 

57-53 

.901 

.274  1527 

2923 

73  oo  12.86 

60.29 

.951 

.288  4239 

2786 

73  49  16.51 

57-47 

.902 

.274  4449 

2920 

73  oi  13.13 

60.24 

.952 

.288  7024 

2784 

73  50  13-95 

57.42 

.903 

.274  7368 

2918 

73  02  13.33 

60.  18 

•953 

.2889806 

2781 

73  51  11.34 

57.36 

.904 

.275  0284 

2915 

73  03  13.48 

60.12 

•954 

.289  2586 

2778 

73  52  08.68 

57.31 

1.005 

1.275  3197 

2912 

73  04  13.58 

60.06 

1.955 

1.289  5363 

2776 

73  53  05.96 

57.25 

.906 

.275  6108 

2909 

73  05  13.61 

60.  oi 

.956 

.289  8137 

2773 

73  5403.18 

57.20 

.907 

.275  9016 

2906 

73  06  13.59 

59-95 

.957 

.290  0009 

2770 

73  55  00.35 

57.14 

.908 

.276  1921 

2004 

73  07  13-51 

59.89 

.958 

.290  3678 

2768 

73  55  57.46 

57.09 

.909 

.276  4823 

2001 

73  08  13-37 

59.83 

•  959 

.290  6444 

2765 

73  56  54.52 

57-03 

1.910 

1.276  7722 

2898 

73  09  13.18 

59.78 

1.960 

1.290  9208 

2762 

73  57  51.53 

56.98 

.911 

.277  0619 

2895 

73  10  12.92 

59.72 

.961 

.291  1969 

2760 

73  58  48.48 

56.92 

.912 

.277  3513 

2893 

73  II  12.62 

59.66 

.962 

.291  4727 

2757 

73  59  45.38 

56.87 

.913 

.277  6404 

2890 

73  12  12.25 

59.6i 

.963 

.291  7483 

2754 

74  oo  42.22 

56.81 

.914 

.277  9292 

2887 

73  13  11.83 

59-55 

.964 

.292  0236 

2752 

74  Oi  39-00 

56.76 

I.9I5 
.916 

1.278  2178 
.278  5061 

2884 
2881 

73  14  n.35 
73  15  10.81 

59.49 
59-43 

'•pjs 

.966 

1.292  2987 
.292  5734 

2749 
2746 

74  02  35.73 
74  03  32.41 

56.70 
56.65 

.917 

.278  7941 

2879 

73  16  10.22 

59.38 

.967 

.292  8480 

2744 

74  04  29.03 

56.60 

.918 

.279  0818 

2876 

73  17  09.56 

59-32 

.968 

.293  1222 

2741 

74  05  25.60 

56.54 

.919 

.279  3693 

2873 

73  18  08.86 

59.26 

.969 

.293  3962 

2739 

74  06  22.12 

56.49 

1.920 

1.279  6565 

2870 

73  19  08.09 

59-21 

1.970 

1.293  6699 

2736 

74  07  18.58 

56.43 

.921 

.279  9434 

2868 

73  20  07.27 

59.15 

.971 

.293  9434 

2733 

74  08  14.98 

56.38 

.922 

.280  2300 

2865 

73  21  06.39 

59-09 

•972 

.294  2166 

2731 

74  09  11.33 

56.32 

.923 

.280  5164 

2862 

73  22  05.46 

59.04 

.973 

.294  4895 

2728 

74  10  07.63 

56.27 

.924 

.280  8024 

2859 

73  23  04-47 

58.98 

.974 

.294  7622 

2725 

74  II  03.87 

56.22 

1.925 

1.281  0883 

2857 

73  24  03.42 

58.92 

1.975 

1.295  0346 

2723 

74  12  00.06 

56.16 

.926 

.281  3738 

2854 

73  25  02.32 

58.87 

.976 

.295  3068 

2720 

74  12  56.20 

56.11 

.927 

.281  6590 

2851 

73  26  01.16 

58.81 

•977 

.295  5786 

2718 

74  13  52.28 

56.05 

.928 

.281  9440 

2849 

73  26  59-94 

58.76 

.978 

.295  8503 

2715 

74  14  48.30 

56.00 

.929 

.282  2288 

2846 

73  27  58.67 

58.70 

•979 

.296  1216 

2712 

74  15  44.28 

55-95 

1.930 

1.282  5132 

2843 

73  28  57-34 

58.64 

1.980 

1.296  3927 

2710 

74  16  40.20 

55.89 

•931 

.282  7974 

2840 

73  29  55.95 

58.59 

.981 

.2966636 

2707 

74  17  36.06 

55.84 

•  932 

.283  0813 

2838 

73  30  54.51 

58.53 

.982 

.296  9342 

2705 

74  18  31.87 

55.78 

.933 
•934 

.283  3649 
.283  6482 

2835 
2832 

73  3i  53.01 
73  32  51.46 

58.47 
58.42 

.983 

.984 

.297  2045 
.297  4745 

2702 
2699 

74  19  27.63 
47  20  23.34 

55.73 
55.68 

1-935 

1.283  9313 

2829 

73  33  49.85 

58.36 

1.985 

1.297  7443 

2697 

74  21  1^.99 

55.62 

.936 

.284  2141 

2827 

73  34  48.18 

58.31 

.986 

.298  0139 

2694 

74  22  14.58 

55-57 

.937 

.284  4967 

2824 

73  35  46.46 

58.25 

.987 

.298  2832 

2692 

74  23  10.13 

55.52 

.938 

.284  7789 

2821 

73  36  44-68 

58.19 

.988 

.298  5522 

2689 

74  24  05.62 

55.46 

.939 

.285  0609 

2819 

73  37  42.85 

58.14 

.989 

.298  8210 

2686 

74  25  01.05 

55.41 

1.040 

1.285  3427 

28l6 

73  38  40.96 

58.08 

1.990 

1.299  0895 

2684 

74  25  56.44 

55.36 

.941 

.285  6241 

2813 

73  39  39.01 

58.03 

.991 

.209  3577 

2681 

74  26  51.77 

55-30 

.942 

.285  9053 

28ll 

73  40  37-01 

57-97 

.992 

.299  6257 

2679 

74  27  47.04 

55-25 

•943 

.286  1862 

2808 

73  4i  34-95 

57.92 

•993 

.299  8934 

2676 

74  28  42.27 

55-20 

.944 

.2864669 

2805 

73  42  32.84 

57-86 

.994 

.300  1609 

2673' 

74  29  37.44 

55.14 

1.945 

1.286  7473 

2802 

73  43  30.68 

57.8o 

1.995 

1.300  4281 

2671 

74  30  32.55 

55.09 

.946 

.287  0274 

2800 

73  44  28.45 

57-75 

.996 

.300  6951 

2668 

74  31  27.62 

55.04 

•947 

.287  3072 

2797 

73  45  26.17 

57.69 

•997 

.300  9618 

2666 

74  32  22.63 

54.98 

.948 

.287  5868 

2794 

73  46  23.84 

57.64 

.998 

.301  2282 

2663 

74  33  17.59 

•949 

.287  8661 

2792 

73  47  21.45 

57.58 

.999 

.301  4944 

2661 

74  34  12.49 

54.88 

1.950 

1.288  1451 

2789 

73  48  19.01 

57-53 

2.000 

1.301  7603 

2658 

74  35  Q7.34 

54.83 

u 

2ta"-1(e°>-i 

co  sech  u 

«"^H* 

w  sech  u 

U 

7T 

CD  sech  u 

«™* 

w  sech  u 

SMITHSONIAN  TABLES 


2Q5 


The  Gudermannian. 


u 

Qdu 

wF0' 

gd  u 

wF0' 

u 

gd  u 

«F0' 

gdu 

«FO' 

2.000 

1.301  7603 

2658 

74  35  07-34 

54*83 

2.050 

1.314  7349 

2533 

o       /        // 

75  19  43-53 

a 

52.24 

.001 

.302  0260 

2655 

74  36  02.14 

54-77 

.051 

.314  988o 

2530 

75  20  35.75 

52.19 

.002 

.302  2914 

2653 

74  36  56.89 

54.72 

.052 

.315  2409 

2528 

75  21  27.91 

52.14 

.003 
.004 

.302  5566 
.302  8215 

2650 
2648 

74  37  51.58 
74  38  46.22 

54.67 
54.61 

.053 
.054 

.315  4936 
.315  7400 

2525 
2523 

75  22  20.03 
75  23  12.09 

52.09 
52.04 

2.005 

1.303  0861 

2645 

74  39  40.81 

54.56 

2.055 

I.3I5  0982 

2520 

75  24  04.11 

51.99 

.006 

.007 

.303  3505 
.303  6147 

2643 
2640 

74  40  35-35 
74  41  29.83 

54-51 
54.46 

.056 
.057 

.316  2501 
.316  5018 

2518 
2516 

75  24  56.07 
75  25  47.98 

51-94 

51.89 

.008 

.303  8786 

2638 

74  42  24.26 

54.40 

.058 

•316  7532 

2513 

75  26  39.85 

51.84 

.009 

.304  1422 

2635 

74  43  18.64 

54-35 

.059 

.317  0044 

2511 

75  27  31.66 

5L79 

2.OIO 

1.304  4056 

2633 

74  44  12.97 

54-30 

2.060 

1.317  2554 

2508 

75  28  23.42 

51.74 

.Oil 

.304  6687 

2630 

74  45  07.24 

54.25 

.061 

.317  5o6i 

2506 

75  29  15.14 

51.69 

.012 

.304  0316 

2627 

74  46  01.46 

54.19 

.062 

.317  7566 

2503 

75  30  06.80 

51.64 

.013 

.305  1942 

2625 

74  46  55.63 

54.14 

.063 

.318  0068 

2501 

75  30  58.41 

5L59 

.014 

.305  4566 

2622 

74  47  49-74 

54.09 

.064 

.318  2568 

2499 

75  31  49.98 

51.54 

2.015 

1-305  7187 

2620 

74  48  43.8i 

54.04 

2.065 

1.318  5065 

2496 

75  32  41-49 

51.49 

.Ol6 

.305  9805 

2617 

74  49  37.82 

53-99 

.066 

.318  756o 

2494 

75  33  32.95 

51.44 

.017 

.306  2421 

2615 

74  50  31-78 

53-93 

.067 

.319  0053 

2491 

75  34  24.37 

51-39 

.018 

.306  5035 

2612 

74  51  25.69 

53-88 

.068 

.319  2543 

2489 

75  35  15.73 

51.34 

.OI9 

.306  7646 

26lO 

74  52  19.54 

53.83 

.069 

.319  5031 

2487 

75  36  07.04 

51.29 

2.O2O 

1.307  0254 

2007 

74  53  13.35 

53.78 

2.070 

L3I9  75i6 

2484 

75  36  58.31 

51.24 

.021 

.307  2860 

2605 

74  54  07.10 

53-73 

.071 

.319  9999 

2482 

75  37  49.52 

51-19 

.022 

.307  5464 

2OO2 

74  55  00.80 

53.67 

.072 

.320  2480 

2479 

75  38  40.69 

5LI4 

.023 

.307  8065 

2600 

74  55  54-45 

53.62 

.073 

.320  4958 

2477 

75  39  31-80 

51.09 

.024 

.3080663 

2597 

74  56  48.05 

53-57 

.074 

•320  7433 

2475 

75  40  22.87 

5L04 

2.O25 

1.308  3259 

2595 

74  57  41-59 

53.52 

2.075 

1.3209907 

2472 

75  41  13.89 

50-99 

.026 

•308  5853 

2592 

74  58  35.o8 

53-47 

.076 

.321  2378 

2470 

75  42  04.85 

50-94 

.027 

.308  8443 

2590 

74  59  28.52 

53.42 

.077 

.321  4846 

2467 

75  42  55-77 

50.89 

.028 

.309  1032 

2587 

75  oo  21.91 

53.36 

.078 

.321  7312 

2465 

75  43  46.64 

50.84 

.O29 

.309  3618 

2585 

75  oi  15.25 

53-31 

.079 

.321  9776 

2463 

75  44  37.46 

50.79 

2.030 

1.309  6201 

2582 

75  02  08.54 

53-26 

2.080 

1.322  2238 

2460 

75  45  28.23 

50.75 

.031 

.309  8782 

2580 

75  03  01.78 

53-21 

.081 

.322  4697 

2458 

75  46  18.95 

50.70 

.032 

.310  1361 

2577 

75  03  54-96 

53.i6 

.082 

.322  7153 

2455 

75  47  09.62 

50.65 

•033 

•310  3936 

2575 

75  04  48.09 

53.ii 

.083 

.322  9608 

2453 

75  48  00.24 

50.60 

.034 

.310  6510 

2572 

75  05  41.17 

53.06 

.084 

.323  2059 

2451 

75  48  50.82 

50.55 

2.035 

I.3IO  9081 

2570 

75  06  34-20 

53-00 

2.085 

1.323  4509 

2448 

75  49  41.34 

50.50 

.036 

.311  1649 

2567 

75  07  27.18 

52.95 

.086 

.323  6956 

2446 

75  50  31-82 

50-45 

.037 

.3H  4215 

2565 

75  08  20.  i  i 

52.90 

.087 

.323  9401 

2444 

75  51  22.25 

50.40 

.038 

.311  6779 

2562 

75  09  12.99 

52.85 

.088 

.324  1843 

2441 

75  52  12.62 

50-35 

.039 

.311  9340 

2560 

75  10  05.81 

52.80 

.089 

.324  4283 

2439 

75  53  02.95 

50.30 

2.040 

1.312  1898 

2557 

75  10  58.59 

52.75 

2.090 

1.324  6721 

2436 

75  53  53.23 

5O.26 

.041 

.312  4455 

2555 

75  II  5L3I 

52.70 

.091 

.324  9156 

2434 

75  54  43.46 

5O.2I 

.042 

.312  7008 

2552 

75  12  43.98 

52.65 

.092 

.325  1589 

2432 

75  55  33.65 

50.16 

.043 

.312  9559 

2550 

75  13  36.60 

52.60 

.093 

.325  4020 

2429 

75  56  23.78 

50.11 

.044 

.313  2108 

2547 

75  1429.17 

52.55 

.094 

.325  6448 

2427 

75  57  13-86 

50.06 

2.045 

I.3I3  4654 

2545 

75  15  21.69 

52.49 

2.095 

1.325  8874 

2425 

75  58  03.90 

50.01 

.046 

.313  7198 

2543 

75  16  14.16 

52.44 

.096 

.326  1297 

2422 

75  58  53-89 

49.06 

.047 

.313  9739 

2540 

75  17  06.58 

52.39 

.097 

.326  3718 

2420 

75  59  43.83 

49.92 

.048 

.314  2278 

2538 

75  17  58.95 

52.34 

.098 

.326  6137 

2418 

76  00  33-72 

49-87 

.049 

.314  48i5 

2535 

75  18  51.27 

52.29 

.009 

.326  8554 

2415 

76  oi  23.56 

49-82 

2.050 

I.3U  7349 

2533 

75  19  43.53 

52.24 

2.100 

1.327  0968 

2413 

76  02   13.36 

49-77 

u 

2  tan-He")-;; 

"  sech  u 

2tan-'(eu>-900 

"sechu 

u 

2  tan-He")-  2 

<»sechu 

2tan-1(e»)-900 

«•  sech  u 

SMITHSONIAN  TABLES 


296 


The  Gudermannian. 


u 

gd  u 

«F«>' 

gdu 

«F</ 

u 

gdu 

"F</ 

gdu 

O.FO' 

o   /   // 

// 

o   /   // 

0 

2.100 

1.327  0968 

2413 

76  02  13.36 

49-77 

2.150 

1.338  8732 

2298 

76  42  42.42 

47.41 

.101 

.327  3380 

2411 

76  O3  O3  .  I  I 

49-72 

.151 

•339  1029 

2296 

76  43  29.81 

47.36 

.102 

.327  5789 

2408 

76  03  52.80 

49.67 

.152 

•339  3325 

2294 

76  44  17.15 

47-32 

.103 

.327  8196 

2406 

76  04  42.45 

49.63 

.153 

•339  56i7 

2292 

76  45  04.44 

47-27 

.104 

.328  oooi 

2404 

76  05  32.06 

49.58 

.154 

.339  7908 

2290 

76  45  51-69 

47-23 

2.105 

1.328  3003 

2401 

76  06  21.  61 

49-53 

2.155 

1.340  0197 

2287 

76  46  38.89 

47.18 

.106 

.328  5403 

2399 

76  07  u.  n 

49.48 

.156 

.340  2483 

2285 

76  47  26.05 

47.13 

.107 

.328  7801 

2397 

76  08  00.57 

49-43' 

.157 

.340  4767 

2283 

76  48  13.16 

47-09 

.108 

.329  0197 

2394 

76  08  49.08 

49-39 

.158 

.340  7049 

2281 

76  49  00.23 

47.04 

.109 

.329  2590 

2392 

76  09  39-34 

49-34 

.159 

.340  9328 

2278 

76  49  47.25 

47.00 

2.  IIO 

1.329  4980 

2390 

76  10  28.66 

49.29 

2.160 

1.341  1605 

2276 

76  50  34-22 

46.95 

.III 

.329  7369 

2387 

76  n  17.92 

49.24 

.161 

.341  388l 

2274 

76  51  21.15 

46.90 

.112 

.329  9755 

2385 

76  12  07.14 

49-19 

.162 

.341  6153 

2272 

76  52  08.03 

46.86 

•113 

.330  2139 

2383 

76  12  56.31 

49-15 

.163 

.341  8424 

2270 

76  52  54.87 

46.81 

.114 

•330  4520 

2380 

76  13  45.43 

49-10 

.164 

.342  0693 

2267 

76  53  41.66 

46.77 

2.IIS 

1.330  6900 

2378 

76  14  34.51 

49-05 

2.165 

1.342  2959 

2265 

76  54  28.40 

46.72 

.116 

.330  9277 

2376 

76  15  23.54 

49.00 

.166 

.342  5223 

2263 

76  55  iS.io 

46.68 

.117 

.331  1651 

2373 

76  16  12.52 

48.96 

.167 

.342  7485 

2261 

76  56  01.76 

46.63 

.118 

.331  4023 

2371 

76  17  01.45 

48.91 

.168 

.342  9744 

2259 

76  56  48.36 

46.59 

.119 

•331  6393 

2369 

76  17  50.33 

48.86 

.169 

.343  2002 

2256 

76  57  34-93 

46.54 

2.I2O 

I.33I  8761 

2367 

76  18  39-17 

48.81 

2.170 

1.343  4257 

2254 

76  58  21.45 

46.50 

.121 

.332  1127 

2364 

76  19  27.96 

48.77 

.171 

•343  6510 

2252 

76  59  07.92 

46.45 

.122 

.332  3490 

2362 

76  20  16.70 

48.72 

.172 

.343  8761 

2250 

76  59  54-35 

46.41 

.123 

.332  5850 

2360 

76  21  05.40 

48.67 

.173 

.344'  1010 

2248 

77  oo  40.73 

46.36 

.124 

.332  8209 

2357 

76  21  54.04 

48.62 

.174 

.344  3256 

2245 

77  oi  27.07 

46.31 

2.125 

1.333  0565 

2355 

76  22  42.64 

4858 

2.175 

1.344  5501 

2243 

77  02  13.36 

46.27 

.126 

•333  2919 

2353 

76  23  31.20 

48.53 

.176 

.344  7743 

2241 

77  02  59.61 

46.22 

.127 

•333  5271 

2350 

76  24  19.70 

48.48 

.177 

-344  9983 

2239 

77  03  45-8i 

46.18 

.128 

•333  7620 

2348 

76  25  08.  16 

48.44 

.178 

.345  2220 

2237 

77  04  31.06 

46.13 

.129 

•333  9967 

2346 

76  25  56.57 

48.39 

.179 

-345  4456 

2234 

77  05  18.08 

46.09 

2.I3O 

1.334  2312 

2344 

76  26  44.94 

48.34 

2.180 

1.345  6689 

2232 

77  06  04.14 

46.04 

.131 

•334  4054 

2341 

76  27  33.26 

48.29 

.181 

-345  8921 

2230 

77  06  50.17 

46.00 

.132 

•334  6995 

2339 

70  28  21.53 

48.25 

,.182 

.346  1150 

2228 

77  07  36.14 

45-95 

•133 

•334  9333 

2337 

76  29  09.75 

48.20 

.183 

.346  3377 

2226 

77  08  22.08 

45.91 

•134 

.335  1668 

2335 

76  29  57-93 

48.15 

.184 

.346  5601 

2224 

77  09  07.96 

45.87 

2.135 

1.335  4002 

2332 

76  30  46.06 

48.11 

2.185 

1.346  7824 

2221 

77  09  53.8i 

45.82 

.136 

•335  6333 

2330 

76  31  34.  14 

48.06 

.186 

.347  0044 

2219 

77  10  39-60 

45-78 

.137 

.335  8662 

2328 

76  32  22.18 

48.01 

.187 

.347  2262 

2217 

77  n  25.36 

45-73 

.138 

.336  0988 

2325 

75  33  10.17 

47-97 

.188 

.347  4478 

2215 

77  12  11.07 

45.69 

•139 

.336  3313 

2323 

76  33  58.11 

47.92 

.189 

.347  6692 

2213 

77  12  56.73 

45.64 

2.140 

1.336  5635 

2321 

76  34  46.01 

47.87 

2.190 

1.347  8904 

221  1 

77  13  42.35 

45-6o 

.141 

.336  7955 

2319 

76  35  33.86 

47.83 

.191 

.348  1114 

2208 

77  14  27.93 

45-55 

.142 

.337  0272 

2316 

76  36  21.66 

47-78 

.192 

.348  3321 

22O6 

77  15  13.46 

45-51 

•143 

.337  2588 

2314 

76  37  09.42 

47-73 

.193 

.348  5526 

22O4 

77  15  58.95 

45.46 

.144 

•337  4901 

2312 

76  37  57.13 

47.69 

.194 

.348  7729 

22O2 

77  16  44-39 

45.42 

2.145 

1.337  7212 

2310 

76  38  44-79 

47.64 

2.195 

1.348  9930 

220O 

77  17  29.79 

45.38 

.I46 

•337  9520 

2307 

76  39  32.41 

47-59 

.196 

.349  2129 

2108 

77  18  15.14 

45-33 

•147 

.338  1826 

2305 

76  40  19.98 

47.55 

.197 

.349  4326 

2ig6 

77  19  00.45 

45.29 

.148 

.338  4131 

2303 

76  41  07.51 

47-50 

.198 

.349  6520 

2193 

77  19  45.72 

45.24 

.149 

.338  6432 

2301 

76  41  54-99 

47.46 

.199 

•349  8713 

2IQI 

77  20  30.94 

45.20 

2.ISO 

1.338  8732 

2298 

76  42  42.42 

47-41 

2.  2OO 

1.3500903 

2189 

77  21  i6.ii 

45.16 

u 

2tan-Ke")~ 

wsechu 

2tan-Ke«)-90° 

w  sech  u 

U 

atan-Keu)— 

osechu 

2tan~1(eu)-900 

<•>  sech  u 

SMITHSONIAN  TABLES 


297 


The  Gude  rmannian. 


u 

gdu 

<oF0' 

gd  u 

«oF0' 

u 

odu 

«F0' 

Odu 

<oF0' 

0          /           // 

// 

O         4          // 

// 

2.2OO 

I.3SO  0003 

2189 

77  21  16.11 

45-l6 

2.250 

1.360  7733 

2085 

77  57  59-64 

43-00 

.201 

•350  3091 

2187 

77  22  01.25 

45-11 

.251 

.360  9817 

2083 

77  58  42.62 

42.96 

.202 

•350  5277 

2185 

77  22  46.34 

45-07 

.252 

.361  1809 

2081 

77  59  25.56 

42.92 

.203 

.350  7461 

2183 

77  23  31.38 

45.02 

.253 

.361  39/8 

2079 

78  oo  08.46 

42.88 

.204 

•350  9643 

2181 

77  24  16.38 

44.98 

•  254 

.361  6056 

2077 

78  oo  51.32 

42.83 

2.2O5 

1.351  1822 

2179 

77  25  01.34 

44-94 

2.255 

1.361  8132 

2075 

78  01  34.13 

42.79 

.206 

.351  4000 

2176 

77  25  46.25 

44-89 

.256 

.362  0205 

2073 

78  02  16.00 

42.75 

.207 

•351  6175 

2174 

77  26  31-12 

44.85 

•  257 

.362  2277 

2071 

78  02   59.63 

42.71 

.208 

•351  8348 

2172 

77  27  15.95 

44-80 

.258 

.362  4347 

2069 

78  03  42.32 

42.67 

.209 

•352  0519 

2170 

77  28  00.73 

44-76 

•259 

.362  6414 

2067 

78  04  24.97 

42.63 

2.210 

1.352  2688 

2168 

77  28  45-47 

44.72 

2.260 

1.362  8480 

2065 

78  05  07.57 

42.58 

.211 

•352  4855 

2166 

77  29  30.16 

44.67 

.261 

.363  0543 

2063 

78  05  50.13 

42.54 

.212 

.352  7020 

2164 

77  30  14-82 

44.63 

.262 

.363  2605 

2060 

78  06  32.66 

42.50 

.213 

•352  9183 

2162 

77  30  59-42 

44-59 

.263 

.363  4664 

2058 

7807  15.14 

42.46 

.214 

•353  1343 

2159 

77  31  43-99 

44.54 

.264 

.363  6722 

2056 

78  07  57-57 

42.42 

2.215 

1.353  3502 

2157 

77  32  28.51 

44-50 

2.265 

1.363  8777 

2054 

78  08  39.97 

42.38 

.216 

•353  5658 

2155 

77  33  12.99 

44.46 

.266 

.364  0831 

2052 

78  09  22.33 

42.33 

.217 

•353  7812 

2153 

77  33  57-42 

44-41 

.267 

.364  2882 

2050 

78  10  04.64 

42.29 

.218 

•353  0064 

2151 

77  34  41-81 

44-37 

.268 

.364  4931 

2048 

78  10  46.91 

42.25 

.219 

•354  2114 

2149 

77  35  26.16 

44-33 

'  .269 

.364  6979 

2046 

78  II  29.14 

42.21 

2.22O 

1.354  4262 

2147 

77  36  10.46 

44-28 

2.270 

1.364  9024 

2044 

78  12  11.33 

42.17 

.221 

.354  6408 

2145 

77  36  54-72 

44-24 

.271 

.365  1068 

2042 

78   12  53.48 

42.13 

.222 

•354  8552 

2143 

77  37  38.94 

44.20 

.272 

.365  3109 

2040 

78  13  35.59 

42.09 

.223 

.355  0693 

2141 

77  38  23.11 

44-15 

.273 

.365  5149 

2038 

78  14  17.66 

42.05 

.224 

•355  2833 

2138 

77  39  07.24 

44.11 

.274 

.365  7i86 

2036 

78  14  59-68 

42.00 

2.225 

1.355  4970 

2136 

77  39  51.33 

44-07 

2.275 

1.365  9221 

2034 

78  15  41.66 

41-06 

.226 

•  355  71.06 

2134 

77  40  35.38 

44.02 

.276 

.366  1255 

2032 

78  1  6  23.61 

41.92 

.227 

•355  9239 

2132 

77  41  19.38 

43.98 

.277 

.366  3286 

2030 

78  17  05.51 

41.88 

.228 

.356  1370 

2130 

77  42  03.34 

43-94 

.278 

.366  5316 

2028 

78  17  47-37 

41.84 

.229 

.356  3499 

2128 

77  42  47-25 

43.89 

.279 

.366  7343 

2026 

78  18  29.19 

41.80 

2.230 

I.356  5626 

2126 

77  43  3LI3 

43.85 

2.280 

1.366  9369 

2024 

78  19  10.97 

41.76 

.231 

.356  7751 

2124 

77  44  14.96 

43.8i 

.281 

.367  1392 

2023 

78  19  52.71 

41.72 

.232 

.356  9874 

2122 

77  44  58.74 

43-77 

.282 

.367  34  U 

2021 

78  20  34-40 

41.68 

•233 

.357  2095 

2I2O 

77  45  42.49 

43.72 

.283 

.367  5433 

2OI9 

78  21  16.06 

41.64 

•234 

•  357  4H4 

2118 

77  4626.19 

43-68 

.284 

.367  7451 

2017 

78  21  57.68 

41.60 

2.235 

1.357  6230 

2116 

77  47  09.85 

43.64 

2.285 

1.367  9466 

2015 

78  22>  39.25 

41.55 

.236 

•357  8345 

2114 

77  47  53-47 

43.6o 

.286 

.368  1480 

2013 

78  23  20.78 

41.51 

.237 

.358  0457 

2III 

77  48  37-04 

43-55 

.287 

.368  3492 

2OII 

78  24  02.28 

41.47 

.238 

.358  2568 

2IO9 

77  49  20.57 

43.51 

.288 

.368  5501 

2OO9 

78  24  43-73 

4L43 

•239 

•358  4676 

2107 

77  50  04.06 

43-47 

.289 

.368  7509 

2007 

78  25  25.14 

41.39 

2.24O 

.241 

1.3586783 
.358  8887 

2105 
2103 

77  50  47-51 
77  51  30.91 

43-43 
43.38 

2.290 

.291 

..3689515 
.369  1519 

2005 
2003 

78  26  06.51 

78  26  47-85 

41-35 
41.31 

.242 

.359  0989 

2101 

77  52  14.27 

43-34 

.292 

.369  3521 

'    2OOI 

78  27  29.  14 

41.27 

.243 

.359  3089 

2099 

77  52  57-59 

43.30 

.293 

.369  5520 

1999 

78  28  10.39 

41.23 

.244 

•359  5i87 

2097 

77  53  40.87 

43-26 

.294 

.369  75i8 

1997 

78  28  51.60 

41.19 

2.245 

1.359  7283 

2095 

77  54  24.10 

43-21 

2.295 

1.369  95U 

1995 

78  29  32.77 

4LI5 

.246 

•359  9377 

2093 

77  55  07.29 

43.17 

.296 

.370  1508 

1993 

78  30  13.89 

41.11 

.247 

.360  1469 

2091 

77  55  50.44 

43.13 

.297 

•370  3500 

1991 

78  30  54.98 

41.07 

.248 

.360  3559 

2089 

77  56  33-55 

43-09 

.298 

.370  5490 

1989 

78  31  36.03 

41.03 

.249 

.360  5647 

2087 

77  57  16.62 

43-04 

.299 

•370  7479 

1987 

78  32  17.04 

40.99 

2.25O 

1.3607733 

2085 

77  57  59.64 

43-00 

2.300 

1-370  9465 

1985 

78  32  58.01 

40.95 

U 

2tan-'(e»)-£ 

usechu 

Ztan-'Ce'O-SO0 

u  sech  u 

u 

2tan-'(eu)-J 

wsechu 

atan-He'O-SO0 

wsechu 

SMITHSONIAN  TABLES 


298 


The  Gudermannian. 


u 

gd  u 

«Fu' 

gd  u 

<oF0' 

u 

gd  u 

«F0' 

gdu 

<-F0' 

2.300 

1.370  9465 

1985 

78°  32'  s8''oi 

40-95 

2.350 

1.380  6331 

1800 

o   /   // 

79  06  16.03 

38^ 

.301 

.371  1449 

1983 

78  33  38.94 

40.91 

•  351 

.380  8221 

1888 

79  06  55-00 

38.9. 

.302 

•371  3431 

I98l 

78  34  19-82 

40.87 

•  352 

.381  0108 

1886 

79  07  33-93 

38.9 

.303 

.371  5412 

1979 

78  35  00.67 

40.83 

•353 

.381  1994 

1885 

79  08  12.  82 

38.8: 

.304 

•371  7390 

1977 

78  35  41.48 

40.79 

•354 

.381  3877 

1883 

79  08  51-67 

38.  a 

2.305 

I-37I  9367 

1975 

78  36  22.25 

40.75 

2.355 

1.381  5759 

1881 

79  09  30.49 

38.8< 

.306 

.372  1341 

1974 

78  37  02.98 

40.71 

.356 

.381  7639 

1879 

79  10  09.27 

38.7< 

.307 

.372  3314 

1972 

78  37  43-66 

40.66 

•357 

•381  9517 

1877 

79  IO  48.01 

38.7 

.308 

.372  5284 

1970 

78  38  24.31 

40.63 

.358 

.382  1394 

1875 

79  II  26.71 

38.0J 

.309 

•372  7253 

1968 

78  39  04.92 

40.59 

•359 

.382  3268 

1874 

79  12  05.37 

38.6, 

2.310 

1.372  9220 

1966 

78  39  45-49 

40.55 

2.360 

1.382  5141 

1872 

79  12  44.00 

38.6 

.311 

.373  n85 

1964 

78  40  26.02 

40.51 

.361 

.382  7012 

1870 

79  13  22.59 

38.5, 

.312 

•373  3148 

1962 

78  41  06.51 

40.47 

.362 

.382  8881 

1868 

79  14  01.14 

38.5 

.313 

•373  5109 

1960 

78  41  46.96 

40.43 

.363 

.383  0748 

1866 

79  14  39.65 

38.4< 

.314 

.373  7068 

1958 

78  42  27.37 

40.39 

•364 

.383  2613 

1864 

79  15  18.12 

38.4< 

2.315 

1-373  9025 

1956 

78  43  07.74 

40.35 

2.365 

1.383  4476 

1863 

79  15  56.56 

38.4: 

.316 

.3740980 

1954 

78  43  48.07 

40.31 

.366 

.383  6338 

1861 

79  16  34.96 

38.3^ 

.317 

•374  2934 

1952 

78  44  28.36 

40.27 

.367 

.383  8198 

1859 

79  17  13.32 

38.3^ 

.318 

•374  4885 

1950 

78  45  08.  6l 

40.23 

.368 

.384  0056 

1857 

79  17  51-64 

38.  3< 

.319 

•374  6835 

1949 

78  45  48.82 

40.19 

.369 

.384  1912 

i855 

79  18  29.93 

38.2. 

2.320 

1.374  8782 

1947 

78  46  28.99 

40.15 

2.370 

1.3843766 

1853 

79  19  08.  18 

38.2, 

.321 

.375  0728 

1945 

78  47  09.13 

40.11 

-371 

.384  5619 

1852 

79  19  46.39 

38.  K 

.322 

.375  2672 

1943 

78  47  49-22 

40.07 

•372 

.384  7470 

1850 

79  20  24.56 

38.1 

.323 

.375  4614 

1941 

78  48  29.28 

40.04 

•373 

.384  93i8 

1848 

79  21  02.70 

38.  L 

.324 

•375  6554 

1939 

78  49  09.29 

40.OO 

•374 

.385  1165 

1846 

79  21  40.80 

38.0J 

2.325 

1.375  8492 

1937 

78  49  49.27 

39.96 

2.375 

1.385  3011 

1844 

79  22  18.86 

38.0, 

1  .326 

.376  0428 

1935 

78  50  29.21 

39.92 

.376 

.385  4854 

1843 

79  22  56.88 

38.  a 

.327 

.376  2362 

1933 

78  51  09.10 

39.88 

.377 

.385  6696 

1841 

79  23  34.87 

37-9, 

.328 

.376  4295 

1931 

78  51  48.96 

39.84 

.378 

.385  8536 

1839 

79  24  12.  81 

37.9. 

.329 

.376  6225 

1930 

78  52  28.78 

39.80 

•  379 

.386  0374 

1837 

79  24  50.73 

37-8< 

2.330 

1.376  8154 

1928 

78  53  08.56 

39.76 

2.380 

1.386  2210 

1835 

79  25  28.60 

37.& 

.331 

.377  0081 

1926 

78  53  48.30 

39.72 

.381 

.386  4044 

1833 

79  26  06.44 

37-8: 

.332 

.377  2006 

1924 

78  54  28.01 

39-68 

.382 

.386  5877 

1832 

79  26  44.24 

37-7* 

•333 

.377  3929 

1922 

78  55  07.67 

39.64 

.383 

.386  7708 

1830 

79  27  22.00 

37-7- 

•334 

.377  5850 

1920 

78  55  47.29 

39.6i 

.384 

.386  9537 

1828 

79  27  59-73 

37-7 

2.335 

1.377  7709 

1918 

78  56  26.88 

39.57 

2.385 

1.387  1364 

1826 

79  28  37.41 

37.6; 

.336 

.377  9686 

1916 

78  57  06.43 

39-53 

.386 

.387  3189 

1824 

79  29  15.07 

37-6, 

•337 

.378  1601 

1914 

78  57  45-94 

39-49 

.387 

.387  5013 

1823 

79  29  52.68 

37-  6( 

.338 

.378  35i5 

1913 

78  58  25.40 

39-45 

.388 

.387  6834 

1821 

79  30  30.26 

37-  5< 

•  339 

.378  5427 

IQII 

78  59  04.84 

39.41 

.389 

•387  8655 

1819 

79  31  07.80 

37.5- 

2.340 

1.378  7336 

1909 

78  59  44.23 

39.37 

2.300 

1.388  0473 

1817 

79  31  45-30 

37-4< 

•341 

.378  9244 

1907 

79  oo  23.58 

39-33 

•  391 

.388  2289 

1816 

79  32  22.77 

37-4! 

•342 

•379  H50 

1905 

79  01  02.89 

39-30 

•  392 

.388  4104 

1814 

79  33  00.20 

37.4] 

1  -343 

•379  3054 

1903 

79  01  42.17 

39.26 

•  393 

.388  5917 

1812 

79  33  37-59 

37.3; 

•344 

•379  4957 

1901 

79  02  21.41 

39.22 

•  394 

.388  7728 

1810 

79  34  14.95 

37-3^ 

2-345 

1.3796857 

1899 

79  03  00.61 

39.18 

2.395 

1.3889537 

1808 

79  34  52.27 

37.  3< 

.346 

•379  8756 

1898 

79  03  39-77 

39.14 

.396 

•389  1345 

1807 

79  35  29.55 

37-  2( 

^348 

.380  0652 
.380  2547 

1896 
1894 

79  04  18.89 
79  04  57.97 

39.10 
39.06 

.397 
.398 

.389  3150 
.389  4954 

1805 
1803 

79  36  06.80 
79  36  44.01 

37.2: 
37-  K 

•  349 

.380  4440 

1892 

79  05  37-02 

39.03 

•  399 

.389  6757 

1801 

79  37  21.18 

37.  if 

2-350 

1.380  6331 

1890 

79  06  16.03 

38.99 

2.400 

1.3898557 

1800 

79  37  58.32 

37-1^ 

u 

2tan-1(e«)-£ 

ws'ch  u 

2  tan-Ke^-SO0 

<«>sech  u 

u 

2tan-J(eu)~ 

wsechu 

2tan-'(e«)-900 

««>  sech  u 

SMITHSONIAN  TABLES 


299 


The  Gude rmannian. 


u 

gd  u 

»Fo' 

gd  u 

wF0' 

u 

gd  u 

«Fo' 

gdu 

«F0' 

2.400 

1.3898557 

1800 

79  37  58.32 

37-12 

2.450 

1.3986356 

1713 

0    /     // 

80  08  09.31 

35-34 

.401 

•390  0356 

1798 

79  38  35-42 

37.08 

•  451 

.398  8069 

I7II 

80  08  44.63 

35.30 

.402 
.403 

•390  2153 
•390  3948 

1796 
1794 

79  39  12.48 
79  39  49.51 

37.05 
37-01 

.452 
.453 

•398  9779 
.399  1488 

I7IO 

1708 

80  09  19.91 

80  09  55.i6 

35.27 
35.23 

.404 

•390  5741 

1792 

79  40  26.50 

36.97 

•454 

.399  3195 

1706 

80  10  30.37 

35-20 

2.405 

1-390  7533 

1791 

79  41  03.45 

36.94 

2.455 

1.399  4901 

1705 

80  II  05.55 

35.i6 

.406 

•390  9323 

1/89 

79  41  40.37 

36.90 

.456 

.3996605 

1703 

80  II  40.70 

35.13 

.407 

.391  mi 

1787 

79  42  17-25 

36.86 

•457 

•399  8307 

1701 

80  12  I5.8l 

35-09 

.408 

.391  2897 

1785 

79  42  54.10 

36.83 

.458 

.400  0007 

1700 

80  12  50.88 

35.o6 

.409 

.391  4681 

1784 

79  43  30.91 

36.79 

•459 

.400  1706 

1698 

80  13  25.92 

35-02 

2.410 

1.391  6464 

1782 

79  44  07.68 

36.75 

2.460 

1.400  3403 

1696 

80  14  00.93 

34.99 

.411 

.391  8245 

1780 

79  44  44.42 

36.72 

.461 

.400  5099 

1695 

80  14  35-00 

34-95 

.412 

.392  0025 

1778 

79  45  21.12 

36.68 

.462 

.400  6793 

1693 

80  15  10.84 

34.92 

^413 

.392  1802 

1777 

79  45  57.78 

36.65 

•463 

.400  8485 

1691 

80  15  45-74 

34.89 

.414 

•392  3578 

1775 

79  46  34.41 

36.61 

.464 

.401  0175 

1690 

80  16  20.61 

34.85 

2.415 

1.392  5352 

1773 

79  47  11.00 

36.57 

2.465 

1.401  1864 

1688 

80  16  55-45 

34.82 

.416 

.392  7124 

1771 

79  47  47.56 

36.54 

.466 

.401  3551 

1686 

80  17  30.25 

34.78 

.417 

.392  8895 

1770 

79  48  24.08 

36.50 

.467 

.401  5237 

1685 

80  18  05.01 

34-75 

.418 

•393  0664 

1768 

79  49  00.57 

36.47 

.468 

.401  6921 

1683 

80  18  39.74 

34.71 

.419 

•393  2431 

1766 

79  49  37-02 

36.43 

.469 

.401  8603 

1681 

80  19  14.44 

34.68 

2.420 

1.393  4196 

1764 

79  50  13.43 

36.39 

2.470 

1.402  0283 

1680 

80  19  49.10 

34.65 

.421 

.393  596o 

1763 

79  50  49.8o 

36.36 

.471 

.402  1962 

1678 

So  20  23.73 

34.6i 

.422 

•393  7722 

1761 

79  51  26.15 

36.32 

.472 

.402  3639 

1676 

80  20  58.33 

34.58 

.423 

•393  9482 

1759 

79  52  02.45 

36.29 

•473 

.402  5315 

1675 

80  21  32.89 

34-54 

.424 

.394  1240 

1758 

79  52  38.72 

36.25 

•474 

.402  6989 

1673 

80  22  07.41 

34.51 

2.425 

1-394  2097 

1756 

79  53  14.96 

36.22 

2.475 

1.402  8661 

1672 

80  22  41.91 

34.48 

.426 

•394  4752 

1754 

79  53  51.15 

36.18 

.476 

.403  0332 

1670 

80  23  16.36 

34-44 

.427 

•394  6505 

1752 

79  54  27.32 

36.14 

•477 

.403  20OI 

1668 

80  23  50.79 

34-41 

.428 

.394  8257 

1751 

79  55  03.44 

36.11 

.478 

.403  3668 

1666 

80  24  25.18 

34-37 

.429 

.395  0006 

1749 

79  55  39-54 

36.07 

•479 

.403  5334 

1665 

80  24  59-54 

34-34 

2.430 

1.395  1754 

1747 

79  56  15.59 

36.04 

2.480 

1.403  6098 

1663 

80  25  33.86 

34-31 

.431 

.395  3501 

1745 

79  56  51.61 

36.00 

.481 

.403  8660 

1662 

80  26  08.15 

34-27 

.432 

•395  5245 

1744 

79  57  27.60 

35-97 

.482 

.404  0321 

1660 

80  26  42.40 

34-24 

•433 

•395  6988 

1742 

79  58  03.55 

35.93 

.483 

.404  1980 

1658 

8O  27  l6.O2 

34-20 

•434 

•395  8729 

1740 

79  58  39.46 

35.90 

.484 

.404  3637 

1657 

80  27  5O.8l 

34-17 

2-435 

1.396  0469 

1739 

79  59  15.34 

35-86 

2.485 

1.404  5293 

1655 

80  28  24.97 

34.14 

.436 

.396  2207 

1737 

79  59  5LI9 

35.83 

.486 

.404  6947 

1653 

80  28  59.09 

34-10 

•437 

.396  3943 

1735 

80  oo  26.99 

35-79 

.487 

.404  8600 

1652 

80  29  33.17 

34-07 

.438 

.396  5677 

1733 

80  01  02.77 

35.76 

.488 

.405  0251 

1650 

80  30  07.23 

34-04 

•439 

.396  7410 

1732 

80  01  38.51 

35.72 

.489 

.405  1900 

1648 

80  30  4L25 

34-00 

2.440 

1.396  9141 

1730 

80  02  14.21 

35.69 

2.490 

1.405  3548 

1647 

80  31  15.23 

33-97 

.441 

.397  0870 

1728 

80  02  49.88 

35.65 

.491 

.405  5194 

1645 

80  31  49-19 

33.94 

.442 

•397  2597 

1727 

80  03  25.51 

35.62 

.492 

.405  6838 

1644 

8O  32  23.IO 

33.90 

•443 

.397  4323 

1725 

80  04  oi.n 

35.58 

•  493 

.405  8481 

1642 

80  32  56.99 

33-87 

.444 

•397  6047 

1723 

80  04  36.67 

35-54 

•494 

.406  0122 

1640 

80  33  30.84 

33.84 

2-445 
.446 

1.397  7770 
•397  9490 

1722 
1720 

8O  05  12.  2O 

80  05  47.69 

35.51 
35.48 

2.495 
.496 

I.4O5  1762 
.406  3400 

1639 
1637 

80  34  04.66 
80  34  38.45 

33-80 
33-77 

•447 

.308  1209 

1718 

80  06  23.15 

35-44 

.497 

.406  5036 

1636 

80  35  12.  20 

33-74 

.448 

.398  2927 

1716 

80  06  58.57 

35.41 

.408 

.406  6671 

1634 

80  35  45-92 

33.70 

.449 

.398  4642 

1715 

80  07  33.96 

35-37 

.499 

.406  8304 

1632 

80  36  19.60 

33-<>7 

2.450 

1.3086356 

1713 

80  08  09.31 

35-34 

2.500 

1.4069936 

1631 

80  36  53-26 

33.64 

u 

2  tan-He0)-^ 

<•>  sech  u 

2tan-Hen)-900 

u>  sech  u 

u 

2tan-'(e«)-£ 

w  sech  u 

2tan-1(eu)-90° 

to  sech  u 

SMITHSONIAN  TABLES 


300 


The  Gude rmannian. 


u 

gd  u 

wF0' 

gd  u 

«Fo' 

u 

gdu 

wF0' 

fldu 

«F</ 

2.500 

1.406  9936 

1631 

o       /        // 

80  36  53.26 

33.64 

2.550 

1.414  9492 

1552 

o       /        // 

81  04  14.22 

// 
32.02 

.501 

.407  1566 

1629 

80  37  26.88 

33.60 

•  551 

.415  1043 

1551 

81  04  46.22 

31-98 

.502 

.407  3194 

1627 

80  38  00.46 

33.57 

.552 

.   .415  2593 

1549 

81  05  18.19 

3L95 

.503 

.407  4821 

1626 

80  38  34-01 

33.54 

.553 

.415  4142 

1548 

81  05  50.13 

31.92 

.504 

.407  6446 

1624 

80  39  07.54 

33-50 

.554 

.415  5688 

1546 

81  06  22.03 

31.89 

2.505 

1.407  8069 

1623 

80  39  41.02, 

33-47 

2.555 

1.415  7234 

1545 

81  06  53.91 

31-85 

.506 

.407  9691 

l62I 

80  40  14.47 

33-44 

.556 

.415  8778 

1543 

81  07  25.75 

31-83 

.507 

.408  1311 

1619 

80  40  47-90 

33-40 

•  557 

.416  0320 

1541 

Si  07  57.56 

31-80 

.508 

.408  2930 

1618 

80  41  21.28 

33-37 

.558 

.416  1860 

1540 

81  08  29.34 

31.76 

.509 

.408  4547 

1616 

80  41  54.64 

33-34 

-559 

.416  3400 

1538 

81  09  01.09 

31-73 

2.510 

1.408  6163 

1615 

80  42  27.96 

33.31 

2.560 

1.416  4937 

1537 

81  09  32.80 

31.70 

.511 

.408  7777 

1613 

80  43  01.25 

33-27 

.561 

.416  6473 

1535 

81  10  04.49 

31.67 

.512 

.408  9389 

1612 

80  43'  34.51 

33-24 

.562 

.416  8008 

1534 

81  10  36.14 

31.64 

.513 

.409  1000 

1610 

80  44  07-73 

33-21 

-563 

.416  9541 

1532 

81  ii  07.77 

31.61 

.514 

.409  2609 

1608 

80  44  40.92 

33-17 

-564 

.417  1073 

1531 

81  ii  39.36 

31.58 

2.515 

1.409  4216 

1607 

80  45  14.08 

33.14 

2.565 

1.417  2603 

1529 

81  12  10.92 

31-54 

.516 

.409  5822 

1605 

80  45  47-20 

33-11 

.566 

.417  4131 

1528 

81  12  42.45 

3I.5I 

.517 

.409  7427 

1604 

80  46  20.30 

33-08 

.567 

.417  5659 

1526 

81  13  13.95 

3L48 

.518 

.409  9029 

1602 

80  46  53.36 

33-04 

.568 

.417  7184 

1525 

81  13  45.41 

3L45 

.519 

.410  0631 

1600 

80  47  26.38 

33.01 

-569 

.417  8708 

1523 

81  14  16.85 

31.42 

2.520 

1.410  2230 

1599 

80  47  59.38 

32.98 

2.570 

1.418  0231 

1522 

81  14  48.25 

31-39 

.521 

.410  3828 

1597 

80  48  32.34 

32.95 

•  571 

.418  1752 

1520 

81  15  19.63 

3L36 

.522 

.410  5425 

1596 

80  49  05.27 

32.91 

•  572 

.418  3271 

1519 

Si  15  50.97 

3L33 

.523 

.410  7020 

1594 

80  49  38.  17 

32.88 

•  573 

.418  4789 

1517 

81  16  22.28 

31.30 

.524 

.410  8613 

1593 

80  50  11.03 

32.85 

•  574 

.418  6306 

1516 

81  16  53.56 

31.27 

2.525 

1.411  0205 

1591 

80  50  43-86 

32.82 

2.575 

1.418  7821 

I5H 

81  17  24.81 

31-23 

.526 

.411  1795 

1589 

80  51  16.66 

32.78 

.576 

.418  9334 

I5U 

81  17  56.03 

31.20 

.527 

.411  3384 

1588 

80  51  49-43 

32.75 

.577 

.419  0847 

I5H 

81  18  27.22 

3LI7 

.528 

.411  4971 

1586 

80  52  22.17 

32.72 

.578 

.419  2357 

1510 

Si  18  58.38 

3I.I4 

.529 

.411  6556 

1585 

80  52  54.87 

32.69 

•  579 

.419  3866 

1508 

81  19  29.50 

31.11 

2.530 

1.411  8140 

1583 

80  53  27.54 

32.65 

2.580 

1.419  5374 

1507 

81  20  00.60 

31-08 

.531 

.411  9722 

1582 

80  54  oo.  18 

32.62 

.581 

.419  6880 

1505 

81  20  31.67 

3i  .05 

.532 

.412  1303 

1580 

80  54  32.78 

32.59 

.582 

.419  8384 

1504 

Si  21  02.70 

31.02 

.533 

.412  2882 

1578 

So  55  05.36 

32-56 

.583 

.419  9888 

1502 

81  21  33.70 

30.99 

•  534 

.412  4460 

1577 

80  55  37.90 

32.53 

.584 

.420  1389 

1501 

8l   22  04.68 

30.96 

2.535 

1.412  6036 

1575 

80  56  10.41 

32.49 

2.585 

1.420  2889 

1499 

Si    22  35.62 

30.93 

.536 

.412  7611 

1574 

80  56  42.89 

32.46 

.586 

.420  4388 

1498 

81  23  06.53 

30.90 

•  537 

.412  9184 

1572 

80  57  15-33 

32.43 

.587 

.420  5885 

1496 

81  23  37.41 

30.87 

.538 

.413  0755 

1571 

80  57  47-75 

32.40 

.588 

.420  7381 

1495 

81  24  08.26 

30.84 

•  539 

.413  2325 

1569 

80  58  20.13 

32.37 

.589 

.420  8875 

1493 

81  24  39.09 

30.81 

2.540 

1.413  3893 

1568 

80  58  52.48 

32-33 

2.590 

1.421  0368 

1492 

81  25  09.88 

30.77 

•  541 

.413  5460 

1566 

So  59  24.80 

32.30 

•  591 

.421  1859 

1491 

81  25  40.63 

30.74 

•  542 

.413  7025 

1564 

So  59  57.o8 

32.27 

•  592 

.421  3349 

1489 

81  26  11.36 

30.71 

•  543 

.413  8589 

1563 

81  oo  29.34 

32.24 

.593 

.421  4837 

1488 

81  26  42.06 

30.68 

•  544 

.414  0151 

1561 

81  01  01.56 

32.21 

•  594 

.421  6324 

1486 

81  27  12.73 

30.65 

2.545 

1.414  1712 

1560 

81  oi  33-75 

32.17 

2.595 

1.421  7809 

1485 

81  27  43.37 

30.62 

.546 

.414  3271 

1558 

81  02  05.91 

32.14 

.596 

.421  9293 

1483 

81  28  13.98 

30.59 

•  547 

.414  4829 

1557 

81  02  38.03 

32.11 

.597 

.422  0776 

1482 

81  28  44-55 

30.56 

.548 

.414  6385 

1555 

81  03  10.13 

32.08 

.598 

.422  2257 

1480 

81  29  15.10 

30.53 

•  549 

.414  7939 

1554 

81  03  42.19 

32.05 

.599 

.422  3736 

1479 

81  29  45.62 

30.50 

2-550 

1.414  9492 

1552 

81  04  14.22 

32.02 

2.600 

1.422  5214 

1477 

81  30  i6.n 

30.47 

u 

2tan-Ke»)-£ 

0  sech  u 

2tan-1(e")-90° 

o>  sech  u 

u 

2tan-Keu)-£ 

»  sech  u 

2tan-1(e")-90° 

u>  sech  u 

SMITHSONIAN  TABLES 


301 


The  Gudermannian. 


u 

gd  u 

.* 

gd  u 

^ 

u 

gd  u 

»F0' 

gd  u 

~^T 

2.600 

1.422  5214 

1477 

0    /     // 

81  30  i6.n 

30*47 

2.650 

1.429  7283 

1406 

0    /    // 

81  55  02.63 

29.00 

.601 

.422  6691 

1476 

81  30  46.56 

30.44 

.651 

.4298688 

1405 

81  55  31.62 

28.97 

.602 

.422  8166 

1474 

81  31  16.99 

30.41 

.652 

.430  0092 

1403 

81  56  00.58 

28.94 

.603 

.422  9640 

1473 

81  31  47-39 

30.38 

.653 

•430  1495 

1402 

81  56  29.51 

28.92 

.604 

.423  III2 

1471 

81  32  17.75 

30.35 

.654 

.430  2896 

1400 

81  56  58.41 

28.89 

2.605 

1.423  2583 

1470 

81  32  48.09 

30.32 

2.655 

1.430  4296 

1399 

81  57  27.28 

28.86 

.606 

.423  4052 

1469 

81  33  18.40 

30.29 

.656 

•430  5694 

1^98 

81  57  56.12 

28.83 

.607 

.423  5520 

1467 

81  33  48.67 

30.26 

.657 

•430  7091 

1396 

81  58  24.94 

28.80 

.608 

.4236986 

1466 

81  34  18.92 

30.23 

.658 

.430  8487 

1395 

Si  58  53.72 

28.77 

.609 

.423  8451 

1464 

81  34  49-iU 

30.20 

.659 

.430  9881 

1394 

81  59  22.48 

28.74 

2.610 

1.423  9915 

1463 

81  35  19.32 

30.17 

2.660 

I.43I  1274 

1392 

81  59  51.21 

28.72 

.611 

.424  1377 

1461 

81  35  49.48 

30.14 

.661 

.431  2665 

1391 

82  oo  19.91 

28.69 

.612 

.424  2837 

1460 

81  36  19.61 

30.11 

.662 

•431  4055 

1389 

82  oo  48.58 

28.66 

.613 

.424  4297 

1458 

81  36  49-71 

30.08 

.663 

.431  5444 

1388 

82  01  17.23 

28.63 

.614 

•424  5754 

1457 

81  37  19.77 

30.05 

.664 

.431  6831 

1387 

82  01  45.84 

28.60 

2.615 

1.424  7211 

1456 

81  37  49-8i 

30.02 

2.665 

1.431  8217 

1385 

82  02  14.43 

28.57 

.6l6 

.4248665 

1454 

81  38  19-82 

29.99 

.666 

.431  9602 

1384 

82  O2  42.99 

28.55 

.617 

.425  0119 

1453 

81  38  49.80 

29.96 

.667 

.432  0985 

1383 

82  O3  11.52 

28.52 

.6l8 

.425  1571 

1451 

81  39  19.75 

29-93 

.668 

.432  2367 

1381 

82  O3  40.02 

28.49 

.619 

.425  3021 

1450 

81  39  49.67 

29.90 

.669 

•432  3747 

1380 

82  O4  O8.5O 

28.46 

2.62O 

1.425  4470 

1448 

81  40  19.56 

29.87 

2.670 

1.432  5127 

1378 

82  04  36.95 

28.43 

.621 

.425  5918 

1447 

81  40  49.42 

29.85 

.671 

.432  6504 

1377 

82  05  05.36 

28.40 

.622 

.425  7364 

1446 

81  41  19.25 

29.82 

.672 

.432  7881 

1376 

82  05  33-75 

28.38 

.623 

.425  8809 

1444 

81  41  49.05 

29.79 

.673 

.432  9256 

1374 

82  06  O2.  12 

28.35 

.624 

.426  0252 

1443 

81  42  18.82 

29.76 

.674 

.433  0629 

.  1373 

82  06  3O.45 

28.32 

2.625 

1.426  1694 

144,1 

81  42  48.56 

29.73 

2.675 

1.433  2002 

1372 

82  06  58.76 

28.29 

.626 

.426  3135 

1440 

81  43  18.28 

29.70 

.676 

.433  3373 

1370 

82  07  27.03 

28.26 

.627 

.426  4574 

1438 

81  43  47.96 

29.67 

.677 

.433  4742 

82  O7  55.28 

28.24 

.628 

.426  6012 

1437 

81  44  17-61 

29.64 

.678 

.433  6110 

1368 

82  08  23.51 

28.21 

.629 

.426  7448 

1436 

81  44  47-24 

29.61 

.679 

•433  7477 

1366 

82  08  51.70 

28.18 

2.630 

1.426  8883 

1434 

81  45  16.83 

29.58 

2.680 

1.433  8843 

1365 

82  09  19-86 

28.15 

.631 

.427  0316 

1433 

81  45  46.40 

29.55 

.681 

.434  0207 

1363 

82  09  48.00 

28.12 

.632 

.427  1748 

81  46  15.94 

29.52 

.682 

.434  1570 

1362 

82  10  16.11 

28.10 

.633 

.427  3179 

1430 

81  46  45-44 

29.49 

.683 

.434  2931 

1361 

82  10  44.20 

28.07 

.634 

.427  4608 

1428 

81  47  14.92 

29.46 

.684 

.434  4291 

1359 

82  ii  12.25 

28.04 

2.635 

1.427  6036 

1427 

81  47  44-37 

29-43 

2.685 

1.434  5650 

1358 

82  ii  40.28 

28.01 

.636 

.427  7462 

1426 

81  48  13.79 

29.41 

.686 

.434  7008 

1357 

82  12  08.28 

27.99 

.637 

.427  8887 

1424 

81  4843.18 

29.38 

.687 

.434  8364 

1355 

82  12  36.25 

27.96 

.638 

.428  0310 

1423 

81  49  12.55 

29.35 

.688 

.434  9719 

1354 

82  13  O4.I9 

27.93 

.639 

.428  1732 

1421 

81  49  41.88 

29.32 

.689 

.435  1072 

1353 

82  13  32.11 

27.90 

2.640 

1.428  3153 

1420 

81  50  ii.  18 

29.29 

2.690 

1.435  2424 

1351 

82  13  59-99 

27.87 

.641 

.428  4572 

1419 

81  50  40.46 

29.26 

.691 

•435  3775 

1350 

82  14  27.86 

27-85 

.642 

.428  5990 

1417 

81  51  09.70 

29.23 

.692 

•435  5124 

1349 

82  14  55.69 

27.82 

.643 

.428  7407 

1416 

81  51  38.92 

29.20 

.693 

.435  6472 

1347 

82  15  23.49 

27.79 

.644 

.428  8822 

1414 

81  52  08.11 

29.17 

.694 

•435  78i9 

1346 

82  15  51.27 

27.77 

2.645 

1.429  0236 

1413 

81  52  37-27 

29.14 

2.695 

1.435  9164 

1345 

82  16  19.02 

27.74 

.646 

.429  1648 

1412 

81  53  06.40 

29.12 

.696 

.436  0508 

1343 

82  16  46.75 

27.71 

.647 

.429  3059 

1410 

81  53  35-50 

29.09 

.697 

.436  1851 

1342 

82  17  14.44 

27.68 

.648 

.429  4468 

1409 

81  54  04.57 

29.06 

.698 

.436  3192 

82  17  42.11 

27.65 

.649 

.429  5876 

1407 

81  54  33.62 

29.03 

.699 

.436  4532 

1339 

82  18  09.75 

27.63 

2.650 

1.429  7283 

1406 

81  55  02.63 

29.00 

2.700 

1.436  5871 

1338 

82  18  37.36 

27.60 

U 

7T 

2 

u  sech  u 

"•"-"•^ 

wsechu 

u 

2  tan-He")-  jj 

wsechu 

2tan-'(e»)-90° 

wsechu 

SMITHSONIAN  TABLES 


302 


The  Gudermannian. 


. 

gdu 

„* 

gdu 

«, 

u 

gdu 

«-F0' 

gd  u 

-w 

2.700 

1.436  5871 

1338 

82°  18  37^36 

27.60 

2.750 

1.443  "44 

1273 

o   /   // 

82  41  03.70 

26^26 

.701 

.436  7209 

1337 

82  19  04.95 

27.57 

•  751 

.443'  2416 

1272 

82  41  29.95 

26.24 

.702 

.436  8545 

1335 

82  19  32.51 

27.54 

•  752 

.443  3688 

1271 

82  41  56.  18 

26.21 

.703 

.436  9879 

1334 

82  20  00.04 

27.52 

•  753 

.443  4958 

1270 

82  42  22.38 

26.19 

•704 

.437  1213 

1333 

82  20  27.54 

27.49 

.754 

.443  6227 

1268 

82  42  48.55 

26.16 

2.705 

1.437  2545 

1331 

82  2O  55.O2 

27.46 

2.755 

1.443  7495 

1267 

82  43  14.70 

26.14 

.706 

.437  3876 

1330 

82  21  22.47 

27.44 

.756 

.443  8761 

1266 

82  43  40.82 

26.11 

.707 

•437  5205 

1329 

82  21  49.89 

27.41 

•  757 

.444  0026 

1265 

82  44  06.02 

26.08 

.708 

.437  6533 

•  1327 

82  22  17.29 

27.38 

.758 

.444  1200 

1263 

82  44  32.99 

26.06 

.709 

.437  7860 

1326 

82  22  44.66 

27-35 

•  759 

.444  2553 

1262 

82  44  59.03 

26.03 

2.710 

1.437  9i86 

1325 

82  23  12.  OO 

27-33 

2.760 

1.444  3814 

1261 

82  45  25.05 

26.01 

.7ii 

.438  0510 

1324 

82  23  39.31 

27.30 

.761 

.444  5074 

1260 

82  45  51.04 

25.98 

.712 

.438  1833 

1322 

82  24  06.60 

27.27 

.762 

.444  6333 

1258 

82  46  17.01 

25.95 

•  713 

.438  3154 

1321 

82  24  33-85 

27.25, 

.763 

.444  7591 

1257 

82  46  42.95 

25.93 

.714 

.438  4475 

1320 

82  25  01.09 

27.22 

.764 

.444  8847 

1256 

82  47  08.87 

25.90 

2.715 

1.438  5794 

1318 

82  25  28.29 

27.19 

2.765 

ri.445  0102 

1255 

82  47  34.76 

25.88 

.7i6 

.438  7in 

1317 

82  25  55.47 

27.17 

.766 

•445  1356 

1253 

82  48  00.62 

25.85 

.717 

.438  8428 

1316 

82  26  22.63 

27.14 

.767 

.445  2609 

1252 

82  48  26.46 

25-83 

.718 

.438  9743 

1314 

82  26  49.75 

27.11 

.768 

.445  386o 

1251 

82  48  52.27 

25.86 

.719 

•439  1057 

1313 

82  27  16.85 

27.08 

.769 

•445  SHI 

1250 

82  49  18.06 

25.77 

2.720 

1.439  2369 

1312 

82  27  43-92' 

27.06 

2.770 

1.445  6360 

1248 

82  49  43.82 

25.75 

.721 

•439  3680 

1310 

•82  28  10.96 

27.03 

.771 

.445  7607 

1247 

82  50  09.56 

25.72 

.722 

-439  4990 

1309 

82  28  37.98 

27.00 

•  772 

.445  8854 

1246 

82  50  35.27 

25.70 

•  723 

•439  6299 

1308 

82  29  04.97 

26.08 

•  773 

.446  0099 

1245 

82  51  00.95 

25.67 

.724 

•439  7606 

1307 

82  29  31.94 

26.95 

•  774 

.446  1343 

1243 

82  51  26.61 

25.65 

2.725 

1.4398912 

1305 

82  29  58.87 

26.92 

2.775 

1.446  2586 

1242 

82  51  52.25 

25.62 

.726 

.440  0216 

1304 

82  30  25.79 

26.90 

.776 

.446  3827 

1241 

82  521  17.86 

25.60 

.727 

.440  1520 

1303 

82  30  52.67 

26.87 

•777 

.446  5068 

1240 

82  52  43.44 

25.57 

.728 

.440  2822 

1301 

82  31  19.53 

26.84 

.778 

.446  6307 

1238 

82  53  09.00 

25.55 

.729 

.440  4123 

1300 

82  31  46.36 

26.82 

.779 

.446  7545 

1237 

82  53  34-53 

25.52 

2.730 

1.440  5422 

1299 

82  32  13.16 

26.79 

2.780 

1.446  8781 

1236 

82  54  00.04 

25.49 

•  731 

.440  6720 

1298 

82  32  39.94 

26.76 

.781 

.447  0017 

1235 

82  54  25.52 

25.47 

.732' 

.440  8017 

1296 

82  33  06.69 

26.74 

.782 

.447  1251 

1234 

82  54  50.98 

25.44 

•  733 

.440  9313 

1295 

82  33  33.42 

26.71 

.783 

.447  2484 

1232 

82  55  16.41 

25.42 

•  734 

.441  0607 

1294 

82  34  oo.ii 

26.68 

.784 

.447  37i6 

1231 

82  55  41.81 

25-39 

2.735 

1.441  1900 

1292 

82  34  26.78 

26.66 

2.785 

1.447  4946 

1230 

82  56  07.19 

25.37 

.736 

.441  3192 

1291 

82  34  53.43 

26.63 

.786 

•447  6175 

1229 

82  56  32.55 

25.34 

.737 

.441  4483 

I2OO 

82  35  20.05 

26.61 

.787 

.447  7403 

1227 

82  56  57-88 

25.32 

.738 

.441  5772 

1289 

82  35  46.64 

26.58 

.788 

.447  8630 

1226 

82  57  23.  19 

25.29 

.739 

.441  7060 

1287 

82  36  13.21 

26.55 

.789 

.447  9856 

1225 

82  57  48.47 

25.27 

2.740 

1.441.8347 

1286 

82  36  39-75 

26.53 

2.790 

1.448  1080 

1224 

82  58  13.72 

25.24 

•  741 

.441  9632 

1285 

82  37  06.26 

26.50 

•  791 

.448  2303 

1223 

82  58  38.95 

25.22 

•  742 

.442  0916 

1283 

82  37  32-75 

26.47 

.792 

.448  3525 

122  1 

82  59  04.16 

25.19 

.743 

.442  2199 

1282 

82  37  59.21 

26.45 

•  793 

.448  4746 

I22O 

82  59  29.34 

25.I7 

.744 

.442  3481 

I28l 

82  38  25.64 

26.42 

•  794 

.4485966 

1219 

82  59  54.49 

25.14 

2.745 

1.442  476l 

1280 

82  38  52.05 

26.40 

2.795 

1.448  7184 

1218 

83  oo  19.62 

25.12 

.746. 

.747 

.442  6040 
•442  73i8 

12.78 
1277 

82  39  18.43 

82  39  44.79 

20.37 
26.34 

.796 
•  797 

.448  8401 
,448  9617 

1217 
1215 

83  oo  44.73 
83  oi  09.81 

25.09 
25.07 

.748 

.442  8594 

1276 

82  40  I'l  .  12 

26.32 

.798 

.449  0832 

1214 

83  oi  34.86 

25.04 

•  749 

.442  9870 

1275 

82  40  37.42 

26.29 

.799 

.449  2045 

1213 

83  oi  59-50 

25.02 

2.750 

1.443  H44 

1273 

82  41  03.70 

26.26 

2.800 

1.449  3258 

1212 

83  02  24.90 

24.99 

u 

JT 

o  sech  u 

2tan-1(e«)-90° 

o>  sech  u 

u 

7T 

to  sech  u 

2tan-1(e")-90° 

w  sech  u 

SMITHSONIAN  TABLES 


303 


The  Gude  rmannian. 


u 

gd  u 

«*>' 

gd  u 

«F0' 

u 

gd  u 

«F0' 

gdu 

«F0' 

2.800 

1.449  3258 

1212 

83  02  24.90 

24-99 

2.850 

1-455  2365 

H53 

o      /       // 
83  22  44.07 

23*78 

.801 

.449  4469 

1211 

83  02  49.88 

24.97 

.851 

•455  3517       H52 

83  23  07.84 

23.76 

.802 

.449  5679 

1209 

83  03  14.84 

24.94 

.852 

.455  4668       1151    83  23  31.58 

23.74 

.803 

.449  6888 

I208 

83  03  39-77 

24.92 

•853 

•455  5819       1150 

83   23   55.31 

23.71 

.804 

.449  8095 

1207 

83  04  04.68 

24.89 

.854 

.455  6968       1148 

83   24    19.01 

23.69 

2.805 

1.449  930i 

I2O6 

83  04  29.56 

24.87 

2.855 

1.455  8115        H47 

83   24  42.69 

23.67! 

.806 

.450  0507 

1205 

83  04  54.42 

24.85 

.856 

•455  9262        1146 

83  25  06.34 

23.64 

.807 

.450  1710 

1203 

83  05  19.25 

24.82 

.857 

.4560408,      1145 

83  25   29.97 

23.62 

.808 

.450  2913 

I2O2i 

83  05  44-06 

24.80 

.858 

.456  1552 

1144 

83  25  53.58 

23-59 

.809 

.450  4115 

I2OI 

83  06  08.84 

24-77 

.859 

.456  2696 

H43 

83  26  17.16 

23.57 

!  2.810 

1-450  5315 

I2OO 

83  06  33.60 

24.75 

2.860 

1.456  3838 

1142 

83  26  40.72 

23.55 

.8u 

.450  6514 

1199 

83  06  58.33 

24.72 

.861 

.456  4979 

1140 

83  27  04.25 

23.52 

.812 

.450  7712 

1198 

83  07  23.04 

24.70 

.862 

.456  6119 

1139 

83  27  27.77 

23.50 

.813 

.450  8909 

U96 

83  07  47-73 

24.67 

.863 

.456  7258 

1138 

83  27  51.26 

23.48 

.814 

.451  0105 

1  195 

83  08  12.39 

24.65 

.864 

.456  8395 

H37 

83  28  14.72 

23.45 

2.815 

1.451  1299 

1  194 

83  08  37.03 

24.62 

2.865 

1.456  9532 

1136 

83  28  38.16 

23-43 

.816 

.451  2492 

1  193 

83  09  01.64 

24.60 

.866 

.457  0667 

1135 

83  29  01.58 

23.41 

.817 

•451  3684 

1191 

83  09  26.23 

24.58 

.867 

.457  1801 

H34 

83  29  24.98 

23.38 

.818 

.451  4875 

1190 

83  09  50.79 

24.55 

.868 

•457  2935 

1  133 

83  29  48.35 

23.36 

.819 

.451  6065 

1189 

83  10  15.33 

24.53 

.869 

.457  4067 

II3I 

83  30  11.70 

23.34 

2.820 

I-45I  7253 

1188 

83  10  39.84 

24.50 

2.870 

1.457  5198 

1130 

83  30  35.03 

23.32 

.821 

.451  8441 

1187 

83  ii  04.33 

24.48 

.871 

.457  6327 

1129 

83  30  58.33 

23.29 

.822 

.451  9627 

1186 

83  ii  28.80 

24.45 

.872 

•457  7456 

1128 

83  31  21.  61 

23.27 

.823 

.452  0812 

1184 

83  ii  53.24 

24-43 

.873 

.457  8584 

1127 

83  31  44.87 

23.25 

.824 

.452  1995 

1183 

83    12   17.66 

24.41 

.874 

•457  9710 

1126 

83  32  08.  II 

23.22 

2.825 

1.452  3178 

1182 

83    12  42.O5 

24.38 

2.875 

1.4580835 

1  125 

83  32  31.32 

23.20 

.826 

•452  4359 

1181 

83    13  06.42 

24.36 

.876 

.458  1959 

1124 

83  32  54.50 

23.18 

.827 

.452  5540 

1180 

83   13  30.76 

24.33 

.877 

.458  3083 

1123 

83  33  17.67 

23.15 

.828 

.452  6719 

1178 

83  13  55.08 

24.31 

.878 

.458  4204 

II2I 

83  33  40.8i 

23.13 

.829 

•452  7897 

1  177 

83  14  19.38 

24.28 

.879 

.458  5325 

II2O 

83  34  03.93 

23.11 

2.830 

1.452  9073 

1176 

83  14  43.65 

24.26 

2.880 

1.458  6445 

III9 

83  34  27.03 

23.08 

.831 

.453  0249 

1175 

83  15  07.90 

24.24 

.881 

.458  7564 

1118 

83  34  50.10 

23.06 

1  .832 

•453  1423 

1  174 

83  15  32.12 

24.21 

.882 

.458  8681 

III7 

83  35  13.15 

23.04 

.833 

•453  2597 

1  173 

83  15  56.32 

24.19 

.883 

.458  9798 

1116 

83  35  36.18 

23.02 

.834 

•453  3769 

1171 

83  16  20.50 

24.16 

.884 

•459  0913 

IH5 

83  35  59.18 

22.99 

2.835 

1.453  4940 

1170 

83  16  44.65 

24.14 

2.885 

1.459  2027 

1114 

83  36  22.16 

22.97 

.836 

.453  6109 

1169 

83  17  08.78 

24.12 

.886 

.459  3140 

IM3 

83  36  45-12 

22.95 

.837 

.453  7278 

1168 

83  17  32.88 

24.09 

.887 

.459  4252 

mi 

83  37  08.06 

22.92 

.838 

.453  8445 

1167 

83  17  56.06 

24.07 

.888 

.459  5363 

I  IIO 

83  37  30.97 

22.90 

.839 

.453  96i2 

1166 

83  18  2  i.  02 

24.04 

.889 

.459  0473 

1109 

83  37  53-86 

22.88 

2.840 

1.454  0777 

1-165 

83  18  45.05 

24.02 

2.890 

1-459  758i 

1108 

83  38  16.73 

22.86 

.841 

.454  1941 

1163 

83  19  09.06 

24.00 

.891 

.4598689 

1107 

83  38  39.57 

22.83 

.842 

.454  3104 

1162 

83  19  33.04 

23-97 

.892 

•459  9795 

1106 

83  39  02.40 

22.  8l 

.843 

.454  4265 

1161 

83  19  57-01 

23-95 

.893 

.460  0901 

1105 

83  39  25.19 

22.79 

.844 

.454  5426 

1160 

83  20  20.94 

23.93 

.894 

.460  2005 

1104 

83  39  47-97 

22.77 

2.845 

1.454  6585 

ii59 

83  20  44-86 

23.90 

2.895 

1.460  3108 

1103 

83  40  10.73 

22.74 

.846 

•454  7743 

1158 

83   21    08.74 

23.88 

.896 

.460  4210 

I  IOI 

83  40  33.46 

.847 

.454  8900 

1156 

83   21    32.6l 

23.85 

.897 

.460  531  I 

1  100 

83  40  56.17 

22.70 

.848 

•455  0056 

ii55 

83   21    56.45 

23-83 

.898 

.460  6411 

1099 

83  41  18.85 

22.68 

.849 

.455  121  I 

ii54 

83   22  20.27 

23.81 

.899 

.460  7510 

1098 

83  41  4L52 

22.65 

2.850 

1.455  2365 

1  153 

83  22  44.07 

23.78 

2.000 

1.460  8607 

1097 

83  42  04.  16 

22.63 

u 

2tan-Ke°)-£ 

wsechu 

2  tan-He"  )-90° 

w  sech  u 

u 

2tan-Ke«)-£ 

wsechu 

2  tan-He")-  90° 

u>sech  u 

SMITHSONIAN  TABLES 


304 


The  Gudermannian. 


u 

gd  u 

iw 

gd  u 

»F</ 

u 

gd  u 

«FO' 

gdu 

o>F</ 

2.900 

1.460  8607 

1097 

o   y   // 

83  42  04.16 

22.63 

2.950 

1.466  21231 

1044 

o   /   // 

84  oo  28.00 

21.53 

.901 

.460  9704 

1096 

83  42  26.78 

22.  6l 

.951 

.466  3167 

1043 

84  oo  49.53 

21.51 

.902 

.461  0800 

1095 

83  42  49.37 

22.59 

•952 

.466  4209 

1042 

84  oi  11.03 

21.49 

.903 

.461  1894 

1094 

83  43  H.95 

22.56 

•953 

.466  5251 

1041 

84  oi  32.51 

21.47 

.904 

.461  2987 

1093 

83  43  34.50 

22.54 

•  954 

.466  6291 

1040 

84  oi  53-97 

21.45 

2.005 

1.461  4080 

1092 

83  43  57.03 

22.52 

2.955 

1.466  7330 

1039 

84  02  15.40 

21.43 

.906 

.461  5171 

1091 

83  44  19.54 

22.50 

.956 

.466  8368 

1038 

84  02  36.82 

21.40 

.007 

.461  6261 

IOOO 

83  44  42.02 

22.47 

•957 

.466  9406 

1037 

84  O2  58.21 

21.38 

.908 

•461  735O 

1088 

83  45  04.48 

22.45 

.958 

.467  0442 

1036 

84  03  19.58 

21.36 

.909 

.461  8438 

1087 

83  45  26.92' 

22.43 

•  959 

.467  1477 

1035 

84  03  40.93 

21.34 

2.910 

1.461  9525 

1086 

83  45  49-34 

22.41 

2.960 

1.467  2511 

1034 

84  04  02.27 

21.32 

.911 

.462  0610 

1085 

83  46  n.73 

2-2.38 

.961 

.467  3544 

1033 

84  04  23.57 

21.30 

.912 

.462  1695 

1084 

83  46  34.I-I 

22.36 

.062 

.467  4576 

1032 

84  04  44.86 

21.28 

.913 

.462  2779 

1083 

83  46  56.46 

22.34 

.963 

.467  5607 

1031 

84  05  06.  13 

21.26 

.914 

.462  3861 

1082 

83  47  18.79 

22.32 

.964 

.467  6637 

1029 

84  05  27.37 

21.23 

2.915 

1.462  4942 

1081 

83  47  41.09 

22.30 

2.065 

1.467  7666 

1028 

84  05  48.60 

21.21 

.916 

.462  6023 

1080 

83  48  03.38 

22.27 

.966 

.467  8694 

1027 

84  06  09.80 

21.19 

.917 

.462  7102 

1079 

83  48  25.64 

22.25 

.967 

.467  9721 

1026 

84  06  30.98 

21.17 

.918 

.462  8180 

1078 

83  48  47.88 

22.23 

.968 

.468  0747 

1025 

84  06  52.14 

21.15 

.919 

.462  9257 

1077 

83  49  10.10 

22.21 

.969 

.468  1772 

1024 

84  07  13.29 

21.13 

2.920 

1.463  0334 

1076 

83  49  32.29 

22.18 

2.970 

1.468  2796 

1023 

84  07  34-40 

21.  II 

.921 

.463  1409 

1074 

83  49  54-47 

22.16 

.971 

.468  3819 

IO22 

84  07  55.50 

21.00 

.922 

.463  2483 

1073 

83  50  16.62 

22.14 

•972 

.468  4841 

1021 

84  08  16.58 

21.07 

•  923 

.463  3555 

1072 

83  50  38.75 

22.12 

•973 

.468  5861 

IO2O 

84  08  37.64 

21.05 

.924 

.463  4627 

1071 

83  5i  00.86 

22.  IO 

•974 

.468  6881 

1019 

84  08  58.67 

21.02 

2.925 

1.463  5698 

1070 

83  Si  22.04 

22.O7 

2.975 

1.468  7000 

1018 

84  09  19.69 

21.  OO 

.926 

.463  6768 

1069 

83  51  45.00 

22.05 

.976 

.468  8918 

1017 

84  09  40.68 

20.08 

.927 

.463  7836 

1068 

83  52  07.05 

22.03 

•977 

.468  9935 

1016 

84  10  01.65 

2O.06 

.928 

.463  8904 

1067 

83  52  29.07 

22.  OI 

.469  0950 

1015 

84  10  22.60 

20.04 

.929 

.463  9970 

1066 

83  52  51.06 

21.99 

•979 

.469  1965 

1014 

&4  10  43-53 

20.02 

2.930 

1.464  1036 

1065 

83  53  13.04 

21.97 

2.980 

1.469  2979 

1013 

84  II  04.44 

20.00 

•931 
•932 

.464  2100 
.464  3163 

1064 
1063 

83  53  34-99 
83  53  56.93 

21.94 
21.92 

;^2 

.469  3992 
.469  5003 

IOI2 
IOII 

84  II  25.33 

84  II  46.20 

20.88 
20.86 

•933 

.464  4226 

1062 

83  54  18.84 

21.90 

.983 

.469  6014 

1010 

84  12  07.05 

20.84 

•934 

.464  5287 

1061 

83  54  40.73 

21.88 

.984 

.469  7024 

1009 

84  12  27.88 

20.82 

2.935 

1.464  6347 

1060 

83  55  02.59 

21.86 

2.985 

1.469  8033 

1008 

84  12  48.68 

20.80 

.936 

.464  7406 

1059 

83  55  24.44 

21.83 

.986 

.469  9040 

1007 

84  13  09-47 

20.78 

.937 

.464  8464 

1058 

83  55  46.26 

21.  8l 

.987 

.470  0047 

1006 

84  13  30.23 

20.75 

.938 

.464  9521 

1056 

83  56  08.07 

21.79 

.988 

.470  1053 

1005 

84  13  50.98 

20.73 

•939 

.465  0577 

1055 

83  56  29.85 

21.77 

.989 

.470  2057 

1004 

84  14  11.70 

20.71 

2.940 

1.465  1632 

1054 

83  56  51.60 

21.75 

2.990 

1.470  3061 

1003 

84  14  32.40 

20.69 

.941 

.465  2686 

1053 

83  57  13.34 

21.73 

.991 

.470  4064 

IOO2 

84  14  53.09 

20.67 

.942 

.465  3739 

1052 

83  57  35.06 

21.70 

.992 

.470  5065 

IOOI 

84  15  13.75 

20.65 

•943 

.465  4790 

1051 

83  57  56.75 

21.68 

.993 

.470  6066 

IOOO 

84  15  34-39 

20.63 

.944 

.465  5841 

1050 

83  58  18.42 

21.66 

.994 

.470  7066 

999 

&4  15  55.01 

20.61 

2.045 

1.465  6891 

1049 

83  58  40.07 

21.64 

2.995 

1.470  8065 

998 

84  16  15.61 

20.59 

.946 

.465  7939 

1048 

83  59  01.70 

21.62 

.996 

.470  9062 

997 

84  16  36.19 

20.57 

•947 

.465  8987 

1047 

83  59  23.31 

21.60 

.471  0059 

996 

84  16  56.75 

20.55 

.948 

.466  0033 

1046 

83  59  44.90 

21.58 

.998 

.471  1055 

995 

84  17  17.29 

20.53 

.949 

.466  1079 

1045 

84  oo  06.46 

21.55 

.999 

.471  2050 

994 

84  17  37.8i 

20.51 

2.950 

1.466  2123 

1044 

84  oo  28.00 

21.53 

3.000 

I.47I  3043 

993 

84  17  58.30 

20.49 

u 

7T 

2  tan—1(eu)  — 
2 

co  sech  u 

»  sech  u 

u 

«>  sech  u 

2  tan~~J(€u)  —  90° 

w  sech  u 

SMITHSONIAN  TABLES 


305 


The  Gudermannian. 


u 

gd  u 

«F0' 

gd  u 

"Fo' 

u 

gd  u 

»F0' 

gdu 

«F0' 

0    I     II 

// 

O    /     // 

// 

3.00 

I.47I  3043 

9933 

84  17  58.30 

204.88 

3-50 

I.5I04I99 

6034 

86  32  26.47 

124.46 

.01 

.472  2927 

9835 

84  21  22.17 

202.8s 

•  51 

.511  0203 

5974 

86  34  30.31 

123.22 

.02 

•473  2713 

9737 

84  24  44.01 

200.84 

.52 

.511  6147 

5915 

86  36  32.92 

122.  OO 

•03 

.474  2401 

9641 

84  28  03.86 

198.85 

•53 

.512  2033 

5856 

86  38  34-31 

120.79 

.04 

•475  1994 

9545 

84  31  21.72 

106.88 

•  54 

•512  7859 

5798 

86  40  34.50 

119-59 

3.05 

1.476  1492 

9451 

84  34  37.63 

194.93 

3-55 

I.5I3  3628 

5740 

86  42  33.49 

118.40 

.06 

.477  0896 

9357 

84  37  51.59 

193-00 

.56 

.513  9340 

5683 

86  44  31.30 

117.22 

.07 

.478  0206 

9264 

84  41  03.64 

IQI.09 

.57 

.514  4995 

5627 

86  46  27.94 

116.06 

.08 

.478  9425 

9173 

84  44  13.78 

189.20 

.58 

.515  0594 

5571 

86  48  23.43 

114.91 

.09 

•479  8551 

9082 

84  47  22.04 

187.32 

.59 

.515  6137 

55i6 

86  50  17.76 

113.66 

3.10 

1.480  7588 

8992 

84  50  28.43 

185.47 

3.60 

1.516  1625 

546i 

86  52  10.96 

112.63 

.11 

.481  6535 

9903 

84  53  32.97 

183.63 

.6r 

.516  7058 

5406 

86  54  03.03 

i  i  i  .  52 

.12 

.482  5393 

8814 

84  56  35.69 

181.81 

.62 

.517  2438 

5353 

86  55  53-99 

110.41 

•  13 

.483  4164 

8727 

84  59  36.59 

180.00 

.63 

.517  7764 

5300 

86  57  43.85 

109.31 

,  .14 

.484  2847 

8640 

85  02  35.70 

178.221 

.64 

.518  3037 

5247 

86  59  32.62 

108.22 

3-15 

1.485  1445 

8555 

85  05  33-04 

176.45 

3.65 

1.518  8258 

5195 

87  01  20.30 

107.15 

.16 

.485  9957 

8470 

85  08  28.61 

174.70 

.66 

.519  3427 

5143 

87  03  06.92  I  106.08 

.17 

.486  8385 

8386 

85  ii  22.45 

172.97 

.67 

•519  8544 

5092 

87  04  52.47  105.03 

.18 

.487  6729 

8303 

85  14  14.56 

171.26 

.68 

.520  3611 

5041 

87  06  36.98 

103.99 

.19 

..488  4991 

8221 

85  17  04.97 

169.56 

.69 

.520  8627 

4991 

87  08  20.45 

102.95 

3.20 

1.489  3170 

8i39 

85  19  53.69 

167.88 

3.70 

I.52I  3593 

4942 

87  10  02.89 

101.93 

.2*1 

.490  1269 

8058 

85  22  40.73 

166.21 

•71 

.521  8511 

4893 

87  u  44.31 

100.92 

.22 

.490  9287 

7978 

85  25  26.12 

164.56 

.72 

.522  3379 

4844 

87  13  24.73 

99.91 

•23 

.491  7226 

7899 

85  28  09.86 

162.93 

•  73 

.522  8i99 

4796 

87  IS  04.14 

98.92 

.24 

.492  5085 

7821 

85  30  51.99 

161.32 

•74 

.523  2971 

4748 

87  16  42.57 

97-94 

3.25 

1.493  2867 

7743 

85  33  32.50 

I59.7I 

3-75 

1.523  7695 

4701 

87  l8  20.02 

96.96 

.26 

.494  0572 

7667 

85  36  11.42 

158.13 

.76 

.524  2373 

4654 

87  19  56.50 

96.00 

.27 

.494  8200 

7590 

85  38  48.77 

156.56 

.77 

.524  7004 

4608 

87  21  32.03 

95-05 

.28 

•495  5753 

7515 

85  41  24.55 

155.01 

.78 

.525  1589 

4562 

87  23  O6.6b 

04.10 

.29 

.496  3231 

7441 

85  43  58.79 

153.47 

•  79 

.525  6128 

4517 

87  24  40.23 

93-17 

3-30 

1.497  0634 

7367 

85  46  31.50 

151.95 

3.8o 

1.526  0622 

4472 

87  26  12.93 

02.24 

•31 

.497  7964 

7294 

85  49  02.69 

150.44 

.81 

.526  507^ 

4428 

87  27  44.71 

91.32 

•32 

.498  5221 

7221 

85  Si  32.38 

148.95 

.82 

.526  9478 

4384 

87  29  15.58 

00.42 

•  33 

.499  2407 

7150 

85  54  00.59 

147.47 

.83 

.527  3839 

4340 

87  30  45.55 

89.52 

•34 

.499  9521 

7079 

85  56  27.32 

146.00 

.84 

.527  8157 

4297 

87  32  14.62 

88.63 

3-35 

1.500  6564 

7008 

85  58  52.60 

144.56 

3.8S 

1.528  2433 

4254 

87  33  42.80 

87.75 

.36 

•501  3537 

6939 

86  01  16.44 

143.12 

.86 

.528  6666 

4212 

87  35  10.  II 

86.87 

•  37 

.502  0441 

6870 

86  03  38.84 

141.70 

.87 

.529  0856 

4170 

87  36  36.55 

86.01 

.38 

.502  7277 

6802 

86  05  59.84 

140.29 

.88 

.529  5005 

4128 

87  38  02.13 

85.15 

•  39 

.503  4045 

6734 

86  08  19.44 

138.90 

.89 

•529  9113 

4087 

87  39  26.86 

84.31 

3-40 
.41 

1.504  0746 
.504  7380 

6667 
6601 

86  10  37.65 
86  12  54.48 

'37.52 
136.16 

3.90 
.91 

1.530  3180 
.5307207 

4047 
4007 

87  40  50.75 
87  42  13.81 

83.47 
82.64 

.42 

•505  3948 

6536 

86  15  09.96 

134.80 

.92 

•  531  H93 

3967 

87  43  36.03  81.82 

•43 

.506  0451 

6471 

86  17  24.10 

133.47 

•93 

.531  5140 

3927 

87  44  57-45 

81.00 

.44 

.506  6889 

6406 

86  19  36.90 

132.14 

.94 

.531  9048 

3888 

87  46  18.05 

80.20 

3-45 

1.507  3264 

6343 

86  21  48.38 

130.83 

3-95 

1.532  2917 

3850 

87  47  37.85 

79-40 

.46 

.507  9575 

6280 

86  23  58.56 

129.53 

.96 

.532  6747 

3811 

87  48  56.85 

78.61 

•  47 

.508  5823 

6217 

8'»  2r)  07.44 

128.24 

.97 

•533  0539 

3773 

87  50  15-07 

77.83 

.48 

.509  2010 

6156 

86  28  15.05 

126.97 

.98 

•533  4294 

3736 

87  51  32.52 

77.o6 

.49 

.509  8135 

6095 

86  30  21.39 

125.71 

•99 

.533  8011 

3699 

87  52  49.19 

76.29 

3.50 

1.5104109 

6034 

86  32  26.47 

124.46 

4-OO 

1.534  1691 

3662 

87  5405.10 

75-53 

u 

2  tan-He")-^ 

<»  sech  u 

2tan-1(eu)-900|Wfcchu 

u 

2tan-'(«u)-| 

oosechu 

2tan~1(e«)-900 

«  sech  u 

SMITHSONIAN  TABLES 


306 


The  Gudermannian. 


u 

gd  u 

^ 

gdu 

« 


u 

gdu 

„* 

gd  u 

«Fo' 

0    /     // 

„ 

0    /     // 

0 

4.00 

1.534  1691 

3662 

87  54  05.10 

75.53 

4-50 

1.548  5792 

2222 

88  43  37-40 

45.82 

.01 

•534  5335 

3626 

87  55  20.26 

74.78 

•  51 

.548  8003 

2199 

88  44  22.99 

45.37 

.02 

•534  8943 

3590 

87  56  34.67 

74.04 

.52 

.549  0191 

2178 

88  45  08.13 

44.92 

•03 

.535  2514 

3554 

87  57  48.33 

73.30 

•  53 

•549  2358 

2156 

88  45  52.82 

44.47 

.04 

•535  6050 

3Sl8 

87  59  01.27 

72.57 

.54 

•549  4503 

2134 

88  46  37-07 

44.03 

4.05 

.05 

1.535  9551 
.536  3017 

3483 
3449 

88  oo  13.48 
88  01  24.97 

71.85 
71.14 

4-55 
.56 

1.549  6627 
.549  8730 

2113 
2092 

88  47  20.88 
88  48  04.25 

43.59 
43.15 

.07 

.536  6449 

3415 

88  02  35.76 

70.43 

•  57 

.550  0811 

2O7I 

88  48  47.19 

42.73 

.08 

.536  9846 

338i 

88  03  45.83 

69.73 

.58 

.550  2873 

2051 

88  49  29.70 

42.30 

.09 

•537  3210 

3347 

88  04  55.22 

69.03 

.59 

•550  4913 

2030 

88  50  11.79 

41.88 

4.10 

1.537  6540 

3314 

88  06  03.91 

68.35 

4.60 

1.550  6933 

2O  IO 

88  50  53.46 

41.46 

.11 

.537  9837 

3281 

88  07  11.91 

67-67 

.61 

•550  8933 

1990 

88  51  34.72 

41.05 

.12 

.538  3102' 

3248 

88  08  19.25 

67.00 

.62 

.551  0914 

1970 

88  52  15.56 

40.64 

•13 

.538  6333 

3216 

88  09  25.91 

66.33 

.63 

.551  2874 

1951 

88  52  56.00 

40.24 

.14 

.538  9533 

3184 

88  10  31.91 

65.67 

.64 

.551  4815 

1931 

88  53  36.04 

39.84 

4.15 

1.539  2701 

3152 

88  ii  37.25 

65.02 

4-65 

i.55i  6737 

1912 

88  54  15.68 

39.44 

.16 

•539  5837 

3121 

88  12  41.94 

64.37 

.66 

.551  8640 

1893 

88  54  54.92 

39.05 

•  17 

.539  8943 

3090 

88  13  45.99 

63.73 

.67 

.552  0523 

1874 

88  55  33.77 

38.66 

.18 

.540  2017 

3059 

88  14  49.40 

63.10 

.68 

.552  2388 

1856 

88  56  12.24 

38.28 

.19 

.540  5061 

3029 

88  15  52.19 

62.47 

.69 

•552  4235 

1837 

88  56  50.33 

37.89 

4.20 

1.540  8074 

2998 

88  16  54-34 

61.85 

4.70 

1.552  6063 

l8l9 

88  57  28.03 

37.52 

.21 

.541  1058 

2969 

88  17  55-88 

61.23 

•  71 

•552  7873 

1801 

88  58  05.36 

37.14 

.22 

.541  4012 

2939 

88  18  56.81 

60.62 

•  72 

.552  9664 

1783 

88  58  42.32 

36.77 

•23 

.541  6936 

2910 

88  19  57.13 

60.02 

.73 

.'553  1438 

1765 

88  59  18.91 

36.41 

.24 

.541  9831 

2881 

88  20  56.85 

59.42 

•  74 

•553  3195 

1748 

88  59  55.14 

36.05 

4.25 

1.542  2698 

2852 

88  21  55.98' 

'S8.83 

4-75 

1.553  4934 

1730 

89  oo  31.01 

35.69 

.26 

•542  5536 

2824 

88  22  54.52 

58.2-5 

.76 

•553  6655 

1713 

89  01  06.52 

35-33 

.27 

.542  8346 

2796 

88  23  52.48 

57.67 

.77 

•553  8360 

1696 

89  oi  41.68 

34.98 

.28 

.543  1128 

2768 

88  24  49.86 

57-09 

.78 

.554  0047 

1679 

89  02  16.48 

34.63 

.29 

.543  3882 

2741 

88  25  46.67 

56.53 

.79 

•554  1718 

1662 

89  02  50.94 

34.29 

4.30 

1.543  6609 

2713 

88  26  42.91 

55.96 

4.80 

1.554  3372 

1646 

89  03  25.06 

33-95 

.311 

•543  9308 

2686 

88  27  38.60 

55.41 

.81 

.554  5010 

1630 

89  03  58.84 

33.6i 

.32 

.544  1981 

2660 

80  28  33-73 

54.86 

.82 

•554  6631 

1613 

89  04  32.28 

33.28 

.33 

.544  4628 

2633 

88  29  28.31 

54.31 

.83 

•554  8236 

1597 

89  05  05.39 

32-94 

.34 

.544  7247 

2607 

88  30  22.35 

53-77 

.84 

•554  9825 

1581 

8905  38.17 

32.62 

4-35 

1.544  9841 

2581 

88  31  15.85 

53.24 

4.85 

1-555  1399 

1566 

89  06  10.63 

32.29 

.36 

.545  2409 

2555 

88  32  08.82 

52.71 

.86 

•555  2957 

1550 

89  06  42.76 

31.97 

•  37 

•  545  4952' 

2530 

88  33  01.27 

52.18 

.87 

1535 

89  07  14.57 

31.65 

.38 

•545  7469 

2505 

88  33  53.19 

51.66 

.88 

.555  6026 

1519 

89  07  46.07 

3L34 

.39 

•545  996i 

2480 

88  34  44-59 

51.15 

.89 

•555  7538 

1504 

89  08  17.25 

3L03 

4.40 

1.546  2429 

2455 

88  35  35-49 

50.64 

4.90 

1.555  9034 

1489 

89  08  48.  12 

30.72 

.41 

.546  4872 

2431 

88  36  25.88 

50.14 

.91 

.556  0516 

1474 

89  09  18.69 

30.41 

.42 

.546  7290 

2407 

88  37  i'S-76 

49-64 

.92 

.556  1983 

1460 

89  09  48.95 

30.11 

.43 

.546  9685 

2383 

88  38  05.15 

49.14 

•93 

.556  3436 

1445 

89  10  18.91 

29.81 

•  44 

•547  2055 

2359 

88  38  54.05 

48.65 

.94 

.556  4874 

1431 

89  10  48.57 

29.51 

4-45 

1.547  4403 

2335 

88  39  42.46 

48.17 

4-95 

1.556  6297 

1417 

89  II  17.93 

29.22 

.46 

.547  6726 

2312 

88  40  30.40 

47.69 

.96 

.556  7707 

1403 

89  II  47.01 

28.93 

•  47 

•547  £027 

2289 

88  41  17.85 

47.22 

«97 

•556  9103 

1389 

89  12  15.79 

28.64 

.48 

.548  1305 

2266 

88  42  04.83 

46.75 

.98 

.557  0484 

1375 

89  12  44.29 

28.36 

.49 

.548  356o 

2244 

88  42  51.35 

46.28 

•99 

•557  1852 

1361 

89  13  12.51 

28.07 

4.50 

1.548  5792 

2222 

88  43  37.40 

45.82 

5.00 

1.557  3206 

1348 

89  13  40.44 

27.79 

U 

2tan-Keu)-? 

<o  sech  u 

*»rwr 

co  sech  u 

u 

2  tan-He")-^ 

co  sech  u 

2tan-1(e«)-900 

<o  sech  u 

SMITHSONIAN  TABLES 


307 


The  Gudermannian. 


H 

gdu 

»Fo' 

gd  u 

o>Fo' 

u 

gd  u 

-FO' 

gdu 

«F0' 

o   /   // 

M 

O    /     // 

S.oo 

1.557  3206 

1348 

89  13  40.44 

27.79 

5.50 

1.562  6228 

817 

89  31  54-10 

16^86 

.01 

•557  4547 

1334 

89  14  08.  io 

27.52 

•  SI 

.562  7042 

809 

89  32  10.87 

16.69 

.02 

•557  5875 

1321 

89  U  35.48 

27.24 

•  52 

.562  7847 

801 

89  32  27.48 

16.53 

•03 

.557  7189 

1308 

89  15  02.58 

26.97 

•  53 

.562  8644 

793 

89  32  43.92 

16.36 

.04 

•557  8490 

1295 

89  15  29.42 

26.71 

•  54 

.562  9433 

785 

89  33  00.20 

16.20 

5.05 

1.557  9778 

1282 

89  15  56.00 

26.44 

5-55 

1.563  0215 

777 

89  33  16.32 

16.04 

.06 

.558  1054 

1269 

89  16  22.30 

26.18 

.56 

.563  0988 

770 

89  33  32.27 

15.88 

.07 

.558  2317 

1256 

89  16  48.35 

25.92 

•  57 

.563  1754 

762 

89  33  48.07 

15.72 

.08 
.09 

.558  3567 
.558  4804 

1244 
1232 

89  17  14.14 
89  17  39.67 

25.66 
25.40 

.58 
.59 

.563  2512 
.563  3263 

755 
747 

89  34  03.71 
89  34  19.20 

15.56 
15.41 

S.io 

1.558  6030 

1219 

89  18  04.94 

25.15 

5.6o 

1.563  4006 

740 

89  34  34-53 

15.25 

.11 

.558  7243 

1207 

89  18  29.97 

24.90 

.61 

.563  4742 

732' 

89  34  49.71 

15.10 

.12 

.558  8444 

H95 

89  18  54-74 

24.65 

.62 

.563  5471 

725 

89  35  04-73 

14.95 

.13 

.558  9633 

Il83 

89  19  19.27 

24.41 

.63 

.563  6192- 

7i8 

89  35  I9.6i 

14.80 

.14 

.559  0811 

1172 

89  19  43.56 

24.16 

.64 

.563  6906 

711 

89  35  34-34 

14.66 

5-15 

1.559  1976 

1160 

89  20  07.60 

23.92 

5.65 

1.563  7613 

703 

89  35  48.93 

14.51 

.16 

•559  3131 

1148 

89  2O  3I.4O 

23.69 

.65 

•563  8313 

697 

89  36  03.36 

14.37 

•17 

•559  4273 

1  137 

89  20  54-97 

23.45 

.67 

.563  9006 

690 

89  36  17.66 

14.22 

.18   .559  5404 

1126 

89  21  I8.3I 

23.22 

.68 

.563'  9692 

683 

89  36  31-81 

14.08 

.19 

.559  6524 

III4 

89  21  41.41 

22.99 

.69 

.564  0372 

676 

89  36  45.  &2 

13.94 

5-20 

1.559  7633 

1103 

89  22  04.28 

22.76 

5.70 

1.564  1044 

669 

89  36  59-70 

13.80 

.21 

•559  8731 

1092 

89  22  26.92 

22.53 

•  71 

.564  1710 

663 

89  37  13.43 

13.67 

.22 

•559  98i8 

1081 

89  22  49.34 

22.31 

.72 

.564  2369 

656 

89  37  27.03 

13.53 

.23 

.560  0894 

1071 

89  23  H.53 

22.08 

•73 

.564  3022 

649 

89  37  40.49 

13.40 

.24 

.560  1959 

1060 

89  23  33.51 

21.86 

.74 

.564  3668 

643 

89  37  53.82 

13.26 

5-25 

1.560  3014 

1049 

89  23  55.26 

21.65 

5-75 

1.564  4308 

637 

89  38  07.01 

13.13 

.26 

.560  4058 

1039 

89  24  16.80 

21.43 

.76 

.564  4941 

630 

89  38  20.08 

13.00 

.27 

.560  5092 

1029 

89  24  38.13 

21.22 

•  77 

.564  5568 

624 

89  38  33-01 

12.87 

.28 

.560  6116 

1018 

89  24  59.24 

21.  OI 

.78 

.564  6189 

618 

89  38  45-82 

12.74 

.29 

.560  7129 

1008 

89  25  2O.I4 

20.80 

•  79 

.564  6804 

612 

89  38  58.50 

12.  6l 

5-30 

1.560  8132 

998 

89  25  40.84 

20.59 

5.8o 

1.564  7412 

606 

89  39  11.05 

12.49 

.31 

.560  9126 

988 

89  26  OI.33 

20.39 

.81 

.564  8015 

599 

89  39  23.48 

12.37 

•32 

.561  0109 

979 

89  26  21.  61 

20.  l8 

.82 

.564  8611 

504 

89  39  35.78 

12.24 

•  33 

.561  1083 

969 

89  26  41.69 

19.98 

.83 

.564  9202 

588 

89  39  47.96 

12.12 

•  34 

.561  2047 

959 

89  27  01.58 

19.78 

.84 

.564  9787 

582 

89  40  00.02 

12.00 

5-35 

1.561  3001 

950 

89  27  21.26 

19.59 

5.85 

1.565  0365 

576 

89  40  11.96 

11.88 

.36 

.561  3946 

940 

89  27  40.75 

19.39 

.86 

.565  0939 

570 

89  40  23.78 

11.76 

•  37 

.561  4881 

931 

89  28  00.05 

19.20 

.87 

.565  1506 

565 

89  40  35.48 

11.65 

.38 

.561  5807 

922 

89  28  19.15 

19.01 

.88 

.565  2068 

559 

89  40  47.07 

"•S3 

•  39 

.561  6724 

912 

89  28  38.06 

18.82 

.89 

.565  2624 

553 

89  40  58.54 

LI.  41 

i 

5.40 

1.561  7632 

903 

89  28  56.79 

18.63 

S.oo 

1.565  3175 

548 

89  41  09.90 

11.30 

.41 

.561  8531 

894 

89  29  15.33 

18.45 

.91 

.565  3720 

542 

89  41  21.15 

11.19 

.42 

.561  9421 

885 

89  29  33.68 

18.26 

.92 

.565  4259 

537 

89  41  32.28 

II.08 

•43 

.562  0302 

877 

89  29  31.85 

18.08 

•93 

.565  4794 

532 

89  41  43.30 

10.97 

.44 

.562  1174 

868 

89  30  09.85 

17.90 

•94 

.565  5323 

526 

89  41  54-21 

10.86 

5-45 

1.562  2038 

859 

89  30  27.66 

17.72 

5-95 

1.565  5847 

521 

89  42  05.02 

10.75 

.46 

.562  2893 

851 

89  30  45-29 

17.55 

.96 

.565  6365 

5i6 

89  42  15.71 

10.64 

•  47 

•562  3739 

842 

89  31  02.75 

17.37 

.97 

.565  6879 

511 

89  42  26.30 

10.54 

.48 

.562  4577 

834 

89  31  20.04 

17.20 

.98 

.565  7387 

506 

89  42  36.79 

10.43 

•49 

.562  5407 

826 

89  31  37.15 

17-03 

.99 

.565  7890 

Soi 

89  42  47.17 

10.33 

5.50 

1.562  6228 

817 

8931  54-10 

16.86 

6.00 

1.565  8388 

496 

89  42  57-44 

10.23 

u 

2tan-Ke°)-£ 

wsechu 

2tan~1(e«)-900 

«•>  sech  u 

u 

2  tan-Ken)— 

o>sechu 

2tan~1(e")-900 

w  sech  u 

SMITHSONIAN  TABLES 


308 


TABLE  VII 

THE  ANMUDERMANNIAN 


m  expressed  in  minutes  in  terms  of  the  Gudermannian, 

gd  u  expressed  in  degrees  and  minutes. 

i  minute  =  o.ooo  2908  8821  radians, 

o.ooo  2908  8821  m  =  logetan  f-L^-J-  —  gd  u)  =  u  radians. 
In  this  table  the  second  decimal  place  is  sometimes  erroneous  by  a  unit. 


309 


The  Anti-Gudermannian. 


gdu 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

gdu 

0' 

o'.oo 

60.00 

120.02 

180.08 

240.  ig 

300.38 

360.66 

421.05 

48i.57 

542.23 

603.07 

0' 

I 

1.  00 

61.00 

121.  02 

181.08 

241.20 

301.38 

361.66 

422.06 

482.58 

543.25 

604.08 

I 

2 

2.OO 

62.00 

I22.O3 

182.08 

242.  «2O 

302.39 

362.67 

423.06 

483.59 

544.26 

605.10 

2 

3 

3.00 

63.00 

123.03 

183.09 

243.20 

303.39 

363.67 

424.07 

484.60 

545-217 

606.12 

3 

4 

4.00 

64.00 

124.03 

184.09 

244.20 

304.40 

364.68 

425.08 

485-61 

546.28 

607.13 

4 

5 

5.00 

65.00 

125.03 

185.09 

245.31 

3P5.40 

365.69 

426.09 

486.62 

547-30 

608.15 

5 

6 

6.00 

66.00 

I26.O3 

186.09 

246.21 

306.40 

366.69 

427.09 

487.63 

548.31 

609.16 

6 

7 

7.00 

67.00 

127.03 

187.09 

247.21 

307.41 

367.70 

428.10 

488.64 

549-32 

610.  18 

7 

8 

8.00 

68.00 

128.03 

188.09 

248.21 

308.41 

368.70 

429.11 

489.65 

550.34 

61  1  .  19 

8 

9 

9.00 

69.00 

129.03 

189.09 

249-22' 

309-42 

369.71 

430.12 

490.66 

55i.  36 

612.21 

9 

IO 

10.  OO 

70.00 

130.03 

190.10 

250.212 

310.42 

370.72 

43LI3 

491.67 

552.36 

613.23 

IO 

ii 

II.  OO 

71.00 

I3L03 

191.10 

251.22 

3H.42 

371.72 

432.13 

492.68 

553  -37 

614.24 

ii 

12 

12.  OO 

72.00 

132.03 

192.10 

252.23 

312.43 

372.73 

43-3.14 

493.69 

554.39 

615.26 

12 

13' 

IS.  oo 

73-00 

IQG.03 

I93.IO 

253.23 

313.43 

373-74 

434.15 

494.70 

555-40 

616.27 

13 

14 

14.00 

74.01 

1314.  03' 

194.10 

254-23 

314.44 

374-74 

435.i6 

495.71 

356.41 

617.29 

U 

IS 

15.00 

75.01 

135.03 

195.10 

255.23 

315.44 

375-75 

436.17 

496.72 

557-43 

618.31 

15 

16 

16.00 

76.01 

136.03 

196.11 

256.24 

316.46 

076.75 

437.17 

497-73 

558.44 

619.32 

16 

17 

I/.  OO 

77.01 

137-04 

197.11 

257.24 

317-45 

377.76 

438.  18 

498.74 

559-45 

620.34 

17 

18 

18.00 

78.01 

138.04 

198.11 

258.24 

318.45 

378.76 

439.19 

499.75 

560.47 

621.36 

18 

19 

19.00 

79.01 

139.04 

199.11 

259.25 

319.46 

379-77 

440.20 

500.76 

561.48 

622.37 

19 

20 

20.00 

So.  01 

140.04 

200.  ii 

200.25 

320.46 

380.78 

441.21 

501.77 

562.49 

623.39 

20 

21 

21.  OO 

81.01 

141.04 

2OI.II 

261.25 

321.47 

381.78 

442.21 

502.78 

563.51 

624.40 

21 

22 

22'.  OO 

82.0)1 

1412.04 

2O2.I2 

262.25 

322.47 

382.79 

443-22 

503-79 

564.52 

625.42 

22 

23 

23.00 

83.01 

143-04 

203-12 

263.26 

323.48 

383.79 

444.23 

504.80 

505.53 

626.44 

23 

24' 

24.00 

84.01 

144.04 

204.12 

264.26 

324.48 

384.80 

445-24 

505-81 

566.55 

627.45 

24 

25 

2'5.00 

85.01 

145.04 

205.12 

265.26 

325.48 

385.81 

446.25 

506.83 

567.56 

628.47 

25 

26 

26.00 

86.01 

146.04 

206.12 

266.27 

326.49 

386.81 

447.26 

507-8^ 

568.57 

629.49 

26 

27 

27.00 

87.01 

147.04 

207.13 

267.27 

327-49 

387.82 

448.26 

508.85 

569.  '59 

630.50 

27 

28 

28.00 

88.01 

148.05 

208.13 

268.i2|7 

328.50 

388.83 

449.27 

509.86 

570.00 

631.52 

28 

29 

29.00 

89.01 

149.05 

209.13 

269.27 

329-50 

389-83 

450.28 

910.87 

571.62' 

632.54 

29 

30 

3O.OO 

90.01 

150.05 

2IQ.I3' 

270.28 

330.51 

390.84 

451.29 

511.88 

572.63 

633.56 

30 

31 

31.00 

91.01 

151.05 

211.  1(3 

271.28 

33'i.'5i 

391.85 

452.30 

512.89 

573.64 

634.57 

Si 

32 

32.00 

92'.  01 

152.015 

212.13 

272.28 

332.52 

392.85 

453-31 

513-90 

574.66 

635-59 

32 

33 

33-00 

93.01 

153-05 

213.14 

273.29 

333-52 

393-86 

454.32 

514.91 

575.67 

636.61 

33 

(34 

34.00 

94.01 

154-05 

214.14 

274.29 

334-53 

394-85 

455-33 

515.93 

576.69 

637.62 

34 

35 

35-00 

95-01 

155-05 

215.14 

275-29' 

335.53 

395.87 

456.33 

516.94 

577.70 

638.64 

35 

36 

36.00 

96.01 

156.05 

216.  14 

276.30 

336.54 

396.88 

4157-34 

517.95 

578.71 

639.66 

36 

37 

37.oo 

97-01 

157-05 

217.14 

277-30    337-54 

397-88 

458.35 

518.96 

579-73 

640.68 

37 

38 

38.00 

98.01 

158.06 

2I8.I5 

278.30 

338.55 

398.89 

459.36 

519.97 

580.74 

641.69 

38 

39 

39.00 

99.01 

i'59-o6 

219.15 

279-31 

339-55 

399-90 

460.37 

520.08 

581.76 

642.71 

39 

40 

40.00 

IOO.OI 

160.06 

22O.I5 

280.31 

340-56 

400.91 

461.38 

521.99 

582.77 

043-73 

40 

41 

41.00 

101.01 

161.06 

221  .  I& 

281.31 

341.56 

401.91 

462.39 

523-01 

583-79 

644.75 

41 

42 

42.00 

IO2.OI 

162.06 

222.15 

282.32 

342.57 

402.92 

463-40 

314.02 

584.80 

645.76 

42 

43 

43.00 

IO3.O2 

163.06 

2123.16 

283.32 

343-57 

403-93 

464.  4  1 

525-03 

585.81 

646.78 

43 

44 

44.00 

104.02 

164.06 

.2i24.l6 

284.32 

344.58 

404.93 

465-41 

526.04 

586.83 

647-80 

44 

45 

45-00 

105.02 

165.06 

22-5.  16 

285.  33 

34'5.58 

405.94 

466.42 

527.05 

587.84 

648.821 

415 

46 

46.00 

IO6.O2 

166.06 

226.16 

286.33 

346.59 

406.95 

467.43 

528.06 

588.86 

649.84 

46 

47 

47.00 

107.02 

167.07 

227.16 

287.33 

347-59 

407.95 

468.44 

529.08 

589.87 

650.85 

47 

48 

48.00 

I08.O2 

168.07 

228.17 

288.34 

348.60 

408.96 

469.45 

530.09 

590.89 

651.87 

48 

49 

49.00 

109.02 

169.07 

229.17 

.289.34 

349-60 

409.97 

470.46 

531-10 

591-90 

652.89 

49 

50 

50.00 

110.02 

170.07 

230.17 

200.34' 

350.61 

410.97 

471.47 

532HI 

592.92 

653-91 

50 

51 

51.00 

in.  02 

171.07 

231  .  17 

291.35 

35i.6i 

4111.98 

4172.48 

533-12 

593-93 

654.93 

51 

52 

52.00 

112.  02 

172.07 

232.18 

292.35 

352.62 

4112.99 

473-49 

534-14 

594-95 

S5S.94 

52 

53 

53.OO 

113.012 

173-07 

233-18 

293.35 

353.62 

414.00 

474.50 

5315.15 

595.96 

£6.56 

53 

54 

54.00 

114.02 

174.07 

234.18 

294.36" 

3154.63 

415.00 

475.51 

536.16 

596.98 

657.98 

54 

55 

55-00 

115.02 

175.07 

235  .'18 

295.36 

355.63 

416.01 

476.52 

537-17 

597-99 

659.00 

55 

56 

56.00 

116.02 

176.08 

236.18 

296.37 

3(56.64 

417.02 

4177.53 

538.18 

509.01 

660.02 

56 

57 

57.OO 

117.02 

177.08 

237.19 

297.37 

357.64 

418.03 

478.54 

539-20 

600.02 

661.04 

57 

58 

•-'/ 

58.00 

118.02 

178.08 

238.19 

298.37 

358.65 

419.03 

479.55 

540.21 

601.04 

662.05 

58 

59 

59.00 

119.02 

179-08 

2-39.19 

299.38 

359.65 

420.04 

480.56 

541.22 

602.05 

663.07 

59 

60 

y* 
60.00 

120.02 

180.08 

2140.19 

300.38 

360.66 

421.05 

481.57 

542.23 

603.07 

664.09 

60 

SMITHSONIAN  TABLES 


310 


The  Anti-Gudermannian. 


gd  u 

11° 

12° 

13° 

I4'° 

15° 

16° 

17° 

18° 

19° 

20° 

gd  u 

(/ 

664/.09 

725.32 

786.78 

848.49 

910.46 

972.73 

1035.30 

1098.22 

1161.49 

1225.14 

<f 

I 

665.11 

'726.34 

787.81 

849.52 

911.50 

973-77 

1036.35 

1099.27 

1162.54 

1226.20 

I 

2 

666.13 

727-37 

788.83 

850.55 

912.53 

974-81 

1037.40 

1100.32 

1163.60 

1227.27 

2 

3 

667.15 

728.39 

789.86 

851.58 

913.57 

975.85 

1038.44 

1101.37 

1164.66 

1228.33 

3 

4 

668.17 

729.41 

•790.89 

852.61 

914.60 

976.89 

1039.49 

1102.42 

1165.72 

P2I29.4O 

4 

5 

669.19 

730.43 

791.91 

853.64 

915.64 

977-93 

1040.53 

1103.47 

1166.78 

1230.46 

5 

6 

670.21 

731.46 

792.94 

854-67 

916.67 

978.97 

1041.58 

1104.53 

1167.83 

1231.53' 

6 

7 

671.212 

732.48 

793-97 

855.70 

917.71 

980.01 

1042.63 

1105.58 

1168.89 

1232.59 

7 

8 

672.24 

733.50 

794.99 

856.73 

918.75 

981.05 

1043.67 

1106.63 

1169.95 

1233.66 

8 

9 

673.26 

734-53 

796.02 

857.  76 

9119.78 

982.09 

1044-72 

1107.68 

1171.01 

1234.72 

9 

10 

674.28 

735-55 

797.04 

858.80 

920.82 

983.13 

1045.77 

1108.74 

1172.07 

1235.79 

10 

ii 

675.30 

736.57 

798.07 

859.83 

9(21.85 

984.17 

1046.81 

1109.79 

H73.I3 

1236.85 

II 

112 

676.32 

737.59 

799.10 

860.86 

922.89 

985.22 

1047.86 

1110.84 

1174.19 

12.37.92 

12 

13 

677.34 

738.62 

800.13 

861.89 

923.93 

986.26 

1048.91 

1111.89 

1175.24 

1238.98 

13 

14 

678.36 

739.64 

801  .  15 

862.92 

924.96 

987.30 

1049.95 

1112,95 

1176/30 

1240.05 

14 

IS' 

679.38 

740.66 

802.18 

863.95 

926.00 

988.34 

1051.00 

1114.00 

1177.36 

1241.11 

15 

16 

680.40 

741.69 

803.21 

864.98 

927.03 

98^.38 

1052.05 

1115.05 

1178.42' 

1242,  18 

16 

17 

681.42 

742.71 

804.24 

866.02 

928.07 

990.42 

1053.09 

1116.  n 

1179.48 

1243.25 

17 

18 

682.44 

743.73 

805.216 

867.05 

929.11 

99,1  -47 

1054.14 

1117.16 

1180.54 

1244.31 

18 

19 

683.46 

744.76 

806.29 

868.08 

930.15 

992.51 

1055.19 

1118.21 

1181.60 

1245.38 

19 

20 

684.48 

745.78 

807.32 

869.11 

931.18 

993-55 

1056.24 

1119.27 

1182.66 

1246.44 

20 

21 

685.50 

746.81 

808.  3'5 

870.14 

932.22 

994-59 

1057.28 

1120.32 

1183.72 

11247.51 

21 

221 

686.52 

747.83 

809.37 

871.18 

933.26 

995.63 

1058.33 

11211.37 

1184.78 

1248.58 

22 

•23 

687.54 

748.85 

810.40 

872.2.1 

934.29 

996.68 

1059.38 

1122,43 

1185,84 

1249.64 

23 

24 

688.56 

749.88 

811.43 

873.24 

935.33 

997.72 

1060,43 

11213.48 

1186.90 

1250.71 

24 

25 

689.58 

750.90 

812.46 

874-27 

936.37 

998.76 

1061.48 

1124.53 

1187.96 

1251.78 

25 

26 

690.60 

751.92 

81/3.49 

875.31 

937.40 

999.80 

1062.512 

1125.59 

1189.02 

1252.85 

26 

27 

691.62 

752.95 

814.52 

876.34 

938.44 

1000.85 

1063.57 

1126.64 

1190.08' 

12-53.91 

27 

28 

692.64 

753-97 

815.54 

877.37 

939.48 

1001.89 

1064.62 

1127.70 

1191.14 

1254.98 

28 

29 

693.66 

755.00 

816.57 

878.40 

940.52 

1002.93 

1065.67 

1128.75 

1192.20 

1256.05 

29 

30 

694.68 

756.02 

817-60 

879.44 

94'i.56 

1003.97 

1066.72 

1129.81 

1193.26 

1257.12 

30 

3>i 

695.70 

757.05 

818.63 

880.47 

942.59 

1005.02 

1067.77 

ri30.86 

1194.32 

1258.18 

31 

32 

696.72 

758.07 

819.66 

881.50 

943.63 

1006.06 

1068.81 

1131.92 

1195.39 

1259.25 

32 

33 

697.74 

759.09 

820.69 

882.54 

944.67 

1007.10 

1069.86 

H30.97 

1196.45 

1260.32 

33 

34 

698.76 

760.12 

8211.71 

883.57 

945.71 

1008.  16 

1070.91 

1134.03 

H97.5I 

1261.39 

34 

35 

699.78 

761.14 

822.74 

884.60 

946.74 

1009.19 

1071.96 

ii<35.o8 

1198.57 

1262.45 

35 

36 

700.80 

762.17 

823.77 

885.64. 

947.78 

1010.23 

1073.01 

1136.14 

1199.63 

1263.52 

36 

37 

701.82 

763.19 

824.80 

886.67 

948.82 

1011.28 

1074.06 

1137.19 

1200.69 

1264.59 

37 

38 

702.85 

764.212 

825-83 

887.70 

049.86 

1013.32 

1075.11 

1138.25 

1201.75 

1265.66 

38 

39 

703.87 

765.24 

826.86 

888.74 

950.90 

1013.36 

1076.16 

1139.30 

1202.82' 

1266.73 

39 

40 

704.89 

766.27 

827.89 

889.77 

951-94 

1014.4-1 

1077.21 

1140.36 

1203.88 

1267.80 

40 

4i 

705-91 

767.29 

828.92 

890.80 

952.98 

1015.45 

1078.26 

1141.41 

1204.04 

1268.87 

41 

42 

706.93 

768.32 

829.95 

891.84 

954.01 

1016.50 

1079.31 

1142.47 

1206.00 

11269.93 

42 

43 

707.95 

769.34 

830.98 

8921.87 

955.05 

1017.54 

1080.36 

1143.52 

1207.06 

1271.00 

43 

44 

708.97 

770-37 

832.00 

893.91 

956.09 

1018.58 

1081.41 

1  144'.  58 

1208.13 

1272.07 

44 

45 

709.99 

•771.39 

833.03 

894.94 

957.13 

1019.63 

1082-.  46 

1145.64 

1209.19 

1273.14 

45 

46 

711.02 

772.42 

834.06 

895.97 

958.17 

1020.67 

1083.51 

1146.69 

1210.25 

1274.21 

46 

47 

712.04 

773-44 

835.09 

897-01 

959.21 

1021.72 

1084.56 

H47.75 

1211.31 

1275.  ,28 

47 

48 

713.06 

774-47 

836.12 

898.04 

960.25 

1022.76 

1085.61 

1148.80 

1212.38 

1276.35 

48 

49 

714.08 

775-49 

837.15 

809.08 

961.29 

1023.81 

1086.66 

1149.86 

1213.44 

1277.42 

49 

50 

7i»5.io 

776.52 

838.18 

goo.  n 

9612.33 

1024,'.  85 

1087.71 

1150.92 

1214.50 

1278.49 

50 

51 

7l6.  12 

777-54 

839.21 

901.15 

963.37 

1025.90 

1088.76 

II5I.97 

1215.57 

1279.56 

5i 

'SB 

717.15 

778.57 

840.24 

902.18 

964.41 

1026.94 

1089.81 

1153.03 

1216.63 

1280.63 

52 

53 

718.17 

779-59 

841.27 

003.212 

965.45 

1027.99 

1090.86 

1154.09 

1217.69 

1281.70 

53 

54 

719.19 

7180.62 

842'.  30 

904.215 

966.49 

1029.03 

1091.91 

H55.I4 

1218.76 

1,282.77 

54 

5S 

72O.2I 

781.65 

843.33 

905.28 

967.53 

1030.08 

1092.96 

1156.20 

1219.82 

11283.84 

55 

56 

7(21.23 

782.67 

844.36 

906.32 

968.57 

1031.12 

1094.01 

1157.26 

1220.88 

1284.91 

56 

57 

722.2^ 

783.70 

845.39 

907.35 

969.61 

1032.17 

1095.06 

1158.32 

1221.95 

1285.98 

57 

58 

723,28 

784.73 

846.42 

908.39 

970.6s 

1033.21 

1006.  n 

1159-37 

1223.01 

1287.05 

58 

59 

724.30 

785.75 

847.45 

909.43 

971.69 

1034.26 

1097.16 

1160.43 

1224.07 

1288.  13 

59 

60 

725.312 

•786.78 

848.49 

910.46 

972.73 

1035.30 

1098.22  1161.49 

1225.14 

1289.20 

60 

SMITHSONIAN  TABLES 


The  Anti-Gudermannian. 


gdu 

51° 

2t2° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

gdu 

O' 

12Z&.20 

1353.69 

1418.63 

1484.06 

1549.99 

1616.47 

1683.52 

1751.16 

1819.44 

1888.38 

0' 

I 

1200.27 

1354.76 

1419.72 

1485.15 

1551.10 

1617.58 

1684.64 

1752.29 

1820.58 

1889.53 

i 

2 

I29L34 

I355.84 

14120.80 

1486.^5 

1552.20 

1618.70 

1685,76 

1753-43 

18121.72 

1890.69 

2 

3 

1292.41 

1356.92 

1421.89 

1487.34 

1553.31 

1619.81 

1686.88 

1754.56 

1822.87 

1891.84 

3 

4 

1293.48 

1358.00 

1422.98 

1488.44 

1554.41 

1620.92 

1688.01 

1755.69 

1824.01 

1893-03 

4 

5 

I294-.55 

1359.08 

1424.06 

1489.53 

I5'55.5i 

1622.04 

1689.13 

1756.83 

18255.16 

1894.15 

5 

6 

1295.63 

1360.  16 

11425.15 

1490.63 

1556.62 

1623.15 

1690.25 

1757.96 

1826.30 

1895.31 

6 

7 

1296.70 

1361.24 

1426.24 

1491.72 

1557.72 

1624.26 

1691.38 

1759.09 

1827.44 

1896.46 

7 

8 

1297-77 

1362.312 

1427.32 

1492.82 

1558.83 

16215.38 

1692.50 

1760.23 

1828.59 

1897.62 

8 

9 

1298.84 

1363.40 

1428.41 

1493.91 

1559-93 

1626.49 

1693.62 

1761.36 

1829.73 

1898.78 

9 

10 

1299.91 

1364-48 

1429-50 

1495.01 

1561.04 

1627.61 

1694.75 

1762.50 

1830.88 

1899-93 

10 

n 

1300.99 

1365.56 

1430.59 

1496.11 

1562.14 

1628.72 

1695.87 

1763.63 

1832.02 

1901.09 

II 

1-2 

1302.06 

1366.64 

1431.68 

1497.20 

1563.  <as 

1629.84 

1697.00 

1764.77 

1833.17 

1902.25 

12 

IQ 

1303.13 

1367.72 

1432.76 

1498.30 

r564.35 

1630.95 

1698.12 

1765.90 

1834.32 

1903.40 

13 

14 

1304.20 

1368.80 

1433.85 

1499.40 

1565.46 

1632.06 

1699.25 

1767.04 

1835.46 

1904.56 

14 

15 

1305.28 

1369.88 

1434.94 

1500.49 

1566.56 

1633.18 

1700.37 

1768.17 

1836.61 

1905.72 

15 

16 

1306.35 

1370.96 

1436.03 

1-501  .59 

1567.67 

1634.29 

1701.50 

1769.31 

1837.75' 

1906.88 

16 

17 

1307.42 

1372.04 

1437.  12 

1502.69 

1568.77 

1635.41 

1702.62 

1770.44 

1838.90 

1908.03 

17 

18 

^1308.50 

1373-12 

1438.21 

1503.78 

1569.88 

1636.512 

1703.75 

1771.58 

1840.05 

1909.19 

18 

19 

1309.57 

1374-20 

1439.29 

1504.88 

1570.99 

1637.64 

1704.87 

1772.71 

1841.19 

1910.35 

19 

20 

1310.64 

1375.28 

1440.38 

1505.98 

1572.09 

1638.76 

1706.00 

1773-85 

1842.314 

I9H.5I 

20 

21 

1311.72 

1376.36 

1441.47 

1507.08 

1573-20 

1639.87 

1707.  12 

1774.98 

1843.49 

1912.67 

21 

22 

1312.79 

1377.44 

1442.56 

1508.17 

1574.31 

1640.99 

1708.25 

1776.121 

1844.64 

1913.83 

212 

1213 

1313.86 

1378.52 

1443.65 

1509.27 

1575.41 

1642  .  10 

1709.37 

1777.26 

1845.78 

1914.98 

23 

24 

1314.94 

i379.6i 

1444.74 

1510.37 

1576.52 

16413.22 

I7IO.5O 

1778.39 

1846.93 

1916.14 

24 

25 

1316.01 

1380.69 

1445.83 

I5H.47 

1577.63 

1644.34 

1711.63 

1779.53 

1848.08 

1917.30 

2>5 

26 

1317.08 

i'38i.77 

1446.92 

I5H2.57 

1578.73 

1645.  4'S 

1712.75 

1780.67 

1849.  23 

1918.46 

26 

27 

1318.16 

1382.85 

1448.01 

1513-67 

1579.84 

1646.57 

1713.88 

1781.81 

1850.37 

1919.62 

27 

28 

1319-  23 

1383-93 

1449.10 

1514.76 

1580.95 

1647.69 

1715-01 

1782.94 

1851.52 

1920.78 

28 

29 

1320.31 

1385.02 

I450'I9 

1515.86 

1582.06 

1648.80 

I7l6.  14 

11784.08 

1852.67 

I92JI.94 

29 

30 

1321.38 

1386.10 

1451.28 

1516.96 

1583.17 

1649.92 

1717.26 

1785.22 

1853.82 

1923.10 

30 

31 

132*2.45 

1387.18 

I45<2.37 

1518.06 

1584.27 

1651.04 

I7I8.39 

1786.36 

1854.97 

1924.26 

31 

32 

1323.53 

1388.26 

1453.46 

1519.16 

1585.38 

1652.16 

1719.52 

1787.50 

1856.  I£l 

192(5.43' 

32 

33 

1324.60 

1389.35 

1454.55 

1520.26 

1586.49 

1653.^7 

1720.65 

1788.60 

1857.27 

1926.59 

33 

34 

1325.68 

11390.43 

1455.64 

1521.36 

1587.60 

1654.39 

.1721.77 

1789.77 

1858.42 

1927.75 

34 

315 

1326.75 

1391-51 

1456.73 

1522.46 

1588.71 

I655.5I 

1722.90 

1790.91 

1859.57 

1928.91 

3*5 

36 

1327-83 

1392.59 

1457.83 

1523.56 

1589.82 

1656.63 

1724.03 

1792.05 

1860.72- 

1930.07 

36 

37 

1328.90 

1393.68 

1458.92 

1524.66 

1.590.92 

1657.75 

1725.16 

1793.19 

1861.87 

1931.23 

37 

38 

1329.98 

1394.76 

1460.01 

1525.76 

1592.03 

1658.87 

1726.29 

1794.33 

1863.02 

1932.40 

38 

39 

I33i.o6 

1395.84 

1461  .  10 

1526.86 

1593.14 

1659-98 

1727.42 

1795-47 

1864.17 

1933.56 

39 

40 

1332.13 

1306.93 

1462.19 

1527.96 

1594.25 

1661  .  10 

•1728.54 

1796.61 

1865.32 

1934.72 

40 

41 

H333.2I 

1398.01 

1463.28 

11529.06 

1595.36 

1662.22 

1729.67 

1797.75 

1866.47 

I935.8S 

41 

42> 

1334.29 

1399-  10 

1464-38 

1530.  16 

1596.47 

1663.34 

1730.80 

1798.89 

1867.62- 

1937.05 

42 

43 

1335.37 

1400.  18 

1465.47 

1531-26 

r597-58 

1664.46 

1731.93 

1800.03 

1868.77 

1938.21 

43 

44 

1336.44 

1401.26 

1466.56 

1532.36 

1598.69 

1665.58 

1733.06 

1801.17 

1869.92 

1939.37 

44 

4-5 

1337.52 

1402.35 

1467.65 

1533.46 

1599.80 

1666.70 

ff734.I9 

1802.31 

1871.08 

1940.54 

45 

46 

13138.60 

1403.43 

1468.75 

1534.56 

1600.91 

1667.82 

1735.32 

1803.45 

1872.23 

1941-70 

46 

47 

1339.67 

1404.52? 

1469.84 

1535-66 

1602.02 

1668.04 

1736.45 

1804.59 

1873.38 

1942.86 

47 

48 

1340.75 

1405.60 

1470.93 

1536.77 

1603.13 

1670.06 

1737.58 

1805.73 

1874.53 

1944.03 

48 

49 

1341.83 

1406.69 

1472.02 

1537.87 

1604.24 

1671.18 

1738.71 

1806.87 

1875.69 

1945.19 

49 

50 

1342.91 

1407.77 

I473-I2 

1538.97 

1605.35 

1672.30 

1739.84 

1808.  01 

1876.84- 

1946.36 

50 

Si 

1343-98 

1408.86 

1474.21 

1540.07 

1606.46 

1673-42 

1740.98 

1809.15 

1877.99 

1947.52 

51 

52 

1345.06 

1409.94 

1475.30 

I54LI7 

1607.58 

1674.54 

1742.11 

1810.30 

1879.  14 

1948.69 

52 

53 

1346.14 

1411.03 

1476.40 

154-2.27 

1608.69 

1675.66 

r743.24 

1811.44.' 

1880.30 

1949.85 

53 

54 

1347.212 

1412.11 

1477.49 

1543.38 

1609.80 

1676.79 

I'744.37 

1812.58 

I88I.45 

1951.02 

54 

55 

1348.29 

1413.20 

1478.59 

1544-48 

1610.91 

1677.91 

1745-50 

1813.72 

1882.60 

1952.18 

55 

56 

1349-37 

1414.28 

1479.68 

1545.58 

1612.02 

1670.03 

1746.63 

1814.86 

1883.76 

1953.35 

56 

57 

1350.45 

Hi'5.37 

1480.77 

1546.69 

1613.13 

1680.15 

1747.76 

1816.01 

1884.91 

I954.5I 

57 

58 

1351.53 

1416.46 

1481.87 

1547-79 

1614.25 

1681.27 

1748.90   I8I7.I5 

1886.07 

1955.68 

58 

59 

1352.61 

1417-54 

1482.96 

1548.89 

1615.36 

1682.39 

1750.03   l8l8.29 

1887.32) 

1056.85 

59 

60 

U53.69 

1418.63 

1484.06 

1549.99 

1616.47 

1683.52 

1751.  i6|  1819.44' 

1888.38 

1958.01 

60 

SMITHSONIAN  TABLES 


312 


The  Anti-Gudermannian. 


odu 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

gdu 

0' 

IQSS'.OI 

2028.38 

2099.53 

2171.48 

2244.29 

2317.99 

2392.63 

2468.26 

2544.93 

2622.69 

tf 

i 

1959.18 

2029.56 

2100.72 

2172.69 

2245.51 

2319.22 

2393-88 

2469.53 

2546.22 

2624.00 

I 

2 

1960.35 

2030.74 

2101.91 

2173.89 

212146.73 

2320.46 

2395.14 

2470.80 

2547-50 

2625.30 

2 

3' 

1961.51 

2031.92 

2103.10 

2175.10 

2247.95 

2321.70 

2396.39 

2472.07 

2548.79 

12626.61 

3 

4 

1962.68 

2033.10 

2104.30 

2176.31 

2249.  17 

2322.93 

2397.64 

2473.34 

2550.08 

2627.91 

4 

5 

1963.85 

2034.28 

2105.49 

i2>!77.  Si 

2250.39 

2324.17 

2398.90 

2474.61 

2551.37 

2629.22 

5 

6 

1965.02 

2035.46 

2106.68 

2178.72 

2251.62 

2325.41 

2400.15 

2475-88 

2552.66 

2630.53 

6 

7 

1066.18 

2036.64 

2107.88 

2179.93 

2252.84 

2*326.65 

2401.40, 

2477.15 

2553-95 

2631  .8^ 

7 

8 

1967.35 

2037.82 

2109.07 

.2181.14 

2254.06 

23.27.  8£ 

2402.66 

2478.42 

2555.23 

2633.  14 

8 

9 

1968.52 

2039.00 

2110.27 

2:182.35 

2255.28 

21329.12 

2403.91 

2479.69 

2556.52 

2634.45 

9 

10 

1969.69 

2040.  19 

2111.46 

2183.55 

2256.51 

2330.36 

2405.17 

2480.97 

2557-81 

2635.76 

10 

ii 

1970.86 

2041.37 

2112.66 

121184.76 

2257.73 

23131.60 

2406.42 

2482.024 

2559.  10 

2637.07 

ii 

12 

1972.03 

2042.55 

2113.85 

2185.97 

2258.95 

2332.84 

2407.68 

2483.51 

2560.39 

2638.38 

12 

13 

1973.20 

2043..  73 

2115.05 

2187.18 

2260.18 

2*334.08 

2408.93 

2484.78 

2561.68 

2639.69 

13 

14 

1974.37 

2044.91 

2116.24 

0188.39 

2261.40 

2335.32 

2410.  19 

.21486.06 

2562.97 

2641.00 

14 

i'3 

1975.54 

2046.10 

2117.44 

2189.60 

2262.63 

2336.56 

2411.44 

2487.33 

2564.27 

2642.31 

15 

16 

1976.71 

2047.28 

2118.63* 

2190.81 

2263.85 

23137.80 

24121.70 

2488.60 

2565.56 

2643.62 

16 

17 

1977.88 

2048.46 

2119.831 

2192.02 

2*265.08 

2339.04 

2413.96 

2489.88 

12566.85 

2644.93 

17 

18 

1979.05 

2049.64 

2121.03 

2193.23 

2266.30 

2340.28 

2415.21 

2491.15 

2568.14 

2646.24 

18 

19 

1980.22 

2050.83 

2122.22 

•21194.44 

2267.53 

2341.52 

2416.47 

2492.43 

2569.413' 

2647.55 

19 

20 

1981.39 

2052.01 

2123.42 

2195-65 

2268.75 

2342.76 

•.2417.73 

2493.70 

2570.73 

2648.86 

20 

21 

1982.56 

2053.19 

121124.62 

2196.86 

2269.98 

2344.00 

2418.99 

2494.97 

2572.02 

2650.  17 

21 

22 

1983.73 

2054-38 

21215.81 

2198.07 

2271.20 

2345.25 

2420.24 

2496.25 

2573.3I 

2651.49 

2J2 

23' 

1984.90 

2055.56 

2127.01 

2199.29 

227.2.43 

2346.49 

2421.50 

2497.52 

2574.61 

2652.80 

23 

24 

1986.07 

2056.75 

2128.21 

22OO.'50 

2273.66 

2347.73 

2422.76 

2498.80 

2575.90 

2654.11 

24 

25 

1987.24 

2057.93 

2129.41 

2201.71 

2274.88 

2348.97 

2424.02 

2.5(00.08 

2577.19 

2655.43 

25 

26 

1988.41 

2059.11 

2I3O.6I 

2202.92 

2276.11 

2350.21 

24215.28 

2501.35 

2578.49 

2656.74 

26 

27 

1989.59 

2060.30 

2I3iI.8b 

2204.14 

2277.34 

2351.46 

2426.54 

2502.63 

2579.78 

2658.05 

27 

28 

1990.76 

12061  .49 

2133-00 

2205.35 

2278.57 

2352.70 

2427.80 

2503.91 

2581.08 

2659.37 

28 

29' 

1991.93 

2062.67 

2134.20 

2206.56 

2279.79 

2353.95 

2429.06 

2505.18 

2582.37 

2660.68 

29 

30 

1993.10 

2063.86 

2135.40 

2207.78 

2281.02 

2355.19 

2430.32 

2506.46 

2583.67 

2662.00 

30 

31 

1994.28 

2065.04 

2136.60 

12-208.  99 

2282.25 

2356.43 

2431.58 

2507.74 

2584.07 

2663.31 

3i 

32 

1995.45 

2066.231 

2137.80 

2210.20 

2283.48 

2357.68 

2432.84 

2509.02 

2586.26 

2664.63 

32 

33 

1996.62 

2057.41 

2139.00 

2211.42 

2284.71 

2358.92 

24134.10 

2510.30 

.2587.56 

2665.04 

33 

34 

1997.80 

2068.60 

2140.20 

2212.63 

2285.94 

2360.17 

2435.36 

2511.58 

2588.86 

34 

3'5 

1998.97 

2069.79 

2141.40 

22113.84 

2287.17 

2361.41 

2436.62 

2512.86 

2590.151 

2668.58 

3'5 

36 

2000.14 

2070.97 

2I42.6O 

2215.06 

2288.40 

2*362.66 

2437.89 

2514-14 

2591.45, 

2669.89 

36 

37 

2001.32 

2072.16 

2143.80 

32l6.27 

2289.63 

2363.00 

2439.15 

2515.41 

2592.75 

2671.21 

37 

38 

2002.49 

2073-35 

2145.00 

2217.49 

2200.86 

2365.15 

2440.41 

2516.69 

2594.05 

2672.53 

38 

39 

2003.67 

2074.54 

2I46.2O' 

2218.70 

12292.09 

2366.40 

2441.68 

2517.97 

2595.35 

•2673.85 

39 

40 

2004.84 

2075.72 

2147.40 

2219.92 

2293.32 

2367.64 

2442.94 

2519.25 

2596.65 

2675.16 

40 

41 

2006.02 

2076.91 

2I48.6I 

2221.14 

2294.55 

2368.89 

2444.20 

2520,54 

2597.95 

2676.48 

41 

42 

2007.19 

2078.10 

2I49.8I 

22212.36 

2295.78 

2370.14 

2445'-  47 

1252  1.  82 

2599.24 

2677.80 

42 

43 

2008.37 

2079.29 

2ISLOI 

2223.57 

2297.01 

2371.38 

2446.73 

2523.  10 

2600.541 

2679.12 

43 

44 

2009.54 

2080.48 

2152.21! 

2224.79 

2298.24 

2372.63 

2447.99 

21524.38 

2601.84 

2680.44 

44 

415 

2010.72 

2081.67 

2153.41 

2226.00 

2299.48 

2373.88 

2449.26 

25125.66 

2603.14 

2681.76 

45 

46 

2011.90 

2082.86 

2154.62 

22-27  •  22 

2300.71 

2375.13 

2450.52 

2526.95 

2604.45 

2683.08 

46 

47 

2013.07 

2084.04 

2155.82 

2228.44 

2301.94 

2376.38 

2451.79 

2528.213 

2605.75 

2684.40 

47 

48 

2014.25 

2085.23 

2157.02 

2229.66 

2303.17 

2377.63 

2453-05 

•2529.51 

2607.05 

2685.72 

48 

49 

2015.43 

2086.42 

2158.23 

2230.87 

2304.41 

2378.87 

2454.32 

2530.79 

2608.35 

2687.04 

49 

SO 

2016.60 

2087.61 

2159.43, 

2032.O9 

2305.64 

2380.12 

2455-58 

2532.08 

2609.65 

2688.36 

50 

51 

:2OI7.78 

2088.80 

2I60.63 

2233.31 

2306.88 

2381.37 

2456.85 

2533-36 

2610.95 

2689.69 

51 

52 

2018.96 

2089.99 

2I6I.84 

2234.53 

2308.11 

2-382.62 

2458.12 

2534-65 

2612.26 

2691.01 

52 

S3 

2020.13 

2091.19 

2163.04 

2235.75 

2309.34 

2383.87 

24'59.39 

2535.93 

2613.56 

2692.33 

53 

54> 

2021.31 

(2092.38 

2164.25 

12036.97 

213:10.58 

2385.12 

2460.65 

2-537.  22 

2614.86 

2693.65 

54 

55 

2022.49 

2093.57 

2165.45 

2238.19 

213,11.81 

2386.37 

2461.92 

2538.50 

2616.17 

2694.98 

55 

56 

2023.67 

2094.76 

2166.66 

2239.41 

121313  -05 

2387.62 

2463.19 

2539-79 

2617.47 

2696.30 

56 

57 

2024.85 

2095.95 

2167.86 

2240.63 

2314.28 

2388.88 

2464.46 

2541.07 

2618.78 

2697-63 

57 

58 

2026.03 

2097-14 

2169.07 

2241.85 

12315.52 

2390.13 

2465.72 

2542.36 

2620.08 

2698.95 

58 

59 

2027.20 

2008.33 

2I7O.28 

2243.07 

2316.75 

2391-38 

(2466.99 

2543.64 

2621.38 

2700.27 

59 

60 

2028.38 

2099.53 

2171.48 

21244.29 

2317.99 

2392.63 

2468.26 

2544.93 

2622.69 

2701.60 

60 

SMITHSONIAN  TABLES 


313 


The  Anti-Gudermannian. 


od  u   41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

gdu 

c/ 

270  1  '.60 

2781.71 

2863.10 

2945.81 

3029.94 

3H5.55 

3202.71 

329L53 

3382.08 

3474-47 

tf 

I 

2702.92 

2783.06 

2864.46 

2947.21 

3031.35 

3116.99 

3204.18 

3293.02 

3383.61 

3476.03 

I 

2 

2704.25 

2784.40 

2865.83 

2948.60 

3032.77 

3118.43 

3205.65 

3294.52 

3385.13 

3477-59 

2 

3 

2705.57 

2785.75 

2667.20 

2949.99 

3034-18 

3119.87 

31207.12 

3296.01 

3386.66 

3479-  14 

3 

4 

2706.90 

2787.09 

2868.57 

2951-38 

3035.60 

3121.31 

3208.58 

3297.51 

3388.18 

3480.70 

4 

5 

2708.23 

2788.44 

2869.94 

2952.77 

3037.02 

3122.75 

3210.05 

3299.01 

3389.71 

3482.26 

5 

6 

2709.55 

2789.79 

2871.31 

2954.16 

3038.43 

3124.19 

3211.52 

3300.51 

3391.24 

3483-82 

6 

7 

2710.88 

2791  .  14 

2872.68 

2955.56 

3039.85 

3125.63 

3212.99 

3302.00 

3392.77 

3485.38 

7 

8 

2712.21 

2792.49 

2874-05 

2956.95 

3041.27 

3127.08 

3214.46 

3303.50 

3394.29 

3486.94 

8 

9 

2713.54 

2793.84 

2875-42 

2958.34 

3042.68 

3128.52 

3215.93 

3305.00 

3395.82 

3488.50 

9 

10 

2714.86 

2795.19 

2876.79 

2959-74 

3044.10 

3129-96 

3217.40 

3306.50 

3397-35 

3490.06 

10 

ii 

2716.19 

2796.54 

2878.  16 

2961  .  13 

3045.52 

3131.41 

3218.87 

3308.00 

3398.88 

3491.62 

ii 

12 

2717.52 

2797.89 

2879.53 

2962.53 

3046.94 

3*132.85 

3220.34 

3309.50 

3400.41 

3493.18 

12 

13' 

2718.85 

2709.24 

2880.90 

2963.92 

3048.36 

3134.30 

32211.82 

3311.00 

3401.04 

3494.74 

13 

14 

2720.18 

2800.59 

2882.28 

2965.32 

3049.78 

3135.75 

3223.29 

3312.50 

3403.47 

3496.31 

U 

15 

2721.51 

2801.94 

2883.65 

2966.71 

3051.20 

3137.19 

3224.76 

3314.00 

3405-00 

3497.87 

15 

16 

2722.84 

2803.29 

2885.02 

2068.  II 

305-2.62 

3138.64 

3226.23 

3315.50 

3406.54 

3499.43 

16 

17 

2724.17 

2804.64 

2886.39 

2969.50 

3054.04 

3140.08,3227.71 

3-3-I7.00 

3408.07 

3501.00 

17 

18 

2/25-50 

2805.99 

2887.77 

2970.90 

3055.46 

3141.53 

3229.18 

33i8.5i 

3409.60 

3502.56 

18 

19 

2726.83 

2807.34 

2889.14 

2972.30 

3056.88 

3142.08 

3230.66 

3320.01 

3411.14 

3504.13 

19 

20 

2728.17 

2808.70 

2890.52 

2973.70 

3058.31 

3144.42 

3232.13 

3321.52 

3412.67 

3505.70 

20 

21 

2729.50 

2810.05 

2891.89 

2975.09 

3059.73 

3U5.87 

3233.61 

3323.02 

3414.20 

3507.26 

21 

22! 

2730.83 

2811.40 

2893.27 

2976.49 

3061.15 

3147.32 

3235.08 

3324.53 

3415.74 

3508.83 

22 

231 

2732.16 

2812.76 

2894.64 

2977.89 

3062.58 

31148.77 

3236.56 

3326.03 

3417.28 

3510.40 

23 

24 

2733.50 

2814.11 

2896.02 

2979.29 

3064.00 

3150.22 

3238.04 

3327.54 

3418.81 

35H.97 

24 

25 

2734.83 

2815.46 

2897.40 

2980.69 

3065.42 

3151.67 

3239.52 

3329.04 

3420.35 

3513.54 

25 

26 

2736.16 

2816.82 

2898.77 

2982.09 

3066.85 

3153.12 

3240.09 

3330.55 

3421.89 

35I5.IT 

26 

27 

2/37.50 

2818.17 

2900.15 

2983.49 

3068.27 

3154.57 

3242.47 

3332.06 

3423-43 

3516.68 

27 

28 

2738.83 

2819.53 

2901.53 

2984.89 

3069.70 

3156.03 

3243.95 

3333.56 

3424.96 

3518.25 

28 

29 

2740.17 

.2820.88 

2902.91 

2986.29 

3071  .  13 

3157.48 

3245.43 

3335.07 

3426.50 

3519.82 

29 

30 

2741-50 

2822.24 

2904.28 

2987.70 

3072.55 

3158.93 

3246.91 

3336.58 

3428.04 

3521.39 

30 

3i 

2742.84 

2823.60 

2905.66 

2989.10 

3073.08 

3160.38 

3248.39 

3338.09 

3429.58 

3522.96 

3i 

32 

2744.17 

2824.95 

2907.04 

2990.50 

3075.41 

3161.84 

3249.87 

3339.60 

34-31.12 

3524.54 

32 

33' 

2745.51 

2826.31 

2908.42 

2991.90 

3076.84 

3163.29 

3251.35 

334i.ii 

3432.66 

3526.li 

33 

34 

2746.84 

2827.67 

2009.80 

2993.31 

3078.26 

3164.74 

3252.84 

3342.62 

3434.20 

3527.68 

34 

35 

2748.18 

2829.03 

2911.18 

2994.71 

3079.69 

3166.20 

3254-32 

3344.14 

3435-75 

3529.26 

35 

36 

2749.52 

2830.39 

2912.56 

2906.12 

3081.12 

3167.65 

3255.80 

3345.65 

3437-29 

3530.83 

36 

37 

2750.85 

2831.74 

2913.94 

2997.52 

3082.55 

3169.11 

3257.28 

3347.16 

3438.83 

3532.41 

37 

38 

2752.19 

2833.10 

2915.32 

2998.93 

3083.98 

3170.57 

3258.77 

3348.67 

3440.38 

3533.99 

38 

39 

2753.53 

2834.46 

2916.71 

3000.33 

3085.41 

31172.02 

31260.25 

3350.  19 

3441.92 

3535.56 

39 

40 

2754.87 

2835.82 

2918.09 

3001.74 

3086.84 

3173.48  3261.74 

3351.70 

3443-47 

3537.14 

40 

41 

2756.21 

2837.18 

2919.47 

3003.14 

3088.27 

3174.0413263.22 

3-353.21 

3445.01 

3538.72 

41 

42 

2757.55 

2838.54 

2920.85 

3004.55 

3089.70 

3176.40 

3264.71 

3354-73 

3446.56 

3540.30 

42 

43 

2758.89 

2839.90 

2922.24 

3005.96 

3091.14 

3177.85 

3266.19 

3356.24 

3448.10 

3541.88 

43 

44 

2760.23 

2841.27 

2923.62 

3007.36 

3092.57 

3179.31 

3267.68 

3357.76 

3449.65 

3543-45 

44 

45 

2761.57 

2842.63 

2925.01 

3008.77 

3094.00 

3i8o.77 

3269.17 

3359.28 

3451.20 

3545.04 

45 

46 

2762.91 

2843.99 

2926.39 

3010.18 

3095.43 

3182.23 

3270.65 

3360.79 

3452.75 

3-546.62 

46 

47 

2764.25 

2845.35 

2927.78 

3011.59 

3096.87 

3183.69  3272.14 

3362.31 

3454.29 

3548.20 

47 

48 

2765.59 

2846.71 

2929.16 

3013.00 

3098.30 

3185.15  3273.63 

3363.83 

3455.84 

3549.78 

48 

49 

2766.93 

2848.08 

2930.55 

3014.41 

3099.74 

3l86.6l  '3275.  12 

3365.35 

3457-39 

3551.36 

49 

50 

2768.«27 

2843.44 

2931.93 

3015.82 

3101.17 

3188.07 

3276.61 

3366.87 

3458.94 

3552.94 

50 

51 

2769.62 

2850.81 

2933-32 

3017.23 

31102.60 

3189.54 

3278.10 

3368.39 

3460.49 

3554-53 

Si 

52 

2770.96 

2852.17 

2934-71 

3018.64 

3104.04 

3191.00  3279.59 

3369.91 

3462.04 

3556.li 

52 

53 

2772.30 

2853-53 

2936.09 

3020.05 

3105.48 

3-192.46  3281.08 

337L43 

3463.60 

3557-70 

53 

54 

2773.64 

2854.90 

2937.48 

3021.46 

3106.02 

3193.92  3282.57 

33712.95 

3465.15 

3559.28 

54 

55 

2774.99 

2856.26 

2938.87 

3022.87 

3108.35 

3195.39 

3284.06 

3374.47 

3466.70 

3560.87 

55 

56 

2776.33 

2857.63 

2940.26 

3024.29 

3109.79 

3196.85 

3285.56 

3375-99 

3468.36 

3562.45 

56 

57 

2777.68 

2858.99 

2041.65 

3025.70 

3111.23 

3198.32 

3287.05 

3377-51 

34'«;.8i 

3564.04 

57 

58 
59 

2779-02 
2780.37 

2860.36 
2861.73 

2043.04 
2944.42 

3027.11 
3028.52 

3112.67 
3H4.IT 

3199.7* 
3201.25 

»  3288,54 
3290.04 

3379-04 
3380.56 

3471.36 
3472.02 

3565.63 

3567.22 

58 
59 

60 

2781.71 

2863.10 

2945.81 

3029.94 

3115.55 

3202.71 

3291.53 

33&2.08 

3474-47 

3568.81 

60 

SMITHSONIAN  TABLES 


The  Anti-Gudermannian. 


gdu 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

gdi 

C/ 

3568'.8i 

3665.19 

3763.76 

3864.64 

3967.97 

4073.90 

4182.62 

4294.30 

4409.14 

4527.37 

0' 

I 

3570.40 

3666.82 

3765.42 

3866.34 

3969.71 

4075.69 

4184.46 

4296.19 

4411.08 

4529.37 

I 

2 

3571-99 

3668.44 

3767.09 

3868.04 

397L46 

4077-48 

4186.29 

4298.07 

4413.03 

453L37 

2 

3 

3573.58 

3670.07 

3768.75 

3869.74 

3973.20 

4079.27 

4188.13 

4299.96 

4414.97 

4533-37 

3 

4 

3575-17 

3671.70 

3770.41 

3871.45 

3974-95 

4081.06 

41189.97 

4301.85 

4416.92 

4535.38 

4 

5 

3576.76 

3673.32 

3772.08 

3873.15 

3976.69 

4082.86 

4191.81 

4303.74 

4418.86 

4537.38 

5 

6 

3578.35 

3674.95 

3773.74 

3874.86 

3978.44 

4084.65 

4193.65 

4305.64 

4420.81 

4539-39 

6 

7 

3579-94 

3676.58 

3775.41 

3876.56 

3980.  19 

4086.44 

4195.49 

4307.53 

4422.76 

4541.39 

7 

8 

358i.54 

3678.21 

3777.08 

3878.27 

3981.94 

4088.24 

4197.33 

4309.  4» 

4424.70 

4543-40 

g 

9 

3583.13 

3679.84 

3778.74 

3879.98 

3983.69 

4000.03 

4199.17 

4311.32 

4426.65 

4545.41 

9 

10 

3584.73 

3681.47 

3780.41 

3881.68 

3985.44 

4091.83 

4201  .02 

4313.21 

4428.60 

4547.42 

10 

ii 

3586.32 

3683.10 

3782.08' 

3883.39 

3987.19 

4003.62 

4202.87 

43IS.  II 

4430.56 

4549.43 

ii 

12 

3587.92 

3684.73 

3783.75 

3885.10 

3988.94 

4095.42 

4204.71 

4317.01 

4432.51 

4551.44' 

12 

13 

3589.51 

3686.36 

3785.42 

3886.81 

3990.69 

4097.22 

4206.56 

4318.91 

4434.46 

4553-45 

13 

14 

359i.ii 

3687.99 

3787.09 

3888.52 

3992.45 

4099.02 

4208.41 

4320.80 

4436.42 

4555.47 

14 

IS 

3592.71 

3689.63 

3788.76 

3890.23 

3994  -£0 

4100.82 

4210.26 

4322.70 

4438.37 

4557.48 

15 

16 

3594.30 

3691.26 

3790.43 

3891.95 

3995.96 

4102.62 

4212.10 

4324-61 

4440.33 

4559.50 

16 

17 

3595-90 

3692.90 

3792.10 

3893.66 

3997.71 

4104.42 

4213.95 

4326.51 

4442.29 

4561.52 

17 

18 

3597-50 

3694.53 

3793.78 

3895.37 

3999.47 

4106.22 

41215.80 

4328.41 

4444.24 

4563.53 

18 

19 

3599-10 

3696.17 

3795-45 

3897.09 

4001.22 

4108.02 

4217.66 

4330.31 

4446.20 

4565.55 

19 

20 

3600.70 

3697.80 

3797-  12 

3898.80 

4002.98 

4109.82 

4219.51 

4332.22 

4448.16 

4567.57 

20 

21 

3602.30 

3699.44 

3798.80 

3900.52 

4004.74 

4111.63 

4221.36 

4334-12 

4450.  12 

4569.59 

21 

22 

3603.90 

3701.08 

3800.47 

3902.23 

4006.50 

4113.44 

4223.22 

4336.03 

44512.09 

4571.61 

22 

23 

3605.50 

3702.71 

3802.15 

3903.  95 

4008.126 

4115.24 

4225.07 

4337-94 

4454.05 

4573.64 

23 

24 

3607.11 

3704.35 

3803.83 

3905.67 

4010.02 

4117-05 

4226.93 

4339.84 

4456.01 

4575-66 

24 

25 

3608.71 

3705.99 

3805.50 

3907.38 

4011.78 

4118.85 

4228.78 

4341.75 

4457.98 

4577.69 

25 

26 

3610.32 

3707.63 

3807.18 

3909.10 

4013.54 

4120.66 

4230.64 

4343-66 

4459.94 

4579.71 

26 

27 

3611.92 

3709.27 

3808.86 

3910.82 

4015.31 

4122.47 

4232.50 

4345.57 

4461.91 

458i.74 

.27 

28 

3613.52 

3710.91 

3810.54 

3912.54 

4017.07 

4124.28 

4234-36 

4347.48 

4463-88 

4583.77 

28 

29 

3615-13 

3712.56 

3812.22 

3914.26 

4018.84 

4126.09 

4236.22 

4349.40 

4465.85 

4585.80 

29 

30 

3616.74 

3714.20 

3813-90 

39^5.99 

4020.60 

4127.90 

4238.08 

435L3I 

4467-82 

4587.83 

30 

3i 

3618.34 

3715.84 

3815.58 

3917.71 

4022.37 

4129.72 

4239.04 

4353.23 

4469.79 

4589.86 

31 

32 

3619.95 

3717.48 

3817.27 

3919.43 

4024.  13 

4I3H.53 

4241.80 

4355.14 

4471.76 

4591.89 

32 

33 

3621.56 

3719.13 

3818.95 

3921  .  16 

4025.90 

4133.34 

4243.67 

4357.06 

4473-73 

4593.92 

33 

34 

3623.17 

3720.77 

3820.63 

3922.88 

4027.67 

4i35.i6 

4245.53 

4358.97 

4475.71 

4595.96 

34 

35 

3624.78 

3722.42 

3822.32 

3924.61 

4029.44 

4136.97 

4247.39 

4360.89 

4477.68 

4598.00 

35 

36 

3626.39 

3724.06 

3824.00 

3926.33 

4031.21 

4138.79 

4249.26 

4362.81 

4479-66 

4600.03 

36 

37 

3628.00 

3725.71 

3825.69 

3928.06 

4032.98 

4140.61 

4251.13 

4364-73 

4481.63 

4602.07 

37 

38 

3629.61 

3727.36 

3827.37 

3929.79 

4034.75 

4142.42 

4252.99 

4366.65 

4483.61 

4604.11 

38 

39 

3631.22 

3729.01 

3829.06 

393L5I 

4036.52 

4144.24 

4254.86 

4368.57 

4485.59 

4606.15 

39 

40 

3632.83 

3730.66 

3830.75 

3933.24 

4038.29 

41146.06 

4256.73 

4370.50 

4487.57 

4608.19 

40 

4i 

3634.44 

373-2-30 

3832.43 

3934-97 

4040.07 

4147.88 

4258.60 

4372.42 

4489.55 

4610.23 

41 

42 

3636.06 

3733-95 

3834.12 

3936.70 

4041.84 

4149.70 

4260.47 

4374-34 

4491.53 

4612.27 

42 

43 

3637.67 

3735.6i 

3835.81 

3938.43 

4043.61 

4151.52 

4262.34 

4376.27 

4493.51 

4614.32 

43 

44' 

3639.28 

3737.26 

3837.50 

3040.16 

4045.39 

4153.35 

4264.212 

4378.20 

4495  .'50 

4616.36 

44 

45 

3640.90 

3738.91 

3839.  19 

3941.90 

4047.17 

4155.17 

4266.09 

4380.  12 

4497.48 

4618.41 

45 

46 

3642.51 

3740.56 

3840.88 

3943.63 

4048.94 

4157.00 

4267.97 

4382.05 

4499-47 

4620.45 

46 

47 

3644.13 

3742.21 

3842.58 

3945.36 

4050.72 

4158.82 

4269.84 

4383.98 

4501.45 

4622.50 

47 

48 

3645.75 

3743.87 

3844.27 

3947.10 

4052.50 

4160.65 

4271.72 

4385.91 

4503.44 

4624.55 

48 

49 

3647.36 

3745-52 

3845.96 

3948.83 

4054.28 

4162.47 

4273.59 

4387.84 

4505.43 

4626.60 

49 

50 

3648.98 

3747.18 

3847.66 

3950-57 

4056.06 

4164.30 

4275.47 

4389.77 

4507.42 

4628.65 

50 

51 

3650.60 

3748.83 

3849.35 

3952.31 

4057.84 

4166.13 

4277.35 

4391.70 

4509.41 

4630.71 

5i 

52 

3652.22 

3750.49 

3851.05 

3954.04 

4059.62 

4167.96 

4279.23 

4393.64 

45'ii.40 

4632.76 

52 

53 

3653.84 

3752.15 

3852.75 

3955.78 

4061.41 

4169.79 

4281  .  i  i 

4395.57 

4513.39 

4634-81 

53 

54 

3655.46 

3753.8o 

3854.44 

3957-52 

4063.19 

4171.62 

4282.99 

4397.51 

4515.39 

4636.87 

54 

55 

3657.08 

3755.46 

3856.  14 

3959.26 

4064.97 

4173.45 

4284.87 

4399.44 

4517.38 

4638.93 

55 

56 

3658.70 

3757-12 

3857.84 

3961.00 

4066.76 

4175.28 

4286.76 

4401.38 

4519.38 

4640.98 

56 

57 

3660.32 

3758.78  3859.54 

3962.74 

4068.54 

4177.12 

4288.64 

4403.32 

4521.37 

4643.04 

57 

58 

3661.95 

3760.44  3861.24 

3964.48 

4070.33 

41178.95 

4290.53 

4405-26 

4523.37 

4645.10 

58 

59 

3663.57 

3762.10  3862.94 

3966.22 

4072.12 

4180.78 

4292.41 

4407.20 

4525.37 

4647.16 

59 

60 

3665.19 

3763.7613864.64 

3967.97 

4073.90 

4182.62 

4294.30 

4409.14 

4527.37 

4649.23 

60 

SMITHSONIAN  TABLES 


315 


The  Anti-Gudermannian. 


gdu 

61° 

62° 

63° 

64° 

65° 

66°    67° 

68° 

69° 

70° 

gd  u 

o' 

4649'-23 

4774.98  4904.94 

5039.42 

5178.81 

5323.5i|  5474.01 

5630.82 

5794.56 

5965.92 

Of 

I 

4651.29 

4777.  ii  4907.  14 

3041.70 

5181.18 

5325.97!5476.57 

5633.49 

5797-35 

5968.84 

I 

2 

4653.35 

4779.  251  4909.  35 

5043.99 

5183.54 

5328.43 

5479-13 

5636.16 

5800.14 

5971.77 

2 

3 

4655.42 

4781.38 

49H.55 

5046.27 

5185.91 

5330.90 

5481.69 

5638.84 

5802.94 

5974.70 

3 

4 

4657.49 

4783.51 

4913-76  5048.56 

5188.29 

5333.36 

5484-26 

5641-51 

5805.74 

5977.63 

4 

5 

4659.55 

4785.65 

4915.97 

5050.85 

5190.66 

5335.83 

5486.83 

5644.19 

5808.54  5980.57 

5 

6 

4661.62 

4787.79 

4918.18 

5053.14 

5193.03 

5338.30 

5489.40 

5646.87 

5811.34 

5983.50 

6 

7 

4663.69 

4789.92 

4920.39 

5055.43 

5I95.4I 

5340.77 

5491.97 

5649.56 

5814.15 

5986.44 

8 

4665.76 

4792.06 

49212.60 

5057.72 

5197.79 

5343.24 

5494.54 

5652.24 

5816.95 

5989.38 

8 

9 

4667.83 

4794-20 

4924.81 

5060.01 

5200.17 

5345.71 

5497-  ii 

5654.93 

5819.76 

5992.33 

9 

10 

4669.91 

479^.34 

4927.03 

5062.30 

5202.55 

5348.18 

5499.69 

5657.61 

5822.57 

5995.27 

10 

ii 

4671.98 

4798.49 

4929-24 

5064.60 

5204.93 

5350.66 

5502.27 

5660.30 

5825.39 

5998.22 

ii 

12 

4674-06 

4800.63 

4931.46 

5066.90 

5207.31 

5353.14 

5504.85 

5663.00 

5828.20 

6001.17 

V2 

13 

4676.13 

4802.77 

4933-68 

5069.19 

5209.70 

5355.61 

5507.43 

5665.69 

5831.02 

6004.13 

13 

14 

4678.21 

4804.92 

4935.90 

5071.49 

52112.08 

5358.09 

5510.01 

5668.38 

5833.84 

6007.08 

14 

15 

4680.29 

4807.07 

4938.12 

5073.80 

5214.47 

5360.58 

5512.60 

5671  .08 

5836.66 

6010.04 

15 

16 

4682.37 

4809.21 

4940-34 

5076.10 

5216.86 

5363.06 

55I5.I8 

5673.78 

5839.48 

6013.00 

16 

17 

4684.45 

4811.36 

4942.57 

5078.40 

5219.25 

5365.55 

5517.77 

5676.48 

5842.31 

6015.96 

17 

18 

4686.53 

4813.51 

4944-79 

5080.71 

5221.64 

5368.03 

5520.36 

5679.19 

5845.13 

6018.93 

18 

19 

4688.61 

4815.67 

4947.02 

5083.01 

5224.04 

5370.52 

5522.95 

5681.89 

5847.96 

6021.90 

19 

20 

4690.70 

4817.82 

4949-24 

5085.32 

52*26.43 

5373.01 

5525.55 

5684.60 

5850.79 

6024.87 

20 

21 

4692.78 

4819.97 

4951-47 

5087.63 

5228.83 

5375-50 

5528.14 

5687.31 

5853.63 

6027.84 

21 

22 

4694.87 

4822.13 

4953.70 

5089.94 

5231.23 

5378.00 

5530.74 

5690.02 

5856.47 

6030.81 

22 

23 

4696.96 

4824.29 

4955-94 

5092.25 

5233.63 

5380.49 

5533-34 

5692.73 

5859.31 

6033.79 

23 

24 

4699.05 

4826.44 

4958.17 

5004.57 

5236.03 

5382.99 

5535-94 

5695.45 

5862.15 

6036.77 

24 

25 

4701.14 

4828.60 

4960.40 

5096.88 

5238.43 

5385.49 

5538.55 

5698.17 

5864.99 

6039.75 

25 

26 

4703.23 

4830.76 

4962.  64 

5099.20 

5240.84 

5387.99 

5541.15 

5700.89 

5867.84 

6042.74 

26 

27 

4705.32 

4832.93 

4964.87 

5101.52 

5243-24 

5390.49 

5543.76 

5703.6i 

5870.69 

6045.73 

27 

28 

4707.41 

4835.09 

4967.11 

5103.84 

5245-65 

5392.99 

5546.37 

5706.33 

5873.54 

6048.72 

28 

29 

4709.51 

4837.25 

4969.35 

5106.16 

5248.06 

5395.50 

5548.98 

5709-06 

5876.39 

6051.71 

29 

30 

4711-60 

4839.42 

4971.59 

5108.48 

5250.47 

5398.01 

5551.59 

57V.  78 

5879.24 

6054.70 

30 

31 

4713.70 

4841.58 

4973.83 

5110.80 

5252.88 

5400.52 

5554.20 

57I4.5I 

5882.10 

6057-70 

31 

32  4715.79 

4843.75 

4976.08 

5113.13 

5255.30 

5403-03 

5556.82 

5717.25 

5884.96 

6060.70 

32 

33  4717.89 

4845-92 

4978.32 

5H5.45 

5257.71 

5405.54 

5559-44 

5719-98 

5887.82 

6063.71 

33 

34 

4719.99 

4848.09 

4980.57 

5117.78 

5260.13 

5408.05 

5562.06  5722.71 

5890.68 

6066.71 

34 

35 

4722.09 

4850.26 

4982.82 

5120.11 

5262.55 

5410.57 

5564.68 

5725.45 

5893.55 

6069.71 

35 

36 

4724.19 

4852.43 

4985-06 

5122.44 

5264.97 

54i3.o8 

5567.30 

5728.19 

5896.41 

6072.72 

36 

37 

4726.30 

4854.61 

4987.  3* 

5124.77 

5267.39 

5415.60 

5569.93 

5730.93 

5899.28 

6075.73 

37 

38 

4728.40 

4856.78 

4989-56 

5127.11 

5269.81 

5418.12 

5572.55 

5733.68 

5902.15 

6078.75 

38 

39 

4730.51 

4858.96 

4991.82 

5129.44 

5272.23 

5420.64 

5575.18 

5736.42 

5905-03 

6081.76 

39 

40 

4732.61 

4861.13 

4994.07 

3131.78 

5274.66 

5423.17 

5577.8i 

5739.17 

5907.90 

6084.78 

40 

41 

4734.72 

4863.31 

4996.32 

5i34.li 

5277.09 

5425.69 

5580.44 

5741.92 

5910.78 

6087.81 

41 

42 

4736.83 

4865.49 

4998-58 

5136.45 

5279.52 

5428.22 

5583.08 

5744.67 

5913.67 

6090.83 

42 

43 

4738.94 

4867.67 

5000.84 

5H38.79 

5281.95 

5430.75 

5585.71 

5747.43 

5916.55 

6093.86 

43 

44 

4741.05 

4869.86 

5003.10 

5141.14 

5284.38 

5433.28 

5588.35 

5750.18 

5919.44 

6096.89 

44 

45 

4743.16 

4872.04 

5005.36 

5143.48 

5286.82 

5435.8i 

5590.09 

5752.94 

5922.32 

6099.92 

45 

46 

4745.28 

4874-22 

5007.62 

5145.83 

5289.25 

5438.35 

5593.64 

5755-70 

5925.22 

6102.95 

46 

47  4747-39 

4876.41 

5009.88 

5148.17 

5291.69 

5440.88 

5596.28 

5758.46 

5928.11 

6105.99 

47 

48  4749.51 

4878.60 

5012.15 

5150.52 

5294.13 

5443.42 

5598.93 

5761.23 

5931.00 

6109.03 

48 

49  4751.63 

4880.79 

5014-41 

5152.87 

5296.57 

5445.96 

5601.57 

5763.99 

5933-90 

6112.07 

49 

50  4753-74 

4882.98 

5016.68 

5155.22 

5299.01 

5448.50 

5604.22 

5766.76 

5936.80 

6115.12 

50 

51  4755-86 

4885.17 

5018.94 

5157.57 

5301-45 

5451.05 

5606.87 

5769.53 

5939.70 

6118.16 

51 

52  4757.98 

4887.36 

5021.21 

5159.93 

5303.90 

5453.59 

5609.53 

5772.31 

5942.61 

6l2I.  21 

52 

53  4760.10 

4889.55 

5023.48 

5162.28 

5306.34 

5456.14 

5612.18 

5775.08 

5945.51 

6124.26 

53 

54  4762.23 

4891.75 

5025.76 

5164.64 

5308.79 

5458.68 

5614.84 

5777-86 

5948.42 

6127.32 

54 

55  4764.35 

4893.94 

5028.03 

5167.00 

53H.24 

5461.23 

5617-50 

5780.64 

5951.33 

6130.38 

55 

56  4766.47 

4896.14 

5030.30 

5169.36 

5313.69 

5463.78 

5620.16 

5783.42 

5954.24 

6133.44 

56 

57  4768.60 

4898.34 

5032.58 

5171.72 

53I6.I5 

5466.34 

5622.82 

5786.20 

5957.16 

6136.50 

57 

58  4770.73 

4900.54 

5034.86 

5174.08 

53i8.6o 

5468.89 

5625.49 

5788.98 

so^o.oS 

6139.56 

58 

59  4772.86 

4902.74  5037.14 

5176.44 

5321.06 

5471.45 

5628.  15 

579L77 

5963.00 

6142.63 

59 

60  14774.98 

4004.9415039.42 

5178.81 

5323.51  5474.01 

5630.82 

5794-56 

5965-92 

6145.70 

60 

SMITHSONIAN  TABLES 


316 


The  Anti-Gudermannian. 


gdu 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

gdu| 

C/ 

6i45'-70 

6334.84 

6534.42 

6745.74 

6970.34 

7210.07 

7467.21 

7744-57 

8045.71 

8375.20 

0' 

I 

6148.77 

6338.08 

6537.85 

6749.37 

6974.20 

7214.20 

7471.66 

7749.38 

8050.95 

8380.96 

I 

2 

6151.85 

6341.32 

6541.27 

6753.01 

6978.07 

7218.35 

7476.11 

7754-20 

8056.20 

8386.73 

2 

3 

6154.93 

6344-56 

6544.70 

6756.64 

6981.95 

7222.49 

7480.57 

7759-02 

8061.46 

8392.52 

3 

4 

6158.01 

6347.81 

6548.13 

6760.28 

6985-83 

7226.64 

7485.03 

7763.86 

8066.73 

8398.31 

4 

5 

6161.09 

6351.06 

6551.57 

6763.93 

6989.71 

7230.80 

7489-50 

7768.70 

8072.01 

8404.11 

5 

6 

6164.18 

6354.31 

6555-01 

6767.58 

6993.60 

7234.96 

7493.98 

7773-55 

8077.29 

8409.92 

6 

7 

6167.27 

6357.56 

6558.45 

6771.23 

6997.49 

7239-12 

7498.46 

7778.40 

8082.58 

8415.74 

7 

8 

6170.36 

6360.82 

6561.89 

6774.89 

7001.38 

7243.29 

7502.95 

7783.26 

8087.88 

8421.57 

8 

9 

6i73.45 

6364.08 

6565.34 

6778.55 

7005.28 

7247.47 

7507.44 

7788.12 

8093-19 

8427.42 

9 

10 

6176.55 

6367.35 

6568.79 

6782.21 

7009.19 

7251.65 

7511.94 

7793.00 

8098.51 

8433.27 

10 

II 

6179.65 

6370.61 

6572.25 

6785.88 

7013.10 

7255.83 

7516.45 

7797.88 

8103.83 

8439.13 

ii 

12 

6182.75 

6373.88 

6575.70 

6789.55 

7017.01 

7260.02 

7520.96 

7802.76 

8109.17 

8445.00 

12 

13 

6185.85 

6377-16 

6579.  16 

6793.22 

7020.93 

7264.22 

7525.47 

7807.66 

8114.51 

8450.88 

13 

14 

6188.96 

6380.43 

6582.63 

6796.90 

7024.85 

7268.42 

7530.00 

7812.56 

8119.86 

8456.77 

14 

15 

6192.07 

6383.71 

6586.10 

6800.58 

7028.77 

7272.62 

7534.53 

7817.46 

8125.212 

8462.67 

15 

16 

6195  .  18 

6386.99 

6589.57 

6804.27 

7032.70 

7276.83 

7539.06 

7822.38 

8130.58 

8468.58 

16 

17 

6198.30 

6390.28 

6593.05 

6807.96 

7036.64 

7281.05 

7543.60 

7827.30 

8135.95 

8474.50 

17 

18 

6201.42 

6393.57 

6596.52 

6811.65 

7040.58 

7285.27 

7548.  15 

7832.23 

8141.33 

8480.43 

18 

19 

6204.54 

6396.86 

6600.01 

6815.35 

7044.52 

7289.49 

7552.70 

7837.16 

8146.72 

8486.37 

19 

20 

6207.66 

6400.15 

6603-49 

6819.05 

7048.47 

7293.72 

7557.26 

7842.10 

8152.12- 

8492.32 

20 

121 

6210.78 

6403.44 

6606.98 

6822.75 

7052.42 

7297.96 

7561.82 

7847.05 

8157.53 

8498.28 

21 

22 

6213.01 

6406.74 

6610.47 

6826.46 

7056.37 

7302.20 

7566.39 

7852.01 

8162.95 

8504.25 

22 

23 

6217.04 

64110.05 

6613.96 

6830.18 

7060.33 

7306.44 

7570.96 

7856.97 

8168.37 

8510.23 

23 

24 

6220.  1  8 

6413-35 

6617.46 

6833-89 

7064.30 

7310.69 

7575-54 

7861.94 

8173.80 

8516.22 

24 

25 

6223.31 

6416.66 

6620.97 

6837.61 

7068.27 

7314.95 

7580.13 

7866.91 

8179-24 

8522.22 

25 

26 

6226.45 

6419.97 

6624.47 

6841.34 

7072.24 

7319.21 

7584.72 

7871.90 

8184.69 

8528.23 

26 

27 

6229.59 

6423.29 

6627.98 

6845.07 

7076.22 

7323.47 

7589.^2 

7876.89 

8190.15 

8534.26 

27 

28 

6232.74 

6426.61 

6631.49 

6848.80 

7080.20 

7327.74 

7593.93 

7881.89 

8195.61 

8540.29 

28 

29 

6235-89 

6429.93 

6635.01 

6852.53 

7084.19 

7332.02 

7598.54 

7886.89 

8201.09 

8546.33 

129 

30 

6239.04 

6433-25 

6638.53 

6856.27 

7088.18 

7336.30 

7603.16 

7891.91 

8206.57 

8552.38 

30 

31 

6242.19 

6436.58 

6642.05 

6860.02 

7092.18 

7340.55 

7607-78 

7896.93 

8212.06 

8558.45 

31 

32 

6245.35 

6439.91 

6645.58 

6863.77 

7096.18 

7344.88 

7612.41 

7901.95 

8217.56 

8564.52 

32 

33 

6248.50 

6443.24 

6649.11 

6867.52 

7100.18 

7349.18 

7617.04 

7906.98 

8223.07 

8570.61 

33 

34 

6251.67 

6446.58 

6652.64 

6871.27 

7104.19 

7353.48 

7621.68 

7912.03 

8228.59 

8576.70 

34 

35 

6254-83 

6449-92 

6656.18 

6875-03 

7108.21 

7357.79 

7626.33 

7917.08 

8234.12 

8582.81 

35 

36 

6258.00 

6453.26 

6659.72 

6878.80 

7112.23 

7362.10 

7630.99 

7922.13 

8239.66 

8588.93 

36 

37 

6261.17 

6456.61 

6663.26 

6882.56 

7116.25 

7366.42 

7635.65 

7927.19 

8245.20 

8595.06 

37 

38 

6264.34 

6459.95 

6666.81 

6886.34 

7120.28 

7370.74 

7640.31 

7932.26 

8250.75 

8601.20 

38 

39 

6267.51 

6463.31 

6670.36 

6890.11 

7124.31 

7375.07 

7644.98 

7937-34 

8256.31 

8607.35 

39 

40 

6270.69 

6466.66 

6673.91 

6893-89 

7128.35 

7379.40 

7649.66 

7942.43 

8261.88 

8613.51 

40 

41 

6273.87 

6470.02 

6677.47 

6897.68 

7132.39 

7383.74 

7654.35 

7947.52 

8267.46 

8619.68 

4i 

42 

6277.05 

6473.38 

6681.03 

6901.46 

7136.43 

7388.08 

7659.04 

7952.62 

8273.05 

8625.86 

42 

43 

6280.24 

6476.74 

6684.59 

6905.25 

7140.48 

7392.43 

7663.74 

7957.72 

8278.65 

8632.05 

43 

44 

6283.43 

6480.11 

6688.16 

6909.05 

7144.54 

7396.79 

7668.44 

7962.84 

8284.25 

8638.26 

44 

45 

6286.62 

6483.48 

6691.73 

6912.85 

7148.60 

7401.15 

7673.15 

7967.96 

8289.87 

8644-47 

45 

46 

6289.82 

6486.86 

6695-31 

6916.65 

7152.67 

7405.51 

7677.87 

7973.09 

8295.49 

8650.70 

46 

47 

6293.01 

6490.23 

6698.89 

6920.46 

7156.74 

7409.88 

7682.59 

7978.23 

8301  .  12 

8656.94 

47 

48 

6296.21 

6493.61 

6702.47 

6924.27 

7160.81 

7414.  ,26 

7687.32 

7983.37 

8306.77 

8663.19 

48 

49 

6299.42 

6497.00 

6706.06 

6928.09 

7164.89 

7418.64 

7692.05 

7988.52 

8312.42 

8669.45 

49 

50 

6302.62 

6500.38 

6709.65 

6931-91 

7168.97 

7423.03 

7696.79 

7993.68 

8318.08 

8675.72 

50 

51 

6305.83 

6503.77 

6713.24 

6935.73 

7173.05 

7427.42 

7701.54 

7998.85 

8323.75 

8682.00 

51 

52 

6309.04 

6507.17 

6716.84 

6939.56 

7177.15 

7431.82 

7706.30 

8004.03 

8329-43 

8688.29 

52 

53 

6312.26 

6510.56 

6720.44 

6943.40 

7181.25 

7436.22 

7711.06 

8009.21 

8335.12 

8694.60 

53 

54 

6315.48 

6513.96 

6724.04 

6947.23 

7185.35 

7440.63 

7715.63 

8014.40 

8340.82 

8700.92 

54 

55 

6318.70 

6517.36 

6727.65 

6951.07 

7189.46 

7445-05 

7720.60 

8019,60 

8346.52 

8707.25 

55 

56 

6321.92 

6520.77 

6731.26 

6954.92 

7193.57 

7449.47 

7725.38 

8024.  81 

8352.24 

8713.59 

56 

57 

6325.14 

65124.18 

6734.88 

6958.77 

7197.69 

7453.89 

7730.17 

8030.02 

8357.96 

8719.94 

57 

58 

6328.37 

6527.59 

6738.50 

6962.62 

7201.81 

7458.33 

7734.96 

8035.24 

8363-70 

8726.30 

58 

59 

6331.61 

6531.01 

6742.12 

6066.48 

7205.04 

7462.76 

7739.76 

8040.47 

8369.44 

8732.68 

59 

60 

6334.84 

6534.42 

6745.74 

6970.34 

7210.07 

7467-21 

7744-57 

8045.71 

8375.20 

8739.06 

60 

SMITHSONIAN  TABLES 


317 


The  Anti-Gudermaimian. 


gd  u 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

gd  u 

<y 

8739'.o6 

9145.46 

9605.82 

10136.89 

10764.62 

11532.52 

12522.11 

13916.43 

16299.56 

O' 

I 

8745-46 

9152.65 

9614.03 

10146.  4^ 

10776.11 

11546.88 

12541.27 

13945.20 

16357.34 

I 

2 

8751.87 

9159.86 

9622.27 

10156.07 

10787.65 

11561.31 

12560.54 

13974-22 

16416.11 

2 

3 

8758.29 

9167.08 

9630.52 

10165.70 

10799.22 

11575.80 

12579.91 

14003.48 

16475.90 

3 

4 

8764.73 

9174.32 

9638.80 

IOI75.37 

10810.82 

11590.34 

12599.40 

14033-00 

16536.76 

4 

5 

8771.17 

9181.57 

9647-09 

10185.05 

10822.47 

11604.95 

12619.00 

14062.77 

16598.69 

5 

6 

8777.63 

9188.84 

9655.40 

IOI94-77 

10834.  16 

11619.62 

12638.70 

14092.80 

16661.78 

6 

7 

8784.10 

9196.13 

0663.74 

10204.51 

10845.89 

11634.36 

12658.53 

14123.09 

16726.04 

7 

8 

8790.58 

9203.42 

9672.09 

10214.28 

10857-65 

11649.16 

12678.46 

14153.66 

16791.53 

8 

9 

8797.08 

9210.74 

9680.47 

10224.08 

10869.46 

11664.02 

12698.52 

14184.49 

16858.29 

9 

10 

8803.58 

9218.07 

9688.86 

10233.90 

10881.31 

11678.94 

12718.69 

14215.61 

16926.36 

10 

ii 

8810.10 

9225.41 

9697.28 

10243.75 

10893.20 

11693.93 

12738.98 

14247.01 

16995-81 

ii 

12 

8816.63 

9232.77 

9705.71 

10253.64 

10905.13 

11708.99 

12759.39 

14278.70 

17066.70 

12 

13 

8823.17 

9240.15 

97H.I7 

10263.54 

10917.10 

11724.11 

12779.92 

14310.68 

17139.09 

13 

H 

8829.73 

9247.54 

9722.64 

10273.48 

10929.11 

H739.30 

12800.58 

14342.97 

17213-03 

14 

15 

8836.30 

9254.95 

9731  .  14 

10283.45 

10941.17 

H754.56 

12821.36 

14375.56 

17288.57 

15 

16 

8842.88 

9262.37 

9739-66 

10293.45 

10953-26 

11769.88 

12842.26 

14408.46 

17365.83 

16 

17 

8849.47 

9269.81 

9748.20 

10303.47 

10965.40 

11785.27 

12863.30 

14441.68 

17444.87 

17 

18 

8856.07 

9277.27 

9756.76 

10313-53 

T0977.59 

11800.73 

12884.46 

H475.23 

17525.77 

18 

19 

8862.69 

9284.74 

9765.34 

10323.61 

10089.81 

11816.26 

12905.75 

14509-  10 

17608.63 

19 

20 

8869.32 

9292.23 

9773-94 

10333.72 

[1002.08 

11831.87 

12927.18 

I4543.3I 

17693-49 

20 

21 

8875-96 

9299.73 

9782.57 

10343-85 

11014.40 

11847.54 

12948.74 

14577.87 

17780.53 

21 

22 

8882.62 

9307.25 

9791.21 

10354-03 

11026.75 

11863.28 

12970.44 

14612.78 

17869.83 

22 

23 

8889.29 

93I4.79 

9799-88 

10364.24 

11039.15 

11879.10 

12092.27 

14648.04 

17961.51 

23 

24 

8895.97 

9322.34 

9808.57 

10374.47 

11051.60 

11894.99 

13014-25 

14683.67 

18055.70 

24 

25 

8902.66 

9329.91 

9817.28 

10384-73 

11064.09 

11910.95 

13036.36 

14719.67 

18152.55 

25 

26 

8909.37 

9337-49 

9826.02 

10395.03 

11076.63 

11926.09 

13058.62 

14756.05 

18252.20 

26 

27 

8916.09 

9345-10 

0834.77 

10405.35 

11089.21 

11943.10 

13081.02 

14792.83 

18354.83 

27 

28 

8922.82 

9352-72 

0843.55 

10415.71 

11101.84 

11959.29 

13103.58 

14830.00 

18460.62 

28 

29 

8929.57 

9360.35 

0852.35 

10426.09 

11114-52 

H975.55 

13126.27 

14867.57 

18569.76 

29 

30 

8936.33 

9368.00 

9861.17 

10436.51* 

11127.24 

11991.89 

13149.12 

14905-56 

18682.49 

30 

31 

8943.10 

9375-67 

9870.02 

10446.96 

11140.01 

12008.31 

13172.13 

14943.08 

18799.03 

31 

32 

8949.88 

93*83.36 

9878.88 

10457.44 

11152.82 

12024.81 

13195.28 

14982.83 

18919.67 

32 

33 

8956.68 

9391.06 

9887.77 

10467.95 

11165.69 

12041.39 

13218.60 

15022.12 

19044.69 

33 

3-1 

8963.49 

9398.79 

9896.69 

10478  .  50 

11178.60 

12058.05 

13242.07 

15061.87 

19174.44 

34 

35 

8970.32 

9406.53 

9005.63 

10489.08 

11191.56 

12074.79 

13265.70 

15102.08 

19309-27 

35 

36 

8977.16 

0414.28 

9914.59 

10409-69 

11204.57 

12091.60 

13289.50 

15142.77 

19449.61 

36 

37 

8984.01 

9422.05 

9923.57 

10510.33 

11217.63 

12108.51 

13313.47 

15183.04 

19595.92 

37 

38 

8990.87 

9429.84 

9932.57 

10521.01 

11230.74 

12125.49 

13337.60 

15225.62 

19748.73 

38 

39 

8097-75 

9437.65 

9941-60 

10531-71 

11243-90 

12142.57 

13361.90 

15267.80 

19908.66 

39 

40 

9004.65 

9445.48 

9950.66 

10542.45 

11257.11 

12159.72 

13386.37 

15310.51 

20076.39 

40 

41 

0011.55 

9453.32 

9959-73 

10553.23 

11270.37 

12176.96 

13411.02 

15353.76 

20252.72 

41 

42 

9018.47 

9461  .  18 

9968.83 

10564.04 

11283.68 

12194.29 

13435.85 

15397.56 

.20438.59 

42 

43 

0025.41 

9469.06 

9977.96 

10574-88 

11297.04 

12211.71 

13460.85 

15441.92 

20635.09 

43 

44 

9032.36 

9476.96 

9987.11 

10585.76 

11310.46 

12229.21 

13486.05 

15486.86 

20843.50 

44 

45 

9039.32 

9484.87 

9996.28 

10596.67 

11323-93 

12246.81 

I35H.43 

15532.40 

21065.37 

45 

46 

9046.29 

9492.81 

10005.48 

10607.62 

11337.45 

12264.49 

13537-00 

15578.55 

21302.55 

46 

47 

9053.28 

9500.76 

10014.70 

10618.60 

11351.02 

12282.26 

13562.75 

15625.32 

21557.31 

47 

48 

9060.29 

9508.73 

10023.95 

10629.61 

11364.65 

12300.13 

13588.71 

15672.75 

21832.48 

43 

49 

9067.31 

95i6.7i 

10033.22 

10640.67 

H378.33 

12318.09 

13614.85 

15720.83 

22131.60 

49 

50 

9074.34 

9524.72 

10042.52 

10651.75 

11392.06 

12336.15 

13641.20 

15769.59 

22459.26 

50 

51 

0081.39 

9532.74 

10051.84 

10662.87 

11405.85 

12354.30 

13667.75 

15819.06 

22821.46 

51 

52 

9088.45 

9540.79 

10061.19 

10674.03 

11419.70 

12372.54 

13694.52 

15869.25 

23226.39 

52 

53 

9095.52 

9548.85 

10070.56 

10685.22 

11433.60 

12300.89 

13721.48 

15920.19 

23685.42 

53 

54 

9102.61 

9556.93 

10079.96 

10696.46 

11447.56 

12409.33 

13748.67 

15971.89 

24215-35 

54 

55 

9109.72 

9565.03 

10080.38 

10707.72 

11461.58 

12427.87 

13776.07 

16024.38 

24842.  12 

55 

56 

57 

9116.84 
9123.97 

9573.15 
9581.29 

10008.83 
10108.30 

10719.03 
10730.37 

"475.65 
11489.78 

12446.51 
12465.26 

13803.68 
13831.53 

16077.68 
16131.82 

25609.23 
26508.21 

56 

57 

58 

9131.12 

9589.45 

10117.81 

I074L75 

H503.97 

12484.10 

13859.60 

16186.83 

27992.10 

58 

59 

9138.28 

9597.62 

10127.33 

10753.17 

11518.21 

12503.05 

13887.00 

162.12.74 

30374-96 

59 

to 

9145.46 

0605.82 

10136.89 

10764.62 

11532.52 

i  2522.  i  i 

13916.43 

16299.56 

GO 

60 

SMITHSONIAN  TABLES 


From  84°  307  onwards  Interpolate  by  second  differences. 


TABLE  VIII 


CONVERSION  OF  RADIANS  INTO  ANfiULAR  MEASURE  AND  VICE  VERSA 


319 


Conversion  of  Angular  Measure  into  Radians. 


n 

Radiant  for  n  degrees 

Radians  for  n  minutes 

Radians  for  n  seconds 

n 

Radians  for  n  degrees 

I 

0.01745  32925  2 

0.00029  08882  I 

o.ooooo  48481  4 

61 

1.06465  08437  2 

2 

.03490  65850  4 

.00058  17764  2 

.00000  96962  7 

62 

.08210  41362  4 

3 

.05235  98775  6 

.00087  26646  3 

.00001  45444  i 

63 

.09955  74287  6 

4 

.00981  31700  8 

.OOIl6  35528  3 

.ooooi  93925  5 

64 

.11701  07212  8 

5 

0.08726  64626  O 

0.00145  44410  4 

0.00002  42406  8 

65 

1.13446  40138  o 

6 

.10471  97551  2 

•00174  53292  5 

.OOOO2  90888  2 

66 

.ISI9I  73063  2 

7 

.12217  30476  4 

.00203  62174  6 

.00003  39369  6 

67 

.16937  05988  4 

8 

.  13962  63401  6 

.00232  71056  7 

.00003  87850  9 

68 

.18682  38913  6 

9 

.15707  96326  8 

.00261  79938  8 

.00004  36332  3 

69 

.20427  71838  8 

10 

0.17453  29252  o 

0.00290  88820  9 

0.00004  84813  7 

70 

1.22173  04764  o 

ii 

.  19198  62177  2 

.00319  97703  o 

.00005  33295  o 

7i 

.23918  37689  2 

12 

.20943  95102  4 

.00349  06585  o 

.00005  81776  4 

72 

.25663  70614  4 

13 

.22689  28027  6 

.00378  15467  i 

.00006  30257  8 

73 

.27409  03539  6 

14 

.24434  60952  8 

.00407  24349  2 

.00006  78739  2 

74 

.29154  36464  8 

15 

0.26179  93878  o 

0.00436  33231  3 

0.00007  27220  5 

75 

1.30899  69390  o 

16 

:  27925  26803  2 

.00465  42113  4 

.00007  75701  9 

76 

.32645  02315  2 

17 

.29670  59728  4 

.00494  50995  5 

.00008  24183  3 

77 

.34390  35240  4 

18 

.31415  92653  6 

.00523  59877  6 

.00008  72664  6 

7& 

.36135  68165  6 

•  19 

.33i6i  25578  8 

.00552  68759  6 

.00009  21146  o 

79 

.37881  01090  8 

20 

0.34906  58504  o 

0.00581  77641  7 

0.00009  69627  4 

80 

1.39626  34016  o 

21 

.36651  91429  2 

.00610  86523  8 

.00010  18108  7 

81 

.41371  66941  2 

22 

.38397  24354  4 

.00639  95405  9 

.00010  66590  i 

82 

.43116  99866  4 

23 

.40142  57279  6 

.00669  04288  o 

.oooii  15071  5 

83 

.44862  32791  6 

24 

.41887  90204  8 

.00698  13170  i 

.oooii  63552  8 

84 

.46607  65716  8 

25 

0.43633  23130  o 

0.00727  22052  2 

O.OOOI2  I2O34  2 

85 

1.48352  98642  o 

26 

•45378  56055  2 

.00756  30934  3 

.00012  60515  6 

86 

.50098  31567  2 

27 

.47123  88980  4 

.00785  39816  3 

.00013  08996  9 

87 

.51843  64492  4 

28 

.48869  21905  6 

.00814  48698  4 

.00013  57478  3 

88 

.53588  97417  6 

29 

.50614  54830  8 

.00843  5758o  5 

.00014  05959  7 

89 

•55334  30342  7 

30 

0.52359  87756  o 

0.00872  66462  6 

0.00014  54441  o 

90 

1.57079  63267  9 

31 

.54105  2068l  2 

.00901  75344  7 

.00015  02922  4 

9i 

.58824  96193  i 

32 

.55850  53606  4 

.00930  84226  8 

.00015  5M03  8 

92 

.60570  29118  3 

33 

•57595  86531  6 

.00959  93io8  9 

.00015  99885  i 

93 

.62315  62043  5 

34 

.59341  19456  8 

.00989  01990  9 

.00016  48366  5 

94 

.64060  94568  7 

35 

o.6io85  52382  o 

0.01018  10873  0 

0.00016  96847  9 

95 

1.65806  27893  9 

36 

.62831  85307  2 

.01047  19755  i 

.00017  45329  3 

96 

.67551  60819  i 

37 

.64577  18232  4 

.01076  28637  2 

.00017  93810  6 

97 

.69296  93744  3 

38 

.66322  5H57  6 

.01105  37519  3 

.00018  42292  o 

98 

.71042  26669  5 

39 

.68067  84082  8 

.01134  46401  4 

.00018  90773  4 

99 

.72787  59594  7 

40 

0.69813  17008  o 

0.01163  55283  5 

0.00019  39254  7 

100 

1.74532  92519  9 

41 

.71558  49933  2 

.01192  64165  6 

.00019  87736  i 

no 

.91986  21771  9 

42 

.73303  82858  4 

.01  22  i  73047  6 

.00020  36217  5 

I2O 

2.09439  51023  9 

43 

.75049  15783  6 

.01250  81929  7 

.00020  84698  8 

130 

.26892  80275  9 

44 

.76794  48708  8 

.01279  90811  8 

.00021  33180  2 

140 

.44346  09527  9 

45 

0.78539  81634  o 

0.01308  99693  9 

o.  00021  81661  6 

ISO 

2.61799  38779  9 

46 

.80285  14559  2 

.01338  08576  o 

.00022  30142  9 

160 

.79252  68031  9 

47 

.82030  47484  4 

.01367  17458  i 

.00022  78624  3 

170 

.96705  97283  9 

48 

.83775  80409  6 

.01306  26340  2 

.00023  27105  7 

180 

3.14159  26535  9 

49 

.85521  13334  8 

.01425  35222  2 

.00023  75587  o 

190 

.31612  55787  9 

50 

0.87266  46260  o 

0.01454  44104  3 

0.00024  24068  4 

200 

3.49065  85039  9 

51 

.89011  79185  2 

.01483  52986  4 

.00024  72549  8 

2IO 

.66519  14291  9 

52 

.90757  12  1  10  4 

.01512  61868  5 

.00025  21031  i 

22O 

.83972  43543  9 

53 
54 

.92502  45035  6 
.94247  77960  8 

.01541  70750  6 
.01570  79632  7 

.00025  69512  5 
.00026  17093  9 

230 
240 

4.01425  72795  9 
.  18879  02047  9 

55 

0.95993  10886  o 

0.01599  88514  8 

0.00026  66475  2 

250 

4-36332  31209  9 

56 

.97738  438l  I  2 

.01628  97396  9 

.00027  14956  6 

260 

.53785  60551  9 

57 

.99483  76736  4 

.01658  06278  9 

.00027  63438  o 

270 

.71238  89803  8 

58 

1.01229  09661  6 

.01687  15161  o 

.00028  11919  4 

300 

5-23508  77559  8 

59 

.02974  42586  8 

.01716  24043  i 

.00028  60400  7 

330 

.75958  65315  8 

60 

1.04719  755120 

0.01745  32925  2 

0.00029  08882  i 

36o 

6.28318  53071  8 

SMITHSONIAN  TABLES 


320 


Conversion  of  Radians  into  Angular  Measure. 


Radians 

Angle 

Radians 

Angle 

O.I 
6.2 

0.3 
0.4 

0     <       // 

05  43  46.48062  47 
ii  27  32.96124  94 
17  ii  19.44187  41 
22  55  05.92249  88 

0.006 
.007 
.008 
.009 

o  20  37-58883  75 
24  03.85364  37 
27  30.11845  oo 
30  56.38325  62 

0.5 
0.6 
0.7 
0.8 
0.9 

28  38  52.40312  35 
34  22  38.8837483 
40  06  25.36437  30 
45  50  n.84499  77 
51  33  58.32562  24 

O.OIOO 

.0001 
.0002 
.0003 
.0004 

o  34  22.64806  25 
oo  20.62648  06 
oo  41.25296  12 

01   01.87944  19 

01  22.50592  25 

I.OO 
0.01 
O.O2 
0.03 
O.O4 

57  17  44.80624  71 
oo  34  22.64806  25 
01  08  45.29612  49 
01  43  07.94418  74 
02  17  30.59224  99 

0.0005 
.0006 
.0007 

.0008 
.0009 

o  01  43.13240  31 
02  03.75888  37 
02  24.38536  44 
02  45.01184  50 
03  05.63832  56 

O.O5 
O.06 

0.07 
0.08 
0.09 

02  51  53.24031  24 
03  26  15.88837  48 
04  oo  38.53643  73 
04  35  01.18449  98 
05  09  23.83256  22 

O.OOIOO 

.00001 
.00002 
.00003 
.00004 

o  03  26.26480  625 
oo  02.06264  806 
oo  04.12529  612 
oo  06.18794  419 
oo  08.25059  225 

O.IOO 
0.001 
O.002 

0.003 
0.004 

05  43  46.48062  47 
oo  03  26.26480  62 
oo  06  52.52961  25 
oo  10  18.79441  87 
oo  13  45.05922  50 

0.00005 
.00006 
.00007 
.00008 
.00009 

o  oo  10.31324  031 
oo  12.37588  837 
oo  14.43853  644 
oo  16.50118  450 
oo  18.56383  256 

0.005 

00   17   11.32403  12 

O.OOOIO 

o  oo  20.62648  062 

SMITHSONIAN  TABLES 


Numerical  Constants.' 


Iog102  =  0.30102    99956   63981 

Ioge2  =  0.69314  71805  59945 

j 

.  —  —0.56418    95835    47756 

logeio=2.30258  50929  94046 

I 

6=2.71828  18284  59045 

Iog10—  =  =  9.75142  50636  52933 

]/    IT 

logioe  =  0-43429  44819  03252 

logiologioe  =  9-63778  43iJ3  00537 

J  ^=1.25331    41373    15500 

ir  =3.  141  59  26535  89793 

\     2 

Iog10ir  =  0.49714  98726  94134 
logeir=  1.14472  98858  49400 

/  2  =0.79788   45608   02865 

\     IT 

—  =  0.31830  98861  83791 

IT 

logio  -J  —  =  9-9OI94  00614  84924 

ir2  =  9.  86960  44010  89359 

i  radian  =  206264.80624  70964  seconds 

—  =  0.10132  11836  42338 

=      3437-74677  07849  minutes 

=          57.29577  95I3I  degrees 

I/  *   =1.77245    38509    05516 

Iog10  206264.80625  =  5.31442  51332 

SMITHSONIAN  TABLES 


32T 


YC 1 02296 


•*3' 
<*^ 


ASTRONOMY 

II8RARY 
UNIVERSITY  OF  CALIFORNIA  LIBRARY 


